* Seuraavan viikon tapahtumat merkitty tähdellä
Eero Virmavirta
Optimizing application placement in private cloud environment under capacity constraints (MSc thesis presentation)
* Monday 28 April 2025, 15:00, M2 (M233)
SAL Seminar
Philine Schiewe (Aalto)
An introduction to computational complexity
Monday 05 May 2025, 14:00, M2 (M233)
When solving optimization problems, we have to consider the resources required for the computation, especially the runtime and the memory requirements. While it is easy to measure the resources needed for a specific implementation, it is often unclear if a more efficient algorithm exists. For example, a shortest path can be computed efficiently (in polynomial time) while finding a longest path is known to be (NP-)hard. In this seminar, we will introduce the basic concepts of computational complexity, to classify (decision) problems according to their (time) complexity. In particular, we will introduce the complexity classes P (polynomial), NP (nondeterministic polynomial) and NPC (NP-complete) and show how polynomial transformations can be used to prove that a specific problem is NP-hard.
SAL Seminar
Aapo Pulkkinen
TBA
Wednesday 07 May 2025, 10:15, M3 (M234)
Seminar on analysis and geometry
Olavi Nevanlinna
Low rank perturbation and Krylov methods
Wednesday 07 May 2025, 14:00, M2 (M233)
We discuss bounds for Krylov methods which are robust in low rank perturbation of the preconditioner.
We first demonstrate using two examples where the spectra are known the different roles of the spectrum and the decay of singular values have in the speed of the iterative processes. Recall that while the spectrum can move dramatically, the singular values do not, and the convergence speed is essentially determine by the decay of singular values.
In the first example a unitary matrix is rank-one perturbation of a nilpotent one and in the second a self-adjoint compact operator is rank-one perturbation of a quasinilpotent one.
Considering the resolvent as a meromorphic function rather than just analytic outside the spectrum it is possible to to show that the behavior seen in those examples is true in general, without assuming anything about how the spectrum moves under the low rank perturbation.
Numerical Analysis seminar
Petteri Kaski
Kronecker scaling of tensors with applications to arithmetic circuits and algorithms
Thursday 15 May 2025, 14:15, M2 (M233)
We show that sufficiently low tensor rank for the balanced tripartitioning tensor $P_d(x,y,z)=\sum_{A,B,C\in\binom{[3d]}{d}:A\cup B\cup C=[3d]}x_Ay_Bz_C$ for a large enough constant $d$ implies uniform arithmetic circuits for the matrix permanent that are exponentially smaller than circuits obtainable from Ryser's formula. We show that the same low-rank assumption implies exponential time improvements over the state of the art for a wide variety of other related counting and decision problems.
As our main methodological contribution, we show that the tensors $P_n$ have a desirable Kronecker scaling property: They can be decomposed efficiently into a small sum of restrictions of Kronecker powers of $P_d$ for constant $d$. We prove this with a new technique relying on Steinitz's lemma, which we hence call Steinitz balancing.
As a consequence of our methods, we show that the mentioned low rank assumption (and hence the improved algorithms) is implied by Strassen's asymptotic rank conjecture [Progr. Math. 120 (1994)], a bold conjecture that has recently seen intriguing progress.
Joint work with Andreas Björklund, Tomohiro Koana, and Jesper Nederlof; cf. https://arxiv.org/abs/2504.05772.
ADM Seminar
Anna-Mariya Otsetova (Midterm review)
Quantitative asymptotics for stochastic evolution equations
Friday 25 April 2025, 11:15, M3 (M234)
Rolf Stenberg
Variational principles. Pitfalls by integration by parts.
Wednesday 23 April 2025, 14:00, M2 (M233)
Piyalee Pattanaik (Aalto)
Midterm review: Combinatorial optimization for sustainable mobility
Thursday 17 April 2025, 11:00, M2 (M233)
Dr. Elena Bessarabova (University of Oklahoma)
Messaging to Prevent Maladaptive Influence: An Inoculation Research Program
Tuesday 15 April 2025, 15:00, M3 (M234)
Dr. Elena Bessarabova (PhD, University of Maryland) is a quantitative social scientist who studies persuasion, focusing on the roles of emotion and cognition in information processing. She is particularly interested in maladaptive decision-making, including bias, misinformation, deception, and conspiratorial beliefs. Her current research focuses on communication strategies that can help mitigate bias and misinformation. This talk presents research testing mitigation strategies designed to prevent conspiratorial beliefs. Using the theoretical framework of inoculation theory, Dr. Bessarabova will discuss two recent projects that tested inoculations potential in preventing the influence of conspiracy propaganda, with a specific focus on antivaccination conspiracies and the 9/11 Truth Movement, which advocates the idea that the U.S. government orchestrated the attacks on September 11, 2001. Some of this research explores the influence of culture and cultural context variables, comparing the effects on U.S. and Finnish participants.
SAL Seminar
Jiasheng Lin (Institut de Mathématiques de Jussieu-Paris Rive Gauche)
Entanglement Entropy and Conical Singularities
Tuesday 15 April 2025, 10:15, M3 (M234)
In this talk we describe the work (arXiv:2501.19014) in collaboration with B. Estienne where we demonstrate a purely mathematical and geometric construction which recovers some results of Cardy and Calabrese on the so-called entanglement entropy. We start by explaining briefly the Segal picture of CFT (and QFT), and its natural relation to path-integral formulation. Then we introduce the entanglement entropy, and relate it to conical surfaces via path-integral and the "replica trick". Then we say briefly about geometry of conical singularities. Finally we formulate the main result of the work: we define CFT "partition functions" on surfaces with conical singularities, using a "Hadamard renormalization'' of the Polyakov anomaly integral. Then for a branched cover $f:\Sigma_d→\Sigma$ of degree $d$, the ratio $Z(\Sigma_d,f^*g)/Z(\Sigma,g)^d$ of partition functions transforms under conformal changes of g like a correlation function of CFT primary operators of specific conformal weights.
Prof. Nageswari Shanmugalingam (University of Cincinnati)
Minicourse: Non-smooth analysis in metric spaces 4/4
Friday 11 April 2025, 14:15, M2 (M233)
The fourth lecture of the course covers the topics:
11. Poincaré inequality and doubling property of the measure - analytic consequences (density of Lipschitz functions, quasicontinuity).
12. Extreme cases: p=1 and p=\infty
This is also the last lecture of the mini course.
Prof. Iván Blanco Chacón (U. Alcalá)
A friendly invitation to Langlands's functoriality
Thursday 10 April 2025, 16:15, M3 (M234)
Elliptic curves and modular forms bring Galois representations (don't worry, these terms will be introduced/recalled in the talk). One of the many versions of Taylor-Wiles modularity theorem rephrases as: "representations attached to rational elliptic curves come from modular forms".
The power of this somewhat abstract statement is that it allows to prove Fermat's Last Theorem (with the aid of Ribet's level lowering theorem and Frey's curve, but that's other story).
In 2007, Dieulefait gave the first proof of the Serre modularity conjecture, generalising Taylor-Wiles, namely: Any rational Galois representation which "looks like" modular, is indeed modular. This statement was generalised in full by Khare and Wintenberger in 2011 (and that's also another story...)
Since then, a series of hits have established that any 2-dimensional "regular enough" Galois representation comes from modular-ish forms (namely, automorphic forms), so establishing a (conjectural) dictionary between arithmetic representations and automorphic ones. However, the following question remains openut (up to some minor results, includig the speaker's ones): to determine which group-theoretical representations preserve automorphicity.
The present talk is an introductory account of these ideas, a discussion of what's open and, time permitting, a statement of two of the works by the speaker.
ANTA Seminar / Hollanti et al.
Hana Ephremidze (Universität Bonn)
Algebraic closure of field of Laurent series in characteristic p > 0
Thursday 10 April 2025, 14:15, M2 (M233)
We study stucture theory of complete discrete valued fields to understand the absolute Galois group of \mathbb{C}((x)) and describe some of its structure for the local field \mathbb{F}_p((x)). In the first part, we cover topics such as Hensel's Lemma, unramified, totally ramified, and tamely ramified extensions, ramification groups, and Artin-Schreier extensions. In the second part we look at specific extensions of characteristic p>0 fields and their Galois groups as well as describe the algebraic closure of \overline{\mathbb{F}_p}((x)) through the introduction of generalized power series.
Algebra & Discrete Mathematics (ADM) Seminar
Prof. Nageswari Shanmugalingam (University of Cincinnati)
Minicourse: Non-smooth analysis in metric spaces 3/4
Wednesday 09 April 2025, 14:15, M2 (M233)
The third lecture of the course covers the topics:
9. Poincaré inequality - examples and connectedness property.
10. Poincaré inequality and doubling property of the measure - geometric consequences.
Aleksis Koski
The internal Douglas condition
Wednesday 09 April 2025, 10:15, M3 (M234)
The Sobolev Jordan-Schoenflies problem asks a simple question: When does an embedding of the unit circle into the plane admit a homeomorphic extension in the Sobolev space W^1,p? Such a question is of basic interest in Nonlinear Elasticity, where Sobolev homeomorphisms describe an acceptable class of deformations between two elastic bodies. In a recent but important development, we have discovered an if and only if condition called the Internal Douglas Condition which gives a pleasingly complete answer to this problem in the planar case. In this talk, we will discuss this result and the related works leading up to it. This talk is based on joint work with Jani Onninen and Haiqing Xu.
Seminar on analysis and geometry
Prof. Dario Gasbarra (University of Vaasa) and Prof. Sangita Kulathinal (University of Helsinki)
Non-homogeneous multistate models for intermittently observed processes
Tuesday 08 April 2025, 15:15, M1 (M232)
Markov processes have a wide range of applications, and in many situations the underlying process is a non-homogeneous Markov (nhm) process. Here the transition probabilities and the initial distribution comprise the parameters. In scenarios where intermittent observations regarding the state occupancy are available, the observations provide only the partial information (the exact transition times are not observed) of the underlying process. In this talk, we will consider a 2-state nhm process {X(t), t ≥ 0} with the state space S = {1, 2}. When the process is observed only intermittently, the likelihood function is expressed in terms of the transition probabilities and numerical algorithms may be needed for the purpose of estimation. We will discuss a data augmentation approach based on Poisson processes for the estimation of the parameters. We will also describe characterisation of the transition intensities and extension of the proposed approach to two correlated processes. This work is motivated by the partial observations of treatment responses in patients of neovascular Age-related Macular Degeneration (nAMD). The characteristic feature of nAMD is the fluid accumulated under the macula due to leakage from abnormal blood vessels and the target of the treatment is to reduce the fluid.
Yoh Tanimoto (University of Rome Tor Vergata)
Wightman and Osterwalder-Schrader axioms for two-dimensional CFT
Tuesday 08 April 2025, 10:15, M3 (M234)
We give an overview of various approaches to quantum field theory in general and an algebraic framework specific to two-dimensional CFT, (full) vertex operator algebras. One can define correlation functions in a full vertex algebra under some regularity conditions. We show that, under unitarity, they satisfy the Osterwalder-Schrader axioms. We sketch how the Wightman fields are recovered. (joint with Maria Stella Adamo, Luca Giorgetti and Yuto Moriwaki)
Prof. Nageswari Shanmugalingam (University of Cincinnati)
Minicourse: Non-smooth analysis in metric spaces 2/4
Friday 04 April 2025, 14:15, M3 (M234)
The second lecture of the course covers the topics:
5. Upper gradients and p-weak upper gradients; minimal ones in L^p-class.
6. Construction of Newton-Sobolev classes.
7. ACC_p-property and lattice property.
8. Banach space property of Newton-Sobolev classes, and substitute for reflexivity.
Luis Brummet (Aalto University)
Midterm Review: Complex Linear Driver, Loewner Equation and Quasiconformal Deformations
Thursday 03 April 2025, 10:15, Y405
We are going to present results from the first year of the doctoral program, mainly a classification result about generated hulls from complex valued linear functions of the Loewner equation. Current research is also discussed aswell as well as some overview about Loewner theory in general.
