* Dates within the next 7 days are marked by a star.
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.
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.
Sari Rogovin
TBA
Wednesday 23 October 2024, 10:15, M3 (M234)
Seminar on analysis and geometry
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Friday 15 November 2024, 09:00, M3 (M234)
Further information
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
Joonas Laaksonen
MSc thesis presentation
Monday 29 April 2024, 14:15, M3 (M234)
Diplomityöesitelmä
Diplomityöesitelmä / Hakula
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
Lauri Nyman
Distance to singularity for matrix pencils via Riemannian optimization
Thursday 25 April 2024, 09:15, M2 (M233)
Lauri Nyman
Distance to singularity for matrix pencils via Riemannian optimization
Thursday 25 April 2024, 09:15, M2 (M233)
Lauri Nyman
Distance to singularity for matrix pencils via Riemannian optimization
Thursday 25 April 2024, 09:15, M2 (M233)
Leevi Kaukonen
MSc thesis presentation
Wednesday 24 April 2024, 14:15, M3 (M234)
Diplomityöesitelmä
Diplomityöesitelmä / Hakula
Anna-Mariya Otsetova
Axisymmetric capillary water waves with vorticity and swirl connecting to static unduloid configurations
Wednesday 24 April 2024, 10:15, M3 (M234)
We study steady axisymmetric water waves with general vorticity and swirl, subject to the influence of surface tension. Explicit solutions to such a water wave problem are static configurations where the surface is an unduloid, that is, a periodic surface of revolution with constant mean curvature. We prove that to any such configuration there connects a global continuum of non-static solutions by means of a global implicit function theorem and topological degree theory. To prove this, the key is strict monotonicity of a certain function describing the mean curvature of an unduloid and involving complete elliptic integrals. From this point of view, this paper is an interesting interplay between water waves, geometry, and properties of elliptic integrals.
This is a joint work with Jörg Weber (University of Vienna) and Erik Wahlén (Lund University).
Seminar on analysis and geometry
Gerald Williams (University of Essex)
Incidence graphs of generalized polygons and star graphs of group presentations with cyclic symmetry
Monday 22 April 2024, 16:15, M3 (M234)
A generalized polygon is a point-line incidence structure that includes projective planes (generalized 3-gons). Incidence graphs of generalized m-gons are connected bipartite graphs of diameter m and girth 2m. Associated to any group presentation is a graph called the star graph, which encodes structural information about the group defined by the presentation. Transitional behaviour can occur for groups defined by presentations whose star graph components are incidence graphs of generalized polygons; such presentations are called special. A cyclic presentation of a group is a type of group presentation that admits a cyclic symmetry. In this talk I will discuss joint work with Ihechukwu Chinyere in which we classify the special cyclic presentations.
Algebra and discrete mathematics seminar
Ivy Woo
Partial Lattice Trapdoors: How to Split Lattice Trapdoors, Literally
Monday 22 April 2024, 13:30, Väre Q203
We introduce a natural technique for sharing lattice trapdoors: splitting them into partial trapdoors of smaller dimensions. We define security properties for these objects and prove these properties for a simple construction. Our proofs are based on the k-MSIS and k-MLWE assumptions together with the following conjecture: sampling two matrices with entries following discrete Gaussian distributions of width \sigma_0 or \sigma_1 and then sampling a matrix with entries following a discrete Gaussian distribution of width \sigma > \poly \cdot \max(\sigma_0, \sigma_1) from the lattices spanned by these two matrices leads to two distributions that are statistically close. We construct simple threshold signatures and IBE schemes from this primitive to illustrate its utility.
Cryptography seminar
prof. Samuli Siltanen (University of Helsinki)
The magic of math: three-dimensional X-ray vision (FMS colloquium)
Wednesday 17 April 2024, 16:15, M1 (M232)
Further information
In the 1970s, a new X-ray based innovation was introduced. Tomography, or slice imaging, revealed the inner structure of a patient point by point as a three-dimensional map of tissues. This opened up a new world for doctors as they could do precise diagnosing based on these "CAT-scans."
Tomography is based on recording X-ray images of the patient along many directions, and then using mathematics in a clever way for combining the information into a 3D image. This talk explains that process in simple terms. An important research topic in modern mathematics is to look for a way to do tomographic imaging with the least possible amount of radiation dose to the patient. Or to compensate for incomplete measurements caused by restrictions in the imaging arrangement. This is based on a process called regularisation, also illustrated in the talk in an easy-to-understand way.
Also: there is a fun quiz revealing natural tomographers among the audience.
SMY kollokvio
Kim Myyryläinen
Parabolic Muckenhoupt weights
Wednesday 17 April 2024, 10:15, M3 (M234)
Seminar on analysis and geometry
Ivy Woo
Obfuscation from Lattice-Based Equivocal Assumption
Tuesday 16 April 2024, 15:15, M2 (M233)
The Learning with Errors (LWE) problem w.r.t. a matrix B asks to recover the secret-error tuple (s,e) given the sample c = sB+e mod q. In typical settings, e.g. when B mod q is uniformly random, the solution (s,e) is uniquely determined by (B,c). In lattice terminology, this is due to the non-existence of short vectors in the lattice spanned by the rows of B modulo q.