Estibalitz Durand Cartagena (UNED, Madrid)
An introduction to metric spaces with small rough angles
Wednesday 02 April 2025, 10:15, M2 (M233)
Seminar on analysis and geometry
Prof. Nageswari Shanmugalingam (University of Cincinnati)
Minicourse: Non-smooth analysis in metric spaces 1/4
Tuesday 01 April 2025, 14:15, M3 (M234)
The first lecture of the course covers the topics:
1. Absolutely continuous functions on intervals - characterization and properties.
2. Beppo-Levi construction of Sobolev functions in Euclidean domains - weak derivatives, smooth approximations, ACLp -property.
3. Metric measure spaces and rectifiable curves; definition of path integrals.
4. p-Modulus of families of curves, and two lemmas of Fuglede.
Workshop on Algebraic Statistics and the Study of Multistate Models
Tuesday 01 April 2025, 10:00, M2 (M233)
Further information
Philine Schiewe (Aalto)
Integrating last-mile logistics and public transportation
Monday 31 March 2025, 15:00, M2 (M233)
To handle the rising demand in last-mile deliveries without further straining the urban infrastructure, new delivery concepts have to be developed. We introduce a mathematical optimization model for two-echelon tour planning where the first echelon is operated by public transport vehicles and the the second echelon by small, potentially autonomous vehicles. We show that the capacity of the second-echelon vehicles as well as their number influence the complexity of the resulting problem and that even small instances cannot be solved by commercial integer programming solvers. However, we identify polynomially solvable special cases and thus develop fast heuristic solution approaches. A computational study along a bus line in Göttingen, Germany, shows that the developed heuristics can solve instances with up to 900 deliveries within minutes. At the same time, the delay imposed upon the bus line is insignificantly small.
SAL Seminar
Vlad Margarint (University of North Carolina at Charlotte)
Law of the Schramm-Loewner Evolution (SLE) tip, and a bridge between Multiple SLEs and Random Matrix Theory
Thursday 27 March 2025, 11:15, M2 (M233)
In the first part of the talk, I will introduce some basic ideas of SLE theory, and discuss one of our results in the one SLE curve case, concerning the law of the SLE tip at a fixed time. In the second part of the talk, I will focus on the multiple SLE curves, and I will describe a new toolbox that connects Multiple Schramm-Loewner Evolutions and Random Matrix Theory. One aspect of this research direction is centered in an interacting particle systems model, namely the Dyson Brownian motion. I will describe the connection with Random Matrix Theory via a first application of our method. I will also discuss some open problems that emerge both in the one SLE curve and Multiple SLE curves picture. The first part is a joint work with O. Butkovsky and Y. Yuan, and the second part is a joint work with A. Campbell and K. Luh.
Mikhail Basok (University of Helsinki)
Random walk on planar graphs through the lens of t-embeddings
Tuesday 25 March 2025, 10:15, M3 (M234)
When an abstract planar graph is endowed with a random walk, various planar embeddings of this graph can be constructed. Classical examples are of Tutte's harmonic embeddings and Brooks-Smith-Stone-Tutte square tilings; they are generalized by the so-called T-graphs introduced by Kenyon and Sheffield. Given a sequence of such embeddings discretizing a given planar domain, it is natural to ask how the scaling limit of the random walk can be described in terms of the embeddings. In this talk we will address this question in the context of T-graphs. The key role in our approach is played by t-embeddings of bipartite graphs and the regularity theory of discrete holomorphic functions on them developed by Chelkak, Laslier and Russkikh. Based on a joint work with Chelkak, Laslier and Russkikh.
Tuomas Kelomäki (Aalto)
Khovanov homology: computations and obstructions
Friday 21 March 2025, 10:15, M3 (M234)
Khovanov homology is a combinatorial homology theory which associates homology groups to knots and links. The theory is also functorial, which in this context means that smooth cobordisms between knots (surfaces in a 4-ball) get associated with homomorphisms between the Khovanov homologies.
The goal of this talk is to give an overview on smooth obstructions from Khovanov homology which allows one to tap into smooth/topological dichotomy of 4D with combinatorics. Additionally, some more recent combinatorial obstructions for tangle replacements are presented as well as some original methods for computing Khovanov homology.
Nageswari Shanmugalingam (University of Cincinnati)
Uniformizing Gromov hyperbolic spaces and potential theory
Wednesday 19 March 2025, 10:15, M2 (M233)
Seminar on analysis and geometry
Léonie Papon (Durham)
Interface scaling limit for the critical planar Ising model perturbed by a magnetic field
Tuesday 18 March 2025, 10:15, M3 (M234)
In this talk, I will consider the interface separating $+1$ and $-1$ spins in the critical planar Ising model with Dobrushin boundary conditions perturbed by an external magnetic field. I will prove that this interface has a scaling limit. This result holds when the Ising model is defined on a bounded and simply connected subgraph of $\delta \mathbb{Z}^2$, with $\delta >0$. I will show that if the scaling of the external field is of order $\delta^{15/8}$, then, as $\delta \to 0$, the interface converges in law to a random curve whose law is conformally covariant and absolutely continuous with respect to SLE$_3$. This limiting law is a massive version of SLE$_3$ in the sense of Makarov and Smirnov and I will give an explicit expression for its Radon-Nikodym derivative with respect to SLE$_3$. I will also prove that if the scaling of the external field is of order $\delta^{15/8}g_1(\delta)$ with $g_1(\delta)\to 0$, then the interface converges in law to SLE$_3$. In contrast, I will show that if the scaling of the external field is of order $\delta^{15/8}g_2(\delta)$ with $g_2(\delta) \to \infty$, then the interface degenerates to a boundary arc.
Prof. Marcus Greferath (University College Dublin/Aalto)
Some old and new ideas on noiseless and noisy group testing
Thursday 13 March 2025, 16:15, M3 (M234)
Group Testing is an area in information and communication sciences that is as well-established as Coding Theory and Cryptography. The author of this talk stumbled over this amazingly interesting topic during the recent COVID-19 pandemic and came to the moderately surprising observation that (non-adaptive) group testing in both the noiseless and the noisy (=error-correcting) case, may be considered as coding theory over the Boolean semi-field (1+1=1). Following this path, he discovered new and re-discovered known results of the theory that now allow for a presentation in a new skin. This talk will delve into the topic and show how Noiseless and Noisy Group Testing can be connected to Partially Ordered Sets, Residuation, Partial Linear Spaces, Configurations, Barbilian Spaces, and Block Designs, which gives raise to further applications of Finite Geometry and Order Theory.
ANTA Seminar / Hollanti et al.
Giacomo Maletto (KTH)
Arrangements of Three Ellipsoids
Thursday 13 March 2025, 14:15, M2 (M233)
We classify arrangements of three ellipsoids in space up to rigid isotopy classes, focusing on nondegenerate configurations that avoid singular intersections. Our approach begins with a combinatorial description of differentiable closed curves on the projective plane that intersect a given arrangement of lines transversally. This framework allows us to label classes of spectral curves associated with ellipsoid configurations, which are real plane quartic curves. We determine necessary and sufficient conditions for these classes to be inhabited through arguments coming from linear algebra, algebraic geometry, combinatorics, and by computations in Mathematica and Macaulay2.
Algebra & Discrete Mathematics (ADM) Seminar
Jere Karttunen
Weak Reverse Hölder Inequalities and Muckenhoupt Weights: Interplay and Implications (Diploma thesis talk)
Wednesday 12 March 2025, 15:15, M2 (M233)
Note that the seminar is in M2 in this period!
Seminar on analysis and geometry
Dr. Ozgur Ceyhan (University of Luxembourg)
Byzantine Fault Tolerance and Mean Field Theory
Tuesday 11 March 2025, 15:15, A1 (A123)
The "Byzantine generals problem" is an allegory describing a distributed system aiming for consensus in the presence of unreliable/malicious elements. A widely known classical approach to Byzantine fault tolerance shows the impossibility of dealing with one-third or more faulty elements, i.e., only f-faulty elements are enough to corrupt a system with 3f or fewer components.
In this talk, I will overview fault tolerance in a toy model and examine it as a spin glass model, a magnetic state characterized by randomness in interactions in spin systems. Finally, I will discuss the threshold for faulty elements through a mean-field solution.
Jinwoo Sung (Chicago)
A quasi-invariant group action on SLE loops
Monday 10 March 2025, 14:15, Y405
Conformal welding is an operation that encodes Jordan curves on the Riemann sphere in terms of circle homeomorphisms. Thus, composition defines a natural group action of circle homeomorphisms on Jordan curves. In this talk, I will discuss a Cameron-Martin type quasi-invariance result for the SLE loop measure under the right group action by Weil-Petersson homeomorphisms. While this result was hinted by Carfagnini and Wang's identification of Loewner energy as the Onsager-Machlup action functional of the SLE loop measure, the group structure of SLE welding has been little understood previously.
Our proof is based on the characterization of the composition operator associated with Weil-Petersson circle homeomorphisms using Hilbert-Schmidt operators and the description of the SLE loop measure in terms of the welding of two independent quantum disks by Ang, Holden, and Sun. This is joint work with Shuo Fan (Tsinghua University and IHES).
Juho Saranpää
Techno-Economic Analysis of Compute Express Link in Radio Networks
Friday 07 March 2025, 14:15, M3 (M234)
Master's Thesis Presentation / Hakula
Håkan Hedenmalm (KTH Stockholm)
Conformally invariant Gaussian analytic functions, holomorphic correlations, and operator symbols of contractions (FMS Colloquium)
Thursday 06 March 2025, 16:15,
Further information
The classical Dirichlet space of holomorphic functions on the unit disk is invariant under Möbius transformations, except that it is equipped with a marked point where the functions vanish. Associated with such a Dirichlet space with a marked point, we get a Gaussian analytic function in a canonical fashion. Then, if we take two such Gaussian analytic functions, say with the same marked point at the origin, we consider the holomorphic correlation function of the two. It turns out to be given in terms a contraction on the area-L2 space on the disk. More precisely, we obtain the operator symbol of the contraction. Some contractions on L2 are perhaps more natural than others. For instance, we can consider the multiplication operator associated with a Beltrami coefficient μ. But we can also consider Grunsky operators, which are prominent in the theory of conformal mapping. We obtain a characterization of the operator symbols of Grunsky operators as solutions to a nonlinear wave equation. We also study the average growth of the L2 means of the operator of a general contraction.
Finnish Mathematical Society colloquium
Thomas Karam (University of Oxford)
Adaptations of basic matrix rank properties to the ranks of tensors
Thursday 06 March 2025, 14:15, Zoom and M2
This Zoom seminar is also watchable in M2!
Tensors are higher-dimensional generalisations of matrices, and likewise the main notion of complexity on matrices - their rank - may be extended to tensors. Unlike in the matrix case however, there is no single canonical notion of rank for tensors, and the most suitable notion often depends on the application that one has in mind. The most frequently used notion so far has been the tensor rank (hence its name), but several other notions and their applications have blossomed in recent years, such as the slice rank, partition rank, analytic rank, subrank, and geometric rank. Unlike their counterparts for the rank of matrices, many of the basic properties of the ranks of tensors are still not well understood. After reviewing the definitions of several of these rank notions, I will present a number of results of a type that arises in many cases when one attempts to generalise a basic property of the rank of matrices to these ranks of tensors: the naive extension of the original property fails, but it admits a rectification which is simultaneously not too complicated to state and in a spirit that is very close to that of the original property from the matrix case.
Link to Zoom: https://aalto.zoom.us/j/66860024175
Algebra & Discrete Mathematics (ADM) Seminar
Duc Khuat (Aalto)
Midterm review: Optimality of Adaptive Sparse Grid Interpolation for Higher Order Uncertain Parameter PDEs
Wednesday 05 March 2025, 13:30, M240
Numerical Analysis seminar
Timo Takala
Preserving uniformity and doubling measure in sphericalization
Wednesday 05 March 2025, 10:15, M2 (M233)
Note that the seminar is in M2 in this period!
Seminar on analysis and geometry
Kostiantyn Tolmachov (Universität Hamburg)
Around the centrality property of character sheaves on a reductive group
Thursday 27 February 2025, 14:15, M2 (M233)
I will report on two recent papers establishing some geometric and categorical properties of character sheaves. In one, joint with Gonin and Ionov, we give a new proof and an extension to non-unipotent setting of the t-exactness of the composition of Radon and Harish-Chandra transforms for character sheaves. In another, joint with Bezrukavnikov, Ionov and Varshavsky, we show that this can be used to compute the Drinfeld center of the abelian Hecke category attached to the same reductive group.
Algebra & Discrete Mathematics (ADM) Seminar
Luis Angel Castillo López (Universidad Nacional Autónoma de México)
Introduction to upper gradients
Wednesday 26 February 2025, 10:15, M2 (M233)
Seminar on analysis and geometry
David Adame-Carrillo (opponent prof. Alessandro Giuliani)
PhD thesis defense: "Lattice models and conformal field theory"
Tuesday 25 February 2025, 13:00, R002/160a R1
Mikko Salervo
Edge-enhancing control of resolution for imaging (master's thesis presentation)
Friday 21 February 2025, 13:15, M3 (M234)
Aki Mori (Setsunan University)
Simplex faces of order and chain polytopes
Thursday 20 February 2025, 14:15, M2 (M233)
Order polytopes and chain polytopes, associated with partially ordered sets, were introduced by Stanley in 1986. In 2016, Hibi and Li proposed the following conjecture concerning the number of faces of these polytopes in each dimension:
(a) For any dimension i (≥1), the number of i-dimensional faces of an order polytope does not exceed that of the corresponding chain polytope.
(b) If the numbers of i-dimensional faces of both polytopes coincide for some i (≥1), then the two polytopes are unimodularly equivalent.
In this talk, we will provide an overview of the current progress on this conjecture and discuss results obtained specifically for faces of simplices.
Algebra & Discrete Mathematics (ADM) Seminar
Vili Kohonen
Hybrid Nitsche method for distributed computing
Wednesday 19 February 2025, 14:00, M2 (M233)
Numerical analysis seminar
Lin Wu (Xiamen University/Aalto University)
Uniform weighted bounds for fractional Marcinkiewicz integrals
Wednesday 19 February 2025, 10:15, M3 (M234)
Seminar on analysis and geometry
Victor Mishnyakov (Nordita)
Algebras and exact solutions of matrix models at finite N
Wednesday 19 February 2025, 10:15, M2 (M233)
The prominent role of matrix models (or random matrices) in physics and mathematics is well known. It is especially interesting that some of those models are exactly solvable, meaning that one can find explicit formulas for correlation functions at finite sizes of the matrix. This phenomenon has also been dubbed as superintegrability of matrix models. The resulting answers involve formulas that appear in various corners of the theory of integrable systems, combinatorics of random partitions, and resemble certain expressions coming from supersymmetric localization. I will review the attempts to study it systematically and search for its algebraic origins, mainly relating it to the well-controlled world of representation theory of various infinite-dimensional algebras from the family of BPS algebras. Specifically, I will present some examples involving the (refined) Chern-Simons matrix model and other (q,t)-deformed eigenvalue models.
Topias Terho (Aalto University)
Optimization models and solution algorithms for influence diagrams (Midterm review)
Wednesday 12 February 2025, 11:00, M240
Ioana Ciotir (INSA Rouen, Normandie Université)
Stochastic porous media equation with Robin boundary conditions, gravity-driven infiltration and multiplicative noise
Wednesday 12 February 2025, 10:15, M3 (M234)
We aim at studying a novel mathematical model associated to a physical phenomenon of infiltration in an homogeneous porous medium. The particularities of our system are connected to the presence of a gravitational acceleration term proportional to the level of saturation, and of a Brownian multiplicative perturbation. Furthermore, the boundary conditions intervene in a Robin manner with the distinction of the behavior along the inflow and outflow respectively. We provide qualitative results of well-posedness, the investigation being conducted through a functional approach.
Joint work with Dan Goreac, Juan Li and Antoine Tonnoir.
Seminar on analysis and geometry
Prof Joni Virta (University of Turku)
Unsupervised linear discrimination using skewness
Wednesday 12 February 2025, 10:15, M237
It is known that, in Gaussian two-group separation, the optimally discriminating projection direction can be estimated without any knowledge on the group labels. In this presentation, we (a) motivate this estimation problem, and (b) gather several unsupervised estimators based on skewness and derive their limiting distributions. As one of our main results, we show that all affine equivariant estimators of the optimal direction have proportional asymptotic covariance matrices, making their comparison straightforward. We use simulations to verify our results and to inspect the finite-sample behaviors of the estimators.
Aalto Stochastics and Statistics Seminar / Leskelä
Prof. Nages Shanmugalingam (University of Cincinnati)
Large-scale behavior of Dirichlet-Sobolev functions in metric measure spaces
Tuesday 11 February 2025, 15:15, M1 (M232)
For certain PDEs, it is not always possible to find smooth solutions; hence traditionally, we tend to relax the requirement of smoothness to finding weak (distributional) solutions to those PDEs, using the theory of Sobolev spaces. In dealing with Sobolev spaces, especially for unbounded regions, we encounter functions that are locally integrable but are not globally integrable, but have globally finite Sobolev energy. Such functions are called Dirichlet-Sobolev functions. Constant functions are certainly of this kind, with zero energy. It is natural to ask whether such functions are always, after subtracting a suitable constant that may depend on the function, globally integrable. The focus of this talk is to present results related to this question in the context of complete metric measure spaces (including Riemannian manifolds and Carnot-Carathéodory spaces) equipped with a locally doubing measure supporting a local Poincaré type inequality.
Sami Vihko (University of Helsinki)
Reconstruction of log-correlated fields from multiplicative chaos measures
Tuesday 11 February 2025, 10:15, M3 (M234)
We consider log-correlated Gaussian fields G on a bounded domain D \subset \R^d. These are random generalized functions, that is, random Schwartz distributions with logarithmic singularity on their covariance kernel. The Gaussian multiplicative chaos (GMC) associated to such a field is formally the exponential e^{\gamma G} with a real parameter \gamma. Rigorously the GMC is constructed as a random measure via a regularization and limiting procedure.
Our main result considers the reverse problem: Given a GMC measure can we retrieve the field from it? The answer is yes. The GMC measure gives full mass to a fractal set called the \gamma-thick points of the underlying field G. Thus, it is surprising that enough information is preserved by the construction of the GMC to reconstruct the field G completely.
The novelty of our result is that the dimension d is arbitrary contrary to previous result with d = 2. We can also cover the critical case \gamma = \sqrt{2d} and mildly non-Gaussian case, and if time permits, we will see what changes in this setup.
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Friday 07 February 2025, 09:15, M2 (M233)
Further information
Martti Ranta: Diplomityöesitelmä
TBA
Thursday 06 February 2025, 14:15, M2 (M233)
Diplomityöesitelmä / Hakula
Jaakko Takala (Aalto)
Diplomityöesitelmä: Wizard's 21 -pelin optimaalinen pelistrategia
Thursday 06 February 2025, 13:00, Y405
Michal Borowski (University of Warsaw)
Approximation in variational problems
Wednesday 05 February 2025, 10:15, M3 (M234)
Seminar on analysis and geometry
Gerardo Barrera (IST Lisbon)
Cutoff phenomenon for the ergodic CIR process and extensions
Tuesday 04 February 2025, 10:15, M3 (M234)
In this talk we investigate the convergence to equilibrium as the noise intensity $\epsilon$ tends to zero for ergodic random systems out of equilibrium driven by multiplicative non-linear noise of the following type
\[
d X^{\epsilon}_t(x)=(b-aX^{\epsilon}_t(x))dt+\epsilon \sqrt{X^{\epsilon}_t(x)}dB_t,\quad X_0=x,
\]
where $x>0$, $a>0$ and $b>0$ are constants, and $(B_t)_{t>0}$ is a one-dimensional standard Brownian motion. More precisely, we establish the occurrence of the so-called profile cutoff phenomenon in the total variation distance and in the renormalized Wasserstein distance when the intensity of the noise tends to zero. Our results include explicit cut-off time, explicit time window, and explicit profile function. Furthermore, asymptotics of the so-called mixing times are given explicitly. This is based in the paper https://arxiv.org/pdf/2402.15457 with Liliana Esquivel, Universidad de Puerto Rico, Puerto Rico.
Liam Hughes (Aalto)
Conformal loop ensembles (part 2)
Tuesday 28 January 2025, 10:15, M3 (M234)
Antti Autio
In search of the hidden structure: approximation of a parametric diffusion equation.
Wednesday 22 January 2025, 14:00, M2 (M233)
Theo Elenius
Anzellotti pairings and applications to problems with linear growth
Wednesday 22 January 2025, 10:15, M3 (M234)
Seminar on analysis and geometry
Liam Hughes (Aalto)
Conformal loop ensembles
Tuesday 21 January 2025, 10:15, M3 (M234)
The conformal loop ensemble CLE_kappa, where kappa is a parameter in (8/3,8), is a loop analogue of SLE_kappa, and is the canonical conformally invariant probability measure on countably infinite sets of non-crossing loops in a planar domain. This talk will explain what ''canonical'' means in the previous sentence, survey some of the discrete models expected or known to converge to CLE in the scaling limit, and explain why in the case kappa in (8/3,4] where the loops are simple one can equivalently construct CLE_kappa via Brownian loop soups.
Professor Klaus Nordhausen (University of Helsinki)
On the usage of joint diagonalization in multivariate statistics
Monday 20 January 2025, 14:15, Y313
Scatter matrices generalize the covariance matrix and are useful in many multivariate data analysis methods, including principal component analysis, which is usually based on the diagonalization of the covariance matrix. The simultaneous diagonalization of two or more scatter matrices goes beyond PCA and is used more and more often. In this talk, we offer an overview of many methods that are based on joint diagonalization. These methods range from the unsupervised context with invariant coordinate selection and blind source separation, which includes independent component analysis, to the supervised context with linear discriminant analysis and sliced inverse regression. They also encompass methods that handle dependent data such as time series or spatial data.
Prof. Guillermo Mantilla-Soler (National U. Colombia Medellin/Aalto)
Seminar course (7.-17.1.): An introduction to Dirichlet's L-functions and a proof of Dirichlet's theorem of primes in arithmetic progressions
Friday 17 January 2025, 10:15, M3 (M234)
Further information
We will begin this course (MS-EV0030) by reviewing Euler's change of paradigm, with respect to Euclid, and his proof on infinitude of primes. Then, we will study the generalization made by Dirichlet, and will prove Dirichlet's theorem on arithmetic progression. Through the course we will learn about the development of L-functions, character theory and the beginning of the relation between Galois representations and certain complex functions.
There will be 5 sessions during 2 weeks. For students interested in credits: attendance gives 2 cr and more can be obtained (upon request) by completing further assignments. Sessions take place on Tue, Thu on the first week and Mon, Wed, Fri the second week, all at 10:15-12.
Zoom: https://aalto.zoom.us/j/68751625629
ANTA Seminar / Hollanti et al.
Nataliia Kushnercuk
Identifiability of Discrete Lyapunov Models (midterm review)
Wednesday 15 January 2025, 11:15, M240
Andreas Rosén (Chalmers)
Sharp weighted non-tangential maximal estimates via Carleson-sparse domination
Wednesday 15 January 2025, 10:15, M3 (M234)
We prove sharp weighted estimates for the non-tangential maximal function of singular integrals mapping functions from R^n to the half-space in R^{1+n} above R^n. The proof is based on pointwise sparse domination of the adjoint singular integrals that map functions from the half-space back to the boundary. It is proved that these map L_1 functions in the half-space to weak $L_1$ functions on the boundary. From this a non-standard sparse domination of the singular integrals is established, where averages have been replaced by Carleson averages.