We propose the notion of "primal lattice trapdoors", a suit of algorithms which generates a matrix B together with a trapdoor, such that the lattice of B contains hidden exceptionally short vectors, allowing LWE samples w.r.t. B to admit multiple solutions, whereas the trapdoor allows to sample from the solution space. We provide a construction and prove that it satisfies a set of desirable properties, either unconditionally or computationally based on the NTRU assumption.
Leveraging our tool, we construct a lattice-based indistinguishability obfuscator, a powerful cryptographic primitive known to imply most in cryptography.
ANTA Seminar / Hollanti et al.
Joaquín de la Barra
Decision models for reinforcing critical infrastructures (Mid-term evaluation)
Tuesday 16 April 2024, 14:30, M3 (M234)
Sampo Niemelä
MSc thesis presentation: Coding theory for federated learning
Tuesday 16 April 2024, 11:15, M2 (M233)
Advisors: Okko Makkonen and Serge Kas Hanna
ANTA MSc thesis presentation / Hollanti
Ville Havu
ELSI Software interface for electronic structure solvers
Thursday 11 April 2024, 09:15, M2 (M233)
Kevin Nguyen
On sales lead optimization of personal insurance covers with multi-armed bandit algorithms (MSc thesis presentation)
Wednesday 10 April 2024, 15:15, M2 (M233)
Lauri Särkiö
Very weak solutions to parabolic p-Laplace systems
Wednesday 10 April 2024, 10:15, M3 (M234)
Seminar on analysis and geometry
Prof. Paul Van Dooren (UCLouvain)
Assigning Stationary Distributions to Stochastic Matrices
Tuesday 09 April 2024, 15:15, M1 (M232)
The target stationary distribution problem (TSDP) is the following: given an
irreducible stochastic matrix G and a target stationary distribution μ^, construct
a minimum norm perturbation, ∆, such that G^ = G + ∆ is also stochastic and
has the prescribed target stationary distribution, μ^. We first consider rank-1
perturbations ∆ and show how to efficiently minimize their norm when such a
solution is feasible. But sparsity and/or connectivity of the graph of G + ∆ may
then get lost. We then impose a constraint on the support of ∆, that is, on the
set of non-zero entries of ∆. This is particularly meaningful in practice since
one cannot typically modify all entries of G. We first show how to construct
a feasible solution G^ that has essentially the same support as the matrix G.
Then we show how to compute globally optimal and sparse solutions using
the component-wise l_1 norm and linear optimization. We propose an efficient
implementation that relies on a column-generation approach which allows us to
solve sparse problems of size up to 10^5 × 10^5 in a few minutes.
Jonas Tölle
Nonlinear (stochastic) PDEs with singular diffusivity
Tuesday 09 April 2024, 10:15, M140
In this talk, we shall discuss properties of solutions to parabolic deterministic (and stochastic) partial differential equations with singular nonlinear divergence-type diffusivity with zero Dirichlet boundary conditions on a bounded Euclidean domain. As these kinds of equations usually lack good coercivity estimates in higher spatial dimensions, we choose to address the general well-posedness question by variational weak energy methods.
Examples include the (stochastic) singular $p$-Laplace equation, the multi-valued (stochastic) total variation flow and the (stochastic) curve shortening flow.
We shall present improved pathwise regularity results and decay estimates for a general class of singular divergence-type PDEs. We shall also address the stochastic case, where the equation is perturbed by additive Gaussian noise.
Based on joint works with Benjamin Gess (Leipzig and Bielefeld), Wei Liu (Xuzhou), Florian Seib (Berlin), and Wilhelm Stannat (Berlin).
Seminar on analysis and geometry
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Tuesday 09 April 2024, 09:00, M203
Further information
Paul Van Dooren
Perfect shifts and the QR algorithm
Thursday 04 April 2024, 09:15, M2 (M233)
Tuomas Hytönen (Aalto)
True and fake generalized eigenvectors of infinite matrices
Tuesday 02 April 2024, 10:15, M3 (M234)
In von Neumann's formulation of Quantum Mechanics, physical observables are represented by self-adjoint operators in some Hilbert space. The spectrum of the operator is interpreted as the set of possible outcomes of a measurement of the observable, which is perhaps the most important physical prediction of this mathematical model. In Physics literature, especially on the introductory level, a somewhat heuristic approach to studying the spectrum is sometimes employed: "generalized eigenvectors" outside the original Hilbert space are acceptable, unless they are too wild to be "physical". The aim of the talk is to provide a rigorous justification of such heuristics under certain conditions, but also to show that these heuristics may miserably fail in some situations.