Seminar on analysis and geometry
Prof. Guillermo Mantilla-Soler (National U. Colombia Medellin/Aalto)
Seminar course (7.-17.1.): An introduction to Dirichlet's L-functions and a proof of Dirichlet's theorem of primes in arithmetic progressions
Wednesday 15 January 2025, 10:15, M134
Further information
We will begin this course by reviewing Euler's change of paradigm, with respect to Euclid, and his proof on infinitude of primes. Then, we will study the generalization made by Dirichlet, and will prove Dirichlet's theorem on arithmetic progression. Through the course we will learn about the development of L-functions, character theory and the beginning of the relation between Galois representations and certain complex functions.
There will be 5 sessions during 2 weeks. For students interested in credits: attendance gives 2 cr and more can be obtained (upon request) by completing further assignments. Sessions take place on Tue, Thu on the first week and Mon, Wed, Fri the second week, all at 10:15-12.
Zoom: https://aalto.zoom.us/j/68751625629
ANTA Seminar / Hollanti et al.
Prof. Dr. Andreas Rosén (Chalmers)
Hypercomplex analysis of Maxwell's equations
Tuesday 14 January 2025, 15:15, A1 (A123)
Maxwell's equations describe electromagnetic wave propagation and the most dominant force in our world. These fundamental equations can be handled in a natural way by a hypercomplex algebra due to W. K. Clifford, a contemporary of J. C. Maxwell.
We shall survey this kind of non-commutative complex analysis, that is useful in solving Maxwell's equations. Making use of a Cauchy integral formula for time-harmonic Maxwell's equations advocated by Alan McIntosh, we describe a recent boundary integral equation reformulation for Maxwell scattering. In recent joint work with Johan Helsing and Anders Karlsson, Lund, we have achieved an efficient solver, with almost down to machine precision, for computationally challenging plasmonic and eddy current electromagnetic scattering problems.
Prof. Guillermo Mantilla-Soler (National U. Colombia Medellin/Aalto)
Seminar course (7.-17.1.): An introduction to Dirichlet's L-functions and a proof of Dirichlet's theorem of primes in arithmetic progressions
Monday 13 January 2025, 10:15, M3 (M234)
Further information
We will begin this course (MS-EV0030) by reviewing Euler's change of paradigm, with respect to Euclid, and his proof on infinitude of primes. Then, we will study the generalization made by Dirichlet, and will prove Dirichlet's theorem on arithmetic progression. Through the course we will learn about the development of L-functions, character theory and the beginning of the relation between Galois representations and certain complex functions.
There will be 5 sessions during 2 weeks. For students interested in credits: attendance gives 2 cr and more can be obtained (upon request) by completing further assignments. Sessions take place on Tue, Thu on the first week and Mon, Wed, Fri the second week, all at 10:15-12.
Zoom: https://aalto.zoom.us/j/68751625629
ANTA Seminar / Hollanti et al.
Sonja Rantala
On extreme value theory approach to riskiness of Helsinki stock exchange at early stages of the Russo-Ukrainian war (MSc thesis presentation)
Thursday 09 January 2025, 13:15, M2 (M233)
Prof. Guillermo Mantilla-Soler (National U. Colombia Medellin/Aalto)
Seminar course (7.-17.1.): An introduction to Dirichlet's L-functions and a proof of Dirichlet's theorem of primes in arithmetic progressions
Thursday 09 January 2025, 10:15, M3 (M234)
Further information
We will begin this course (MS-EV0030) by reviewing Euler's change of paradigm, with respect to Euclid, and his proof on infinitude of primes. Then, we will study the generalization made by Dirichlet, and will prove Dirichlet's theorem on arithmetic progression. Through the course we will learn about the development of L-functions, character theory and the beginning of the relation between Galois representations and certain complex functions.
There will be 5 sessions during 2 weeks. For students interested in credits: attendance gives 2 cr and more can be obtained (upon request) by completing further assignments. Sessions take place on Tue, Thu on the first week and Mon, Wed, Fri the second week, all at 10:15-12.
Zoom: https://aalto.zoom.us/j/68751625629
ANTA Seminar / Hollanti et al.
Lisa Schätzle (Karlsruhe Institute of Technology)
Far field operator splitting and completion for inhomogeneous medium scattering
Wednesday 08 January 2025, 14:00, M2 (M233)
We consider scattering of time-harmonic acoustic waves by compactly supported inhomogeneous objects in a homogeneous background medium. These inhomogeneous objects, which we call scatterers, are illuminated by a known incident plane wave, and the scattering process is described by the Helmholtz equation together with the Sommerfeld radiation condition. The associated far field is the asymptotic angular-dependent behavior of the scattered wave far away from the scatterer. Our object of interest is the associated far field operator, which maps superpositions of incident waves to the far field of the corresponding scattered wave. In this talk we consider two inverse problems. Given the far field operator for a system of two well-seperated scatterers we want to recover the individual far field operator components of both scatterers, i.e., we want to remove multiple scattering. We refer to this as far field operator splitting problem. Secondly, we study a far field operator completion problem, where the aim is to restore
missing far field data. We use sparse representations of the involved far field operator components to approximate the solutions of both problems by the solutions of suitable ℓ1 × ℓ1 minimization problems. We investigate the stability of these problems and relate them to concrete conditions on the scatterers geometry. We validate our results for the far field operator completion problem by numerical tests featuring both synthetic and experimental data. Finally, we test whether our reconstructions are appropriate as input for shape-reconstruction methods. Hereby, we study the visual improvement achieved by applying the factorization method on our restored data compared to the original incomplete data.
Prof. Guillermo Mantilla-Soler (National U. Colombia Medellin/Aalto)
Seminar course (7.-17.1.): An introduction to Dirichlet's L-functions and a proof of Dirichlet's theorem of primes in arithmetic progressions
Tuesday 07 January 2025, 10:15, M3 (M234)
Further information
We will begin this course (MS-EV0030) by reviewing Euler's change of paradigm, with respect to Euclid, and his proof on infinitude of primes. Then, we will study the generalization made by Dirichlet, and will prove Dirichlet's theorem on arithmetic progression. Through the course we will learn about the development of L-functions, character theory and the beginning of the relation between Galois representations and certain complex functions.
There will be 5 sessions during 2 weeks. For students interested in credits: attendance gives 2 cr and more can be obtained (upon request) by completing further assignments. Sessions take place on Tue, Thu on the first week and Mon, Wed, Fri the second week, all at 10:15-12.
Zoom: https://aalto.zoom.us/j/68751625629
ANTA Seminar / Hollanti et al.
Stochastic Sauna 2024
Workshop on Probability and Statistics
Thursday 19 December 2024, 11:50, M1 (M232)
Further information
See workshop homepage:
https://math.aalto.fi/en/research/stochastics/sauna2024/
Jonas Tölle
Mikko Rosenberg
Master thesis talk: Monte Carlo-based performance projection for remote road weather measurement
Thursday 19 December 2024, 10:15, M2 (M233)
MSc (Tech) Leevi Olander
Mid-term review presentation
Wednesday 18 December 2024, 14:00, M2 (M233)
Mid-term review presentation by Leevi Olander
(exact title will be confirmed nearer the date)
Matti Rehell (VTT)
Master thesis talk Hyperbolicity and Stability of Two-phase Six-equation Model for Nuclear Safety Analysis
Wednesday 18 December 2024, 10:15, M2 (M233)
Anestis Tzogias (U. Neuchatel/Aalto)
Lattice theta series extrema problems: The Regev conjectures
Wednesday 11 December 2024, 16:15, M3 (M234)
After a recent talk on the extrema of the lattice theta series and its strong connections to error-correcting codes and cryptography, we will dive a bit deeper into the mathematical side of this problem. More specifically, we will discuss the Regev and Stephens-Davidowitz conjectures, which state that the integer lattice maximises the theta series among stable lattices and integral lattices. We will present the main ideas behind two papers of the above authors, motivate how their conjectures arose and connect them to other areas of interest in lattice theory.
ANTA Seminar / Hollanti et al.
Qingxin Yang
Parallel Repetition of Nonlocal Games (MSc thesis presentation)
Wednesday 11 December 2024, 11:00, M2 (M233)
Anna-Mariya Otsetova
Invariant measures for SPDEs
Wednesday 11 December 2024, 10:15, M3 (M234)
Seminar on analysis and geometry
Eric Schippers (University of Manitoba)
Faber-Tietz forms and series on Riemann surfaces
Tuesday 10 December 2024, 10:15, M3 (M234)
Faber polynomials are polynomials associated to a conformal map onto a planar domain. It is classical that one can approximate holomorphic functions on the complement of this domain by series of Faber polynomials, and there is a well-developed theory of Faber series in various analytic settings. Results on approximation in the Bergman space norm by Faber series are surprisingly recent and hold precisely for quasicircles. Based on work of H. Tietz, we generalize Faber polynomials and Faber series to compact Riemann surfaces with conformal maps onto quasidisks, and show that one-forms on the complement have a convergent Faber-Tietz series in $L^2$. Joint work with M. Shirazi.
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Monday 09 December 2024, 09:00, M3 (M234)
Further information
Tobias Boege
Graphical continuous Lyapunov models
Tuesday 03 December 2024, 15:15, M2 (M233)
The classical tool for representing cause-effect relationships in statistical modeling is a Bayesian network. This statistical model postulates noisy functional dependencies among random variables according to a directed graph. Despite their widespread use, Bayesian networks have two shortcomings:
(1) different causal mechanisms may define the same statistical model, so cause-effect relationships cannot be deduced reliably from observational data alone, and
(2) if the directed graph contains cycles (which may be interpreted as "feedback loops"), the model is no longer globally identifiable.
A different paradigm in causal modeling has recently been proposed, which takes the stationary distributions of a family of diffusion processes as a statistical model. This temporal perspective easily accommodates feedback loops. For Ornstein--Uhlenbeck processes whose drift matrix has a specified sparsity pattern, this results in semialgebraic statistical models of
Gaussian random variables now known as graphical continuous Lyapunov models.
In this talk I want to introduce these models and survey recent results on identifiability, model equivalence and conditional independence. I will also discuss the algebraic challenges that lie ahead.
This is based on joint works with Carlos Améndola, Mathias Drton,
Benjamin Hollering, Sarah Lumpp, Pratik Misra and Daniela Schkoda.
ADM seminar
Hanz Cheng
Recovery of material parameters in induction motor rotors
Thursday 28 November 2024, 11:00, M2 (M233)
We discuss some numerical algorithms for recovering parameters in eigenvalue problems for linear elasticity of transversely isotropic materials. Specifically, the algorithms are used to recover the elastic constants of a rotor core. Numerical tests show that in the noiseless setup, two pairs of bending modes are sufficient for recovering one to four parameters accurately. To recover all five parameters that govern the elastic properties of induction motors accurately, we require three pairs of bending modes and one torsional mode. Moreover, we study the stability of the inversion method against multiplicative noise; for tests in which the data contained multiplicative noise of at most 1\%, we find that all parameters can be recovered with an error less than $10\%$.
Stanislav Hencl (Charles University, Prague)
Ball Evans approximation problem: Recent progress and open problems
Wednesday 27 November 2024, 10:15, M3 (M234)
In this talk we give a short overview about the Ball-Evans approximation problem, i.e. about the approximation of Sobolev homeomorphism by a sequence of diffeomorphisms (or piecewise affine homeomorphisms) and we recall the motivation for this problem. We show some recent planar results and counterexamples in higher dimensions, and we give a number of open problems connected to this problem and related fields. We concentrate in detail on the joint result with A. Pratelli [1] about the approximation on planar W1,1-homeomorphisms by a sequence of piecewise affine homeomorphisms.
Seminar on analysis and geometry
Lizao Ye
Geometric Langlands and vertex algebras
Tuesday 26 November 2024, 15:15, M2 (M233)
Geometric Langlands seems very abstract, does it have any concrete applications? Ill explain how to use it to construct (new) vertex algebras.
ADM seminar
Dr. Olli Herrala (Aalto University)
A novel strong duality-based reformulation for trilevel infrastructure models in energy systems development
Monday 25 November 2024, 15:15, Riihi (Y225a)
Further information
We explore the class of trilevel equilibrium problems with a focus on energy-environmental applications and present a novel single-level reformulation for such problems, based on strong duality. To the best of our knowledge, only one alternative single-level reformulation for trilevel problems exists. This reformulation uses a representation of the bottom-level solution set, whereas we propose a reformulation based on strong duality. Our novel reformulation is compared to this existing formulation, discussing both model sizes and computational performance. In particular, we apply this trilevel framework to a power market model, exploring the possibilities of an international policymaker in reducing emissions of the system. Using the proposed approach, we are able to obtain globally optimal solutions for a five-node case study representing the Nordic countries and assess the impact of a carbon tax on the electricity production portfolio.
SAL Weekly Seminar
Xavier Poncini (Aalto)
Transformer mechanistic interpretability
Friday 22 November 2024, 14:30, M2 (M233)
The transformer architecture is the key algorithmic ingredient underlying modern large language models. Scaling laws suggest more capable models can be achieved by simply "stacking more layers", with resource limitations projected to bite only around 2030. Unfortunately, our understanding of these models is limited and is not scaling appropriately. Mechanistic interpretability is a nascent field that addresses this concern by reverse engineering algorithms and internal representations of neural networks. After giving a mathematical treatment of the transformer architecture, I will present an early success of the mechanistic interpretability approach -- the identification of so-called induction heads, which are responsible for a type of in-context learning exhibited by such models.
Vanni Noferini
What is a tropical root and what can it do for you?
Thursday 21 November 2024, 11:00, M2 (M233)
Olavi Nevanlinna
Extracts from metric functional analysis
Wednesday 20 November 2024, 10:15, M3 (M234)
We shall concentrate on metric compactification of Banach spaces, in order to highlight differences and similarities between metric and linear functional analysis.
We discuss weak convergences via metric functionals, indicate connections to invariant subspace problem, present a metric version of Eberlein-Shmulian theorem. As an example related to fixed point theorems we show a metric version of Markov-Kakutani theorem. The talk is based on discussions and work with Armando Gutiérrez.
Recommended non-technical reading:
Anders Karlsson, From linear to metric functional analysis, PNAS July 9, 2021.
Seminar on analysis and geometry
Konstantin Izyurov (University of Helsinki)
Bosonization of the critical Ising correlations
Tuesday 19 November 2024, 10:15, M3 (M234)
I will explain an identity between scaling limits of the Ising correlations in arbitrary finitely connected planar domains, and correlations of a suitable version of a Gaussian free field, yielding explicit formulae for the former. The proof is based on (rigorously established) operator product expansions for the Ising and GFF correlation, and a limiting version of a classical identity between Szegö and Bergman kernel on Riemann surfaces. Joint work with Baran Bayraktaroglu, Tuomas Virtanen and Christian Webb.
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Friday 15 November 2024, 09:00, M3 (M234)
Further information
Joanna Bisch
Model order reduction for parametric generalised EVPs
Thursday 14 November 2024, 11:00, M2 (M233)
We look for approximate eigensolutions of the pencil $( A(\sigma),M)$ for several values of the $d$-dimensional parameter vector $\sigma$. We are interested in few of the smallest eigenvalues that lie in the spectral interval of interest $(0,\Lambda)$. Both matrices are assumed to be s.p.d for any admissible parameter vector. In addition, the matrix $A(\sigma)$ is assumed to be spectrally equivalent to an s.p.d. average matrix $\overline{A}$.
For this purpose we develop a Ritz method that uses the same subspace for any parameter value. The subspace is designed using the observation that any eigenvector can be split into two components. The first component belongs to an easily computable subspace. The second component is defined by a correction formula that is a $d+1$ dimensional analytic function. Accordingly, the Ritz space is defined using this splitting and polynomial interpolation of the second component.
We give estimates for the approximation error and illustrate the method by numerical examples. The advantage of our approach is that the analysis easily treats eigenvalue crossings that typically have posed technical challenges.
Numerical Analysis seminar
Aino Weckman
Optimising emission reduction actions in organisations' climate work (MSc thesis presentation)
Thursday 14 November 2024, 10:00, M2 (M233)
Yu Liu (Aalto University)
Optimisation with neural network surrogate models embedded (Midterm review)
Wednesday 13 November 2024, 13:00, M3 (M234)
Leah Schätzler
Existence of variational solutions for doubly nonlinear equations in noncylindrical domains
Wednesday 13 November 2024, 10:15, M3 (M234)
I will talk about the existence of variational solutions to doubly nonlinear parabolic PDEs in noncylindrical domains $E \subset \mathds{R}^n \times [0,\infty)$.
This setting arises from models where the underlying domain $E^t := \{ x \in \mathds{R}^n : (x,t) \in E \}$ changes in time.
The prototype of the considered PDEs is
$$
\partial_t \big( |u|^{q-1} u \big) - \operatorname{div}\big( |Du|^{p-2} Du \big) = 0
\quad\text{in } E
$$
with parameters $q \in (0,\infty)$ and $p \in (1,\infty)$, which combines the porous medium equation and the parabolic $p$-Laplacian.
The talk is based on joint work (in progress) with Christoph Scheven, Jarkko Siltakoski and Calvin Stanko.
Seminar on analysis and geometry
Prof. Hiroshi Kawabi (Keio University/University of Oxford)
A graph discretized approximation of diffusions with drift and killing on a complete Riemannian manifold
Tuesday 12 November 2024, 15:15, M1 (M232)
In this talk, we present a graph discretized approximation scheme for diffusions with drift and killing on a complete Riemannian manifold M. More precisely, for a given Schrödinger operator with drift on M having the form A = −∆ − b + V, we introduce a family of discrete time random walks in the flow generated by the drift b with killing on a sequence of proximity graphs, which are constructed by partitions cutting M into small pieces. As a main result, we prove that the drifted Schrödinger semigroup {e^{−tA}}_{t≥0} is approximated by discrete semigroups generated by the family of random walks with a suitable scale change. This result gives a finite dimensional summation approximation of a Feynman-Kac type functional integral over M. Furthermore, when M is compact, we also obtain a quantitative error estimate of the convergence.
This talk is based on a joint work with Satoshi Ishiwata (Yamagata University) and the full paper can be found on https://doi.org/10.1007/s00208-024-02809-9 (online-first article in Mathematische Annalen).
Joona Oikarinen (Aalto)
Small deviations of Gaussian multiplicative chaos and the massless Sinh--Gordon model
Tuesday 12 November 2024, 10:15, M3 (M234)
I will explain what Gaussian multiplicative chaos (GMC) measures are, and prove new small deviations estimates for the total mass of GMC measures. Then I will show how to use GMC to construct the path integral formulation of the massless Sinh--Gordon model on the 2-dimensional torus. Finally, I will show how the small deviations bounds can be used to derive lower and upper bounds for the free energy of the massless Sinh--Gordon model on the infinite torus. Based on joint work with Nikolay Barashkov (MPI Leipzig) and Mo Dick Wong (Durham).
Rohit Kumar
Optimal Capacity Expansion for the Nordic Energy System A 10-Year Analysis of Battery Market Development and Renewable Integration (MSc thesis presentation)
Monday 11 November 2024, 15:15, Riihi (Y225a)
SAL Weekly Seminar
Andrew Granville (Université de Montréal)
Extremal problems for multiplicative functions (Finnish Mathematical Society remote colloquium)
Wednesday 06 November 2024, 16:15, U6 (U149)
Nowadays there are two prominent approaches to questions about the distribution of prime numbers: Riemann's classical methods using zeros of zeta functions, and the recent pretentious theory of multiplicative functions (which is mostly a combination of older "ad hoc" techniques). In this talk we present the basics of this newer theory, how it relates closely to the theory of integral-delay equations and then focus on some recent work on extremal problems (in joint work of the speaker with Kevin Church, Kaisa Matomaki, Kannan Soundararajan and Daodao Yang).
Finnish Mathematical Society colloquium
Mark Veraar (Delft University of Technology)
Stochastic PDEs in critical spaces
Wednesday 06 November 2024, 11:15, M3 (M234)
Seminar on analysis and geometry
Jan van Neerven (Delft University of Technology)
Spectral multiplier theorems for abstract harmonic oscillators on UMD lattices
Wednesday 06 November 2024, 10:15, M3 (M234)
Seminar on analysis and geometry
Alex Takeda (Uppsala University)
Properadic formality of Poincaré duality structures
Tuesday 05 November 2024, 15:15, M2 (M233)
The original idea of formality applies to a dg algebra, such as cochains on a space, and characterizes those dg algebras whose structure can be recovered from their cohomology, up to quasi-isomorphism. There is an obstruction-theoretic perspective on formality: a dg algebra is formal if and only if a certain characteristic class, called the Kaledin class, vanishes. From studying this class one deduces the formality of the algebra of cochains on spheres and other highly connected spaces. In this talk I will describe how an extension of this definition for properadic algebras allows us to address formality questions not only of space in its own, but of (possibly noncommutative) spaces endowed with a certain type of Poincaré duality structure. I will then describe a simple calculation of these obstructions for spheres. This is joint work with Coline Emprin.
ADM seminar
Julien Roussillon (Aalto)
On the Virasoro fusion kernel at any irrational central charge
Tuesday 05 November 2024, 10:15, M3 (M234)
The conformal bootstrap is a powerful approach to two-dimensional conformal field theories (CFTs) developed forty years ago by Belavin, Polyakov and Zamolodchikov. The Virasoro fusion kernel appears naturally in this approach and carries non-trivial information about CFTs in general. In this talk, I will first review the conformal bootstrap approach to CFTs, and I will take the examples of Liouville theory for central charges c>25 and of its imaginary analog for c<1. I will finally introduce the Virasoro fusion kernel and describe its construction by Ponsot and Teschner for c>25. If time permits, I will discuss my recent construction of its imaginary analog for c<1.
Prof. Raimo Hämäläinen (Aalto University)
Taking stock of behavioural OR: A review of behavioural studies with an intervention focus
Monday 04 November 2024, 15:15, Riihi (Y225a)
Further information
We surveyed the relevant OR literature covering a 30-year period and developed a typology to organise the reviewed studies. The typology is comprised of four types of studies, each type representing a distinctive approach in terms of its assumptions about behaviour (determinist or voluntarist) and the research methodologies they use (variance or process). By categorising studies in this way, and drawing on research in associated cognate areas where relevant, eight empirically-generated knowledge themes emerge: intervention configurations, individual differences, model-driven support impacts, (un)intended use, model building process, engagement paths and strategies, facilitated modelling practice, and social dynamics. Each of these knowledge themes provides important insights into the behavioural factors that affect, or are affected by, OR-supported activity.
SAL Weekly Seminar
Henri Lahdelma
Parabolic techniques for reverse Hölder classes (diploma thesis talk)
Wednesday 30 October 2024, 10:15, M3 (M234)
Seminar on analysis and geometry
Petteri Kaski
A universal sequence of tensors for the asymptotic rank conjecture
Tuesday 29 October 2024, 15:15, M2 (M233)
The exponent $\sigma(T)$ of a tensor $T\in\mathbb{F}^d\otimes\mathbb{F}^d\otimes\mathbb{F}^d$ over a field $\mathbb{F}$ captures the base of the exponential growth rate of the tensor rank of $T$ under Kronecker powers. Tensor exponents are fundamental from the standpoint of algorithms and computational complexity theory; for example, the exponent $\omega$ of matrix multiplication can be characterized as $\omega=2\sigma(\mathrm{MM}_2)$, where $\mathrm{MM}_2\in\mathbb{F}^4\otimes\mathbb{F}^4\otimes\mathbb{F}^4$ is the tensor that represents $2\times 2$ matrix multiplication.
Our main result is an explicit construction of a sequence $\mathcal{U}_d$ of zero-one-valued tensors that is universal for the worst-case tensor exponent; more precisely, we show that $\sigma(\mathcal{U}_d)=\sigma(d)$ where $\sigma(d)=\sup_{T\in\mathbb{F}^d\otimes\mathbb{F}^d\otimes\mathbb{F}^d}\sigma(T)$. We also supply an explicit universal sequence $\mathcal{U}_\Delta$ localised to capture the worst-case exponent $\sigma(\Delta)$ of tensors with support contained in $\Delta\subseteq [d]\times[d]\times [d]$; by combining such sequences, we obtain a universal sequence $\mathcal{T}_d$ such that $\sigma(\mathcal{T}_d)=1$ holds if and only if Strassen's asymptotic rank conjecture [Progr. Math. 120 (1994)] holds for $d$. Finally, we show that the limit $\lim_{d\rightarrow\infty}\sigma(d)$ exists and can be captured as $\lim_{d\rightarrow\infty} \sigma(D_d)$ for an explicit sequence $(D_d)_{d=1}^\infty$ of tensors obtained by diagonalisation of the sequences $\mathcal{U}_d$. As our second result we relate the absence of polynomials of fixed degree vanishing on tensors of low rank, or more generally asymptotic rank, with upper bounds on the exponent $\sigma(d)$. Using this technique, one may bound asymptotic rank for all tensors of a given format, knowing enough specific tensors of low asymptotic rank.
Joint work with Mateusz Michałek (U. Konstanz).
arXiv: https://arxiv.org/abs/2404.06427
ADM seminar
Augustin Lafay (Aalto)
Coulomb Gas representation of loop and web models
Tuesday 29 October 2024, 10:15, M3 (M234)
In this talk, I will present a non-rigorous method known in the physics litterature as Coulomb Gas. I will focus on the O(N) loop models and, if time permits, I will discuss its higher rank counterpart, the A_2 web models. The Coulomb Gas method identifies scaling limit of partition and correlation functions of the lattice models with quantities obtained from the compactified imaginary Liouville, and A_2 Toda, conformal field theories. From a mathematician point of view, it can be seen as a tool to obtain conjectures on, for instance, conformal weights of (the scaling limit of) lattice observables.
Jussi Leppinen (Aalto University)
An Optimization Model for Determining Cost-Efficient Maintenance Policies for Multi-Component Systems with Economic and Structural Dependencies
Monday 28 October 2024, 15:15, Riihi (Y225a)
Further information
In most multi-component systems, the cost-efficiency of maintenance policies depends on technical structural dependencies. Motivated by the recognition that these dependencies must be accounted for in the development of optimal maintenance policies, we develop an optimization model to determine cost-efficient maintenance schedules for multi-component systems. Our main contribution is twofold. First, we introduce directed graphs as an expressive tool to represent the economic and structural dependencies of the system, including situations in which the maintenance of a given component may require other components to be disassembled or maintained. Second, we formulate a Markov Decision Process model, which is solved through the modified policy-iteration algorithm to determine the most cost-efficient policy. This policy indicates which maintenance actions consisting of disassembly and component replacement decisions are optimal when mandatory replacements must be made whenever the system fails, or the reliability of the system falls below a predefined reliability threshold. To our knowledge, this is the first model that provides optimal maintenance policies that comply with reliability requirements in the presence of constraints arising from technical structural dependencies. We illustrate the model with a realistic case study on the development of cost-efficient maintenance policies and show that its results compare favorably with heuristic maintenance policies.
SAL Weekly Seminar
Leo Laitinen
Optimal offering strategy for a base station virtual power plant via stochastic programming (MSc thesis presentation)
Monday 28 October 2024, 15:15, Riihi (Y225a)
SAL Weekly Seminar
Dr. Maiara Bollauf (Simula, U. Bergen)
The extremum of the lattice theta series
Monday 28 October 2024, 14:15, M2 (M233)
The theta series describes the geometry of a lattice by characterizing the number of lattice vectors with a given norm. In this talk, we will explore the minimum and the maximum of the lattice theta series and its respective applications to secure wiretap channel communications and lattice-based cryptography.
ANTA Seminar / Hollanti et al.
Yu Liu (Aalto University)
TBA
Thursday 24 October 2024, 15:22,
Vili Kohonen
Distributed Domain Decomposition in the Cloud (Midterm review)
Thursday 24 October 2024, 09:15, M3 (M234)
Seminar on Numerical Analysis
Sari Rogovin
Linear dilatation and absolute continuity
Wednesday 23 October 2024, 10:15, M3 (M234)
Seminar on analysis and geometry
Xavier Poncini (Aalto)
The multi-parametric Yang--Baxter equation and planar algebraisation
Tuesday 22 October 2024, 10:15, M3 (M234)
The Yang--Baxter equation (YBE) plays a role in diverse and interrelated areas of mathematical physics, including statistical mechanics, quantum field theory, knot theory and quantum groups. Focusing on applications to statistical mechanics, I consider a generalisation of the YBE known as the multi-parametric YBE (mYBE), where each $R$-operator solution can be used to construct a family of commuting multi-parametric transfer operators. In an effort to identify algebraic structures admitting solutions to the mYBE I will introduce a construction called planar algebraisation, which can be thought of as embedding a particular algebraic structure (a tower of algebras) within a planar algebra. By considering the planar algebraisation of the tower of Temperley--Lieb algebras, I identify a tower of coupled Temperley--Lieb algebras and find that this tower admits a solution to the mYBE. If time permits, I will sketch how planar algebraisation may serve as a general tool for discovering further solutions.
Prof. Philine Schiewe (Aalto University)
A Bi-Objective Optimization Model for Fare Structure Design in Public Transport
Monday 21 October 2024, 15:15, Riihi (Y225a)
Further information
Fare planning in public transport is important from the view of passengers as well as of operators. Here, we propose a bi-objective model that maximizes the revenue as well as the number of attracted passengers. The potential demand per origin-destination pair is divided into demand groups that have their own willingness how much to pay for using public transport, i.e., a demand group is only attracted as public transport passengers if the fare does not exceed their willingness to pay. We study the bi-objective problem for flat and distance tariffs and develop specialized algorithms to compute the Pareto front in quasilinear or cubic time, respectively. Through computational experiments on structured data sets we evaluate the running time of the developed algorithms in practice and analyze the number of non-dominated points and their respective efficient solutions.
This is joint work with Reena Urban and Anita Schöbel.
SAL Weekly Seminar
Tapani Matala-aho
An analogue of Siegel's determinant
Wednesday 16 October 2024, 16:15, M3 (M234)
The Siegel-Shidlovskii theory is a powerful method for studying transcendence and algebraic independence questions of analytic functions, in particular, of E-functions including entire hypergeometric series.
A crucial step in this method involves a non-vanishing proof for the determinants attached to the linear forms, derivatives of an auxiliary function L(t). Instead of the usual derivative D we use the derivative tD.
We give a short proof for the non-vanishing of modified determinants for a class of differential equations including a subclass of hypergeometric differential equations. As a corollary we get an irreducible criterion for the corresponding differential operator. Further, by some basics from differential modules we prove a converse statement.
ANTA Seminar / Hollanti et al.
Sergej Monavari (EPFL)
Partitions, motives and Hilbert schemes
Wednesday 16 October 2024, 14:15, M2 (M233)
Counting the number of higher dimensional partitions is a hard classical problem. Computing the motive of the Hilbert schemes of points is even harder, and should be seen as the geometric counterpart of the classical combinatorial problem. I will discuss some structural formulas for the generating series of both problems, their stabilisation properties when the dimension grows very large and how to apply all of this to obtain (infinite) new examples of motives of singular Hilbert schemes. This is joint work with M. Graffeo, R. Moschetti and A. Ricolfi.
ADM seminar
David Adame-Carrillo (Aalto)
The fermionic GFF, local UST patterns and scaling limit CFT
Tuesday 15 October 2024, 10:15, M3 (M234)
The fermionic GFF (fGFF) a discrete version of the symplectic fermions CFT is known to be suitable to compute edge probabilities in the uniform spanning tree (UST). In turn, the UST has been linked to CFT at central charge -2 the same central charge as the symplectic fermions. In this talk, I will explain how to make a one-to-one correspondence between lattice local fields of the fGFF and local fields of the symplectic fermions in a way that the (suitably renormalized) correlation functions of the former converge, in the scaling limit, to the corresponding correlation functions of the latter. This result, applied to the UST, allows us to understand the scaling limit of correlation functions of local patterns that is, prescribed open collection of edges in a neighbourhood of a point as symplectic fermions correlation functions.
Based on joint work with W. Ruszel (Uni. Utrecht).
Prof. Rob Corless (Western University)
Gamma and Factorial in the Monthly
Tuesday 08 October 2024, 15:15, M1 (M232)
By 2016, the American Mathematical Monthly had published roughly fifty papers on the Γ function or Stirling's formula. We survey those papers (discussing only our favourites in any detail) and place them in the context of the larger mathematical literature on Γ. We also discuss a surprising blank spot: there had been very little published work on the functional inverse of this function. This omission has been rectified somewhat, since.
Osama Abuzaid (Aalto)
Precompactness of random variables revisited
Tuesday 08 October 2024, 10:15, M3 (M234)
When proving that a sequence of random variables converges, usually one first needs to establish precompactness, i.e. that every subsequence has a converging subsequence. If the random variables take values in some metric space, Prokhorov's theorem states that so called tightness of the sequence implies precompactness. I will provide another sufficient condition of precompactness which I call complete approximability. Every tight sequence is completely approximable, but the converse doesn't hold in general unless the metric space is separable and complete. The proof for sufficiency of complete approximability avoids some prerequisites that proofs for Prokhorov's theorem I'm aware of require.
In the first half of the talk, I will briefly discuss notions of convergence for sequences of random variables, motivate the definition of complete approximability, and explore some ways in which it differs essentially from tightness. In the second half I will sketch the proof of sufficiency of complete approximability and, if time permits, demonstrate how to apply complete approximability for sequences of random curves.
Kai Hippi
Quantum chaos for random Riemannian surfaces (midterm review presentation)
Friday 04 October 2024, 14:15, M2 (M233)
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Friday 04 October 2024, 09:15, M3 (M234)
Further information
Kari Vilonen
Character sheaves and Hessenberg varieties
Tuesday 01 October 2024, 15:15, M2 (M233)
Characters play a key role in representation theory. Lusztigs character sheaves and Springer theory provide one way to work with characters geometrically. In this talk I will explain how to develop the theory of character sheaves in the context of graded Lie algebras. Graded Lie algebras naturally arise from the Moy-Prasad filtration of p-adic groups. In the graded case interesting Hessenberg varieties arise. Affine bundles over these varieties provide a paving of certain affine Springer fibers. At the end of the talk I will explain how one obtains a complete classification of the cuspidal character sheaves on graded Lie algebras via a near by cycle construction. The new results presented are joint work with Grinberg, Liu, Tsai, and Xue.
ADM seminar
Anne Schreuder (Cambridge)
TBA
Tuesday 01 October 2024, 10:15, M3 (M234)
Vigdis Toresen
Localized Model Reduction for Parametric PDEs (Master thesis talk)
Friday 27 September 2024, 10:15, M2 (M233)
Juha Ponkkonen
Modelling CXL Performance in Multiprocessor Architectures
Thursday 26 September 2024, 15:00, M3 (M234)
MSc Thesis Presentation / Hakula
Kalle Kytölä
Boundary visits of SLE and lattice model interfaces
Tuesday 24 September 2024, 10:15, M3 (M234)
mathematical physics seminar
Maxwell Forst
On the geometry of lattice extensions
Wednesday 18 September 2024, 16:15, M3 (M234)
Given a lattice L, an extension of L is a lattice M of strictly greater rank such that the intersection of M and the subspace spanned by L is equal to L. In this talk we will discuss constructions of such lattice extensions where particular geometric invariants of M, such as the determinant, covering radius and successive minima, are related the corresponding geometric invariants of L. This talk is based on joint work with Lenny Fukshansky.
ANTA Seminar / Hollanti et al.
Masashi Misawa
On regularity for doubly nonlinear parabolic type equations by the positivity-expansion
Wednesday 18 September 2024, 10:15, M3 (M234)
We shall consider the second-ordered partial differential equations of parabolic type, which have the p-Laplacian operator and the time-derivative of power-nonlinearity. We call the equations the doubly nonlinear parabolic type equations. Some interactions of fast and slow diffusions may appear and have some effect on regularity of solutions. Our aim is to study the regularity of weak solutions. It is generally necessary to treat sign-changing solutions because the equations considered here are not translation-invariant on unknown functions. We modify the so-called expansion of positivity to obtain the decay of local oscillation of sigh-changing solutions. Our method simplifies the previous proof of regularity in the fast-fast diffusion case and leads to the boundary regularity.
Seminar on analysis and geometry
Marko Lahtinen
Pre-optimization of projection angles in dental sparse-view cone-beam computed tomography
Friday 13 September 2024, 15:15, M3 (M234)
Prof. Martin Lotz (University of Warwick)
Pfaffian Incidence Geometry and Applications
Tuesday 10 September 2024, 15:15, M1 (M232)
Pfaffian functions are real or complex analytic functions that satisfy triangular systems of first-order partial differential equations with polynomial coefficients. Pfaffian functions, and by extension Pfaffian and semi-Pfaffian sets, play a crucial role in various areas of mathematics. Incidence combinatorics has recently experienced a surge of activity, fuelled by the introduction of the polynomial partitioning method of Guth and Katz. While traditionally restricted to simple geometric objects such as points and lines, focus has shifted towards incidence questions involving higher dimensional algebraic or semi-algebraic sets. We present a generalization of the polynomial partitioning method to semi-Pfaffian sets and illustrate how this leads to generalizations of classic results in incidence geometry, such as the Szemerédi-Trotter Theorem. Finally, we outline an application of semi-Pfaffian geometry to the robustness of neural networks.
Jinwoo Sung (Chicago)
Loewner energy reversibility revisited
Tuesday 10 September 2024, 10:15, M3 (M234)
The Loewner energy of a chord in a simply connected domain is defined as the Dirichlet energy of the driving function for the corresponding Loewner chain. In a pioneering work, Yilin Wang identified Loewner energy as the large deviation rate function for chordal Schramm--Loewner evolution as the parameter κ decreases to 0. With this interpretation, she deduced from the reversibility of chordal SLE that the Loewner energy or a chord does not depend on reversing its orientation. I will present a deterministic proof of this fact by reversing the chord in small increments, highlighting similarities and differences from Dapeng Zhan's proof of SLE reversibility.
Mathematical Physics
Prof. Giovanni Pantuso (University of Copenhagen)
Solution of Two-Stage Stochastic Programs with Decision-Dependent Uncertainty
Thursday 05 September 2024, 16:15, U3 (U141)
In this talk, I present an exact solution method for two-stage stochastic programs under decision-dependent uncertainty.
In such problems, first-stage decisions determine the probability distribution of second-stage uncertain parameters.
Particularly, we focus on a broad class of problems where the number of potential probability distributions is finite
but exponentially large. In these problems, the recourse function is non-convex and discontinuous even for problems with continuous second-stage.
The proposed method extends the well-known L-Shaped method and is applicable also to two-stage stochastic programs with integer variables at both stages.
We show that the algorithm converges finitely and propose a number additional improvements that facilitate convergence, such as valid inequalities.
Results of numerical experiments on a facility location problems under endogenous uncertainty show promising scalability and efficiency also on very challenging problems.
Gamma-optinars - Seminars on the Group of Applied Mathematical Modelling and Optimisation (GAMMA-OPT))
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Tuesday 27 August 2024, 09:00, M3 (M234)
Further information
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Friday 23 August 2024, 13:00, M3 (M234)
Further information
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Friday 23 August 2024, 09:00, M3 (M234)
Further information
Armaan Hooda (TUKOKE competition awardee)
Exploring time-dependent carrying capacity in the logistic population growth model
Tuesday 20 August 2024, 10:15, M3 (M234)
Prof. Bruno Fanzeres (Pontifical Catholic University of Rio de Janeiro)
Task-Based Prescriptive Trees for Two-Stage Linear Decision-Making Problems: Reformulations, Heuristic Strategies, and Applications
Tuesday 13 August 2024, 15:15, M1 (M232)
Most decision-making under uncertainty problems found in industry and studied by the scientific community can be framed as a two-stage stochastic program. In the past decades, the standard framework to address this class of mathematical programming problems follows a sequential two-step process, usually referred to as estimate-then-optimize, in which a predictive distribution of the uncertain parameters is firstly estimated, based on some machine/statistical learning (M/SL) method, and, then, a decision is prescribed by solving the two-stage stochastic program using the estimated distribution. In this context, most M/SL methods typically focus only on minimizing the prediction error of the uncertain parameters, not accounting for its impact on the downstream decision problem. However, practitioners argue that their main interest is to obtain near-optimal solutions from the available data with minimum decision error rather than a least-error prediction. Therefore, in this talk, we discuss the new framework referred to as task-based learning in which the M/SL training function also accounts for the downstream decision problem. As the M/SL method, we focus on decision trees, and study decision-making problems framed as a two-stage linear program. We present an exact Mixed-Integer Linear Program (MILP) formulation for the task-based learning method and construct two efficient recursive-partitioning Heuristic Strategies for the MILP. We conclude the talk by analyzing a set of numerical experiments illustrating the capability and effectiveness of the task-based prescriptive tree learning framework, benchmarking against the standard estimate-then-optimize framework, and discussing the computational capability of the constructed heuristic strategies vis-à-vis the MILP formulation.
Prof. Dr. Stefan Ruzika (RPTU)
Multiobjective Optimization An Introduction and Some Current Research Topics
Monday 12 August 2024, 15:15, Y225a
Multiobjective optimization is about making decisions while considering multiple conflicting objective functions. This field of research is theoretically fascinating and practically extremely useful. In this presentation, we give a brief and understandable introduction to multiobjective optimization and present a few important results. In particular, we will survey some notions of optimality, discuss the relevance of scalarization methods, and present the concept of approximation algorithms for multiobjective optimization problems.
Matilde Costa and Antti Haavikko: Student project presentations
Modular forms and curves
Friday 09 August 2024, 10:00, M3 (M234)
There will be two 45 min talks 10:00-10:45 and 11:00-11:45. The topic for the first talk is an introduction to modular forms (Diamond-Schurman Chapter 1, Sections 1,2) and the second an introduction to modular curves (Diamond Schurman Chapter 1 Section 5 and Chapter 2 Sections 1,2). Project advisor Iván Blanco-Chacón.
ANTA Seminar / Hollanti et al.
Title. Firstname Lastname (Home organisation)
TBA
Friday 09 August 2024, 08:52,
Title. Firstname Lastname (Home organisation)
TBA
Friday 09 August 2024, 08:52,
Lukas Olenborg (Aalto)
MSc thesis: Clustering hierarchical purchasing categories for procurement benchmarking using sentence embeddings
Thursday 08 August 2024, 14:15, M2 (M233)
Mikko Seesto
Efficient compression of raw pressure-angle data of a combustion engine
Wednesday 07 August 2024, 15:00, M3 (M234)
Tuomas Kelomäki
Discrete Morse theory for additive categories and Khovanov homology
Friday 02 August 2024, 14:15, M3 (M234)
The original Discrete Morse theory (Forman 1998) is a method for simplifying CW-complexes while preserving their homotopy equivalence. The combinatorial nature of this tool has proven its use in both theoretical mathematics and in applications. In this talk, we will take an algebraic view towards discrete Morse theory (Sköldberg 2005) while simultanously trying to keep the original geometric picture in mind. We will observe that that Sköldberg's formalisation generalizes from R-modules to additive categories. This allows for effective applications towards Khovanov homology, a homology theory for knots and links which categorifies the Jones polynomial. The results we present in Khovanov homology will be both of theoretical and computational in nature. Based on https://arxiv.org/abs/2306.11186 and recent work.
mathematical physics seminar
Ian Välimaa (Aalto University)
Spectral clustering of random hypergraphs (MSc presentation)
Friday 02 August 2024, 11:15, M2 (M233)
Multiway clustering is a clustering problem with multidimensional data arrays. Such data can be used to represent higher-order interactions, hypergraphs and multilayer networks. This has various applications such as gene clustering from multitissue gene expression data or higher-order gene interactions, and personalized web search from clickthrough data. The main objective of this thesis is to determine when an underlying true cluster structure can be recovered from large and noisy data. Specifically, assuming a statistical model (tensor block model), how sparse a data array can be for a fast algorithm to recover the underlying clusters with high probability. This thesis develops a spectral clustering algorithm to solve this statistical problem, proves weak consistency with mathematical rigor and demonstrates it with numerical simulations. The weak consistency is proved by developing concentration inequalities for certain random matrices. The obtained weak consistency regime improves existing results.
Aalto Stochastics and Statistics Seminar / Leskelä
Yaël Dillies
Lean: The slightly less basic (formalization workshop 2)
Thursday 01 August 2024, 14:00, M3 (M234)
In this second workshop, we will build on what we will have done on Tuesday (and on the homework you will hopefully have completed) to move to more advanced notions like the use of filters in topology.
Motivated learners will be able to join the ForAlli meeting happening right after.
ForAlli Lean tutorials
Yaël Dillies
Lean: The basics (formalization workshop 1)
Tuesday 30 July 2024, 14:00, M3 (M234)
In this first workshop, I will explain the fundamentals of using Lean: Basic syntax, how to install it, where to find learning material, how to read the documentation, differences to other programming languages...
I will also have additional exercises for more advanced learners.
ForAlli Lean tutorials
Teemu Tasanen (Aalto)
Giving Meaning to Divergent Asymptotic Power Series: Borel Summation along the Real Line
Tuesday 30 July 2024, 11:15, M3 (M234)
The talk provides an overview of Borel summation as a method to recover functions from their divergent asymptotic power series expansions. Borels method is introduced through a heuristic approach of "summing" an arbitrary power series, and an integral from a toy quantum field theory is presented to illustrate the method's relevance in the context of asymptotic expansions.
Central to this is the understanding of a Laplace-like transform and its inverse, which through consecutive application, define the operation of Borel summation. The theory of asymptotics is also briefly reviewed, and the talk concludes with remarks about Nevanlinnas theorem and its proof, guaranteeing the unique recovery of a function from its diverging asymptotic power series under certain conditions.
Yaël Dillies
Formalisation in Lean: Why care?
Monday 29 July 2024, 11:00, M3 (M234)
What's this craze about theorem proving? You must have heard of it, but do you know what it is actually about? Do we really care about absolute correctness? or is this some kind of gimmick to make the cover of popular science magazines?
In this talk, I will explain the basic principles of Lean and argue that the true reason behind the launch of formal mathematics as an established subject is neither a matter of informality crisis on the part of mathematicians nor a publicity stunt, but the manifestation of a much more fundamental background shift in the social practice of mathematics, and that now is the time to join the formalisation bandwagon.
I will illustrate my point with my personal journey through formal mathematics, from bored undergrad to collaborator of Terence Tao, sprinkled with examples from my own subject: additive combinatorics.
No Lean experience nor knowledge of additive combinatorics will be assumed.
Antti Haavikko (MSc thesis presentation)
Fast polynomial multiplication in maximal real subfields of cyclotomic extensions
Tuesday 23 July 2024, 10:15, M3 (M234)
Further information
Advisor: Wilmar Bolanos
ANTA Seminar / Hollanti et al.
Joel Hakavuori
MSc thesis presentation: l^2-invariants and the topology of right-angled Coxeter groups
Monday 08 July 2024, 17:15, M3 (M234)
Algebra and discrete mathematics seminar
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Wednesday 26 June 2024, 12:00, M3 (M234)
Further information
Toni Annala (IAS)
Motivic homotopy theory
Tuesday 25 June 2024, 14:15, M3 (M234)
Cohomology theories are an integral part of modern algebraic geometry. In algebraic topology, (stable) homotopy theory provides a convenient framework to study various cohomology theories and their interrelations. In algebraic geometry, a similar role should be played by motivic homotopy theory, which strictly generalizes Grothendieck's dream of motives.
In the first part of the talk, I will motivate the necessity of homotopy theory to study cohomology theories in algebraic topology and algebraic geometry. I will also introduce A^1-homotopy theory, defined by Morel and Voevodsky in the late 90s. In the second part of my talk, I will introduce the motivic stable homotopy theory, which is the subject of my long-term project with Marc Hoyois, Ryomei Iwasa, and others. The goal of this theory is to build a framework for studying all cohomology theories in algebraic geometry simultaneously. I will give some sample results, and explain what concrete consequences can be derived from our results.
Algebra & Discrete Math Seminar
Ryosuke Sato (Chuo University)
CAR algebras and stochastic processes on random point processes
Tuesday 25 June 2024, 10:15, M3 (M234)
CAR algebras are fundamental operator algebras that appear in various fields of mathematics and mathematical physics. In this talk, we will focus on its relationship to random point processes, which are mathematical descriptions of random interacting particles. In particular, after discussing the relation between quasi-free states of CAR algebras and determinantal point processes, we will investigate how the operator algebraic framework provides stochastic processes on random point processes.
Katherine Maxwell (Kavli IPMU)
Superstring measure extended to supergrassmannian space
Thursday 20 June 2024, 10:15, M3 (M234)
I will describe an extension of the integration measure for calculating scattering amplitudes in (super)string theory to a large (super)grassmannian space, known as the super Sato grassmannian. In comparison to bosonic string theory, superstring theory provides some simplifications in the properties of the integration measure, which I will highlight in my talk. On the other hand, superstring theory is intrinsically related to the supermoduli space of super Riemann surfaces, which poses challenges because of the supergeometric structure. I will explain why working with supergrassmannian space could be a good solution to these problems. This is based off of joint work with Alexander Voronov.
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Wednesday 19 June 2024, 09:00, M3 (M234)
Further information
Okko Makkonen
Midterm review: Algebraic methods in homomorphic secret sharing
Thursday 13 June 2024, 11:15, M3 (M234)
ANTA Seminar / Hollanti et al.
Shinji Koshida (Aalto)
Building Natural Number Game from scratch
Tuesday 11 June 2024, 10:15, M3 (M234)
I will present a non-expert view on type theory taking formalization of natural numbers as an example. In particular, I will define natural numbers and the operation of addition, prove the unit laws, associativity and commutativity. If time permits, I will also prove Peano's 7th and 8th axioms. The demonstration will go in a proof assistant Agda. (This presentation is not about a conventional topic from mathematical physics.)
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Tuesday 11 June 2024, 09:15, M3 (M234)
Further information
Starting time corrected!
Professor Dan Brown, University of Waterloo
Algorithmic information theory, creativity and communication
Monday 10 June 2024, 14:00, T3
We build an analysis based on Algorithmic Information Theory of computational creativity and extend it to revisit computational aesthetics. Our approach gives an interesting basis to novelty, value, typicality, and a number of other basic concepts in aesthetics, while also focusing on how information is communicated between creators and audiences. In more recent work, we extend this to considering the process of review, which we present as a task that conveys information among various actors, including creators, audiences and reviewers.
Philine Schiewe
Optimization - A first look (2x45min)
Thursday 06 June 2024, 14:15, M2 (M233)
In this seminar, we will revisit various key areas of mathematical
optimization. Starting from linear optimization and classical solution
approaches exploiting the polyhedral feasible sets, we will continue to
mixed-integer linear programming. Here, solution approaches from linear
programming can be transferred in the context of cutting-plane and
branch-and-bound methods striving towards integral polyhedra. As a
special case of mixed-integer linear programs, we consider combinatorial
optimization. Classical combinatorial optimization problems contain both
polynomially solvable problems such as matchings and minimum spanning
trees as well as many famous NP-hard problems such as the traveling
salesperson problem and maximum cut.
As a second generalization of linear programming, we consider
semidefinite optimization. Here, we see how combinatorial optimization
problems can be approximated by semidefinite programs and have a look at
interior-point-based solution approaches.
ANTA Seminar / Hollanti et al.
Prof. Sueli I. R. Costa (Unicamp, Brazil)
On lattices applied to coding for reliable and secure communications
Monday 03 June 2024, 13:15, M2 (M233)
This talk aims to present a general approach to some lattice applications in communications emphasizing topics we have been working on recently as well others of interest. Those are related to spherical codes, index coding, multilevel coding/ decoding, Construction Pi-A from Hurwitz quaternions, twisted embeddings in lattice based cryptography and federated learning.
ANTA Seminar / Hollanti et al.
Aada Hakula
Diffuse Optical Tomography with an Inaccurate Forward Operator in the Linearized Inverse Problem (Master's Thesis Presentation)
Monday 03 June 2024, 13:00, M3 (M234)
Patricija Sapokaite
Midterm review: Cycles in hypergraphs and matroids
Friday 31 May 2024, 13:15, M2 (M233)
Algebra and discrete mathematics seminar
Joonas Vättö
Segal axioms for the massless, free boson (midterm review presentation)
Friday 31 May 2024, 10:15, M3 (M234)
After a review of the geometric axiomatisation scheme to two-dimensional conformal field theories (CFTs) in the spirit of Kontsevich and Segal, I will explicitly show how to construct the chiral CFT for the free, massless boson on arbitrary compact Riemann surfaces. The construction provides a rich playground for the interplay of distant areas of mathematics (Kähler spaces, C*-algebras, geometric function theory, etc.). Time permitting, I will sketch connections to Teichmüller theory, global analysis, and the Atiyah-Singer index theory.
Valtteri Lipiäinen, Johan Dinesen, Tuomo Valtonen, Neehar Verma
Course presentations: Applications of Coding Theory to Security
Thursday 30 May 2024, 12:00, M2 (M233)
12:00 Valtteri Lipiäinen: CodedPaddedFL and CodedSecAgg: Straggler mitigation and secure aggregation in federated learning.
12:30 Johan Dinesen: McEliece cryptosystem.
13:15 Tuomo Valtonen: Secure distributed matrix multiplication.
13:45 Neehar Verma: Private polynomial computation from Lagrange encoding.
ACTS Course Presentations / Hollanti et al.
Stephen Moore (IMPAN)
Representations of the Reflection Equation Algebra
Tuesday 28 May 2024, 10:15, M3 (M234)
The reflection equation was introduced in relation to quantum integrable systems with boundary condition and is closely related to the Yang-Baxter equation. The reflection equation algebra was in turn introduced to allow the algebraic study of solutions of the reflection equation, similar to the connection between quantum groups and the Yang-Baxter equation. We will describe the basic properties of the reflection equation algebra and explain the classification of its bounded *-representations. This is based on joint work with Kenny De Commer.
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Friday 24 May 2024, 09:15, M3 (M234)
Further information
Markus Hirvensalo
Midterm review: Extending the linearized Calderon problem to unbounded perturbations
Thursday 23 May 2024, 09:15, M2 (M233)
Heikki Kettunen
TBA (Master's Thesis Presentation)
Wednesday 22 May 2024, 14:15, M2 (M233)
Diplomityöesitelmä / Hakula
Meri Aho
On the quality of mathematical writing produced by ChatGPT and Gemini (MSc thesis presentation)
Wednesday 22 May 2024, 11:15, M240
Thilini Panagoda
On Temperature changes in Finland (MSc thesis presentation)
Monday 20 May 2024, 09:30,
Kalle Kytölä
Introduction to formalized mathematics with convergence in distribution as an example
Thursday 16 May 2024, 16:15, M3 (M234)
Rolf Stenberg
Courant vs. Nitsche
Thursday 16 May 2024, 09:15, M2 (M233)
Kai Hippi
Quantum ergodicity of a surface with a weak point scatterer
Wednesday 15 May 2024, 14:15, M3 (M234)
Seminar on analysis and geometry
Lauri Särkiö
Regularity of parabolic double-phase equations (Midterm review)
Wednesday 15 May 2024, 11:15, M3 (M234)
Prof. Alberto Ravagnani (Eindhoven University of Technology)
The Service Rate Region Polytope
Tuesday 14 May 2024, 15:15, M1 (M232)
In distributed data storage, information is distributed across multiple servers with redundancy, in such a way that multiple users can access it at the same time. The access requests that a distributed data storage system can support are described by a convex polytope, called the service rate region of the system. This talk is about the properties of the service rate region, and about how the algebra of the system determines the geometry of the corresponding polytope.
Lilja Metsälampi
Midterm review
Monday 13 May 2024, 16:15, M3 (M234)
Algebra and discrete mathematics seminar
Dr. Benjamin Jany (TU Eindhoven)
Bounds and field size for locally recoverable codes
Monday 13 May 2024, 14:15, M2 (M233)
In the last decade, Locally Recoverable Codes (LRC) have been a critical topic in communication and distributed storage. In addition to the minimum distance, dimension and length of a code, LRCs also consider the locality parameter, i.e. the minimum number of entries needed to recover a given entry for any codeword. The parameters of LRCs are subject to a general Singleton bound and codes achieving the bound are called optimal LRCs. Constructions are known when the underlying field size of the code is larger than the length of the code. However, still little is known about the existence of optimal LRCs over small underlying field sizes. In this talk, I will show how we established new bounds that depend on locality and the field size of code using a duality theory of LRCs and
the combinatorial structure of the code. This talk is based on joint work with A. Gruica and A. Ravagnani.
ANTA Seminar / Hollanti et al.
Dmitrii Vasilev
Performance analysis of neural likelihood approximation methods for decision making models
Wednesday 08 May 2024, 16:15, M3 (M234)
Rodrigo Martín Sánchez-Ledesma (Complutense U. Madrid / INDRA)
Overview and extension of root-based attacks against PLWE instances
Tuesday 07 May 2024, 15:15, M2 (M233)
The Polynomial Learning With Errors problem (PLWE) serves as the background of two of the four cryptosystems standardised in July 2022 by the National Institute of Standards and Technology to replace non-quantum resistant current primitives like those based on RSA, finite field based Diffie-Hellman and its elliptic curve analogue. Although PLWE is highly believed to be quantum resistant, unlike other post-quantum proposals like multivariate and some code based ones, this fact has not yet been established. Moreover, several vulnerabilities have been encountered for a number of specific instances. In a search for more flexibility, it becomes fully relevant to study the robustness of PLWE based on other polynomials, not necessarily cyclotomic. In 2015, Lauter et al. found a good number of attacks based on different features of the roots of the polynomial. In the present talk we present an overview of the approximations made against PLWE derived from these work, along with several new attacks which refine those by Lauter exploiting the order of the trace of roots over finite extensions of the finite field under the three scenarios laid out by Lauter et al, allowing to generalize the setting in which the attacks can be carried out. This is joint work with I. Blanco-Chacón and R. Durán.
ANTA Seminar / Hollanti et al.
Teemu Mäki
MSc thesis presentation: Side-channel attacks in digital forensics
Tuesday 07 May 2024, 14:15, M2 (M233)
Advisors: Lassi Helanti (National Bureau of Investigation Forensic Laboratory) and Estuardo Alpirez Bock (Xiphera)
ANTA Seminar / Hollanti et al.
Oula Kekäläinen
MSc thesis presentation: Generalization of Descartes' rule of signs to multivariate polynomials with real exponents
Monday 29 April 2024, 16:15, M3 (M234)
Algebra and discrete mathematics seminar
Tunç Köse (Aalto University)
Community recovery with variational inference and stochastic block models (MSc presentation)
Monday 29 April 2024, 14:15, M222 (Kappa)
Lasse Leskelä
Joonas Laaksonen
MSc thesis presentation
Monday 29 April 2024, 14:15, M3 (M234)
Diplomityöesitelmä
Diplomityöesitelmä / Hakula
Sivusta vastaa: webmaster-math [at] list [dot] aalto [dot] fi