Thomas Wasserman (Oxford)
Functorial Field Theory and Defects
Tuesday 26 March 2024, 10:15, M3 (M234)
I will give an overview of functorial field theories, a mathematical formalisation of quantum field theories as functors out of some (higher) category of bordisms between manifolds. It is particularly well suited for describing topological quantum field theories. In the first half of this talk I will explain the Cobordism Hypothesis: a classification result for topological quantum field theories. In the second half, I will explain how one thinks about defects (interfaces between different quantum field theories) in this formalism, and how this relates to the bulk-boundary correspondence between three-dimensional topological quantum field theories and two-dimensional conformal field theories. I will aim to make this talk accessible to a broad audience.
mathematical physics seminar
Toni Karvonen
The relation between asymptotic and worst-case settings in numerical integration
Thursday 21 March 2024, 09:15, M2 (M233)
Jani Onninen (Syracuse University)
Quasiregular values
Wednesday 20 March 2024, 10:15, M3 (M234)
Quasiregular maps form a higher-dimensional class of maps with many similar properties to holomorphic maps, such as continuity, openness, discreteness, and versions of the Liouville and Picard theorems. In this talk, we give a pointwise definition of quasiregularity. We show that this condition yields counterparts to many fundamental properties of quasiregular maps at a single point. The studied maps have already shown to play a key part in various important 2D results. Joint work with Ilmari Kangasniemi.
Seminar on analysis and geometry
Luis Brummet (Aalto)
Survey on complex driven Loewner chains
Tuesday 19 March 2024, 10:15, M3 (M234)
In this talk we provide some basic facts about Loewner chains driven by both deterministic functions and stochastic processes. In the second half of the talk we provide some insights about the current development on Loewner chains driven by deterministic complex-valued functions and complex Brownian motion.
Aapo Laukkarinen
Convex body domination and its applications to matrix-weighted norm inequalities
Wednesday 13 March 2024, 10:15, M3 (M234)
Seminar on analysis and geometry
Prof. Henrik Garde (Aarhus University)
Obstacles in Calderóns inverse conductivity problem
Tuesday 12 March 2024, 15:15, U6 KONECRANES (U149)
I will discuss the inverse conductivity problem on recovering interior information about the electrical conductivity of a body from exterior electrical measurements. I will show how one can reconstruct the exact shape and position (called obstacles/inclusions) of inhomogeneities, using energy-comparisons with Neumann-to-Dirichlet maps.
The method is at the same time both simple and surprisingly general, allowing inhomogeneities with parts that are finite positive and negative perturbations, parts that are superconducting or insulating, and parts originating from a Muckenhoupt weight (leading to degenerate/singular problems). The method can also recover collections of cracks in the form of hypersurfaces.
If time permits it, I will also discuss how to handle more practical electrode models and noisy measurements in a rigorous way.
Osama Abuzaid (Aalto)
Random matrices, multiple SLEs and large deviations
Tuesday 12 March 2024, 10:15, M3 (M234)
A fundamental goal in random matrix theory is to understand the eigenvalues of a given random matrix model. Schramm-Loewner evolution SLE(κ) is a one-parameter family of random curves arising from two-dimensional conformal geometry. In this talk I will show how the evolution of eigenvalues of certain Itô-diffused random matrices coincide with the driving functions of multiple interacting SLE(κ) curves of some special values of κ. If time permits, in the end I will present a large deviation principle which quantifies the exponential rate of convergence of SLE(κ)-curves to deterministic SLE(0) in the limit κ->0.
Prof. Francesco De Pretis (University of Modena )
Making decisions with evidential probability and objective Bayesian calibration inductive logics
Monday 11 March 2024, 15:15, Y225a
Calibration inductive logics are based on accepting estimates of relative frequencies, which are used to generate imprecise probabilities. In turn, these imprecise probabilities are intended to guide beliefs and decisions a process called calibration. Two prominent examples are Henry E. Kyburg's system of Evidential Probability and Jon Williamson's version of Objective Bayesianism. There are many unexplored questions about these logics. How well do they perform in the short-run? Under what circumstances do they do better or worse? What is their performance relative to traditional Bayesianism? In this article, we develop an agent-based model of a classic binomial decision problem, including players based on variations of Evidential Probability and Objective Bayesianism. We compare the performances of these players, including against a benchmark player who uses standard Bayesian inductive logic. We find that the calibrated players can match the performance of the Bayesian player, but only with particular acceptance thresholds and decision rules. Among other points, our discussion raises some challenges for characterising cautious reasoning using imprecise probabilities. Thus, we demonstrate a new way of systematically comparing imprecise probability systems, and we conclude that calibration inductive logics are surprisingly promising for making decisions.
Marko Huhtanen
Non-Hermitian quantum mechanics eigenvalue problem
Thursday 07 March 2024, 08:59, M2 (M233)
Wontae Kim
Hölder regularity of the parabolic double phase equation
Wednesday 06 March 2024, 10:15, M3 (M234)
Seminar on analysis and geometry
Tuukka Himanka
Physics-Informed Neural Networks in Probabilistic Spatio-Temporal Modelling
Friday 01 March 2024, 14:15, M3 (M234)
Diplomityöesitelmä / Hakula
Jalo Nousiainen
Machine learning and inverse problems in extreme adaptive optics
Thursday 29 February 2024, 09:15, M2 (M233)
Timo Takala
Preserving Besov energy in sphericalization and flattening
Wednesday 28 February 2024, 10:15, M3 (M234)
Seminar on analysis and geometry
Baptiste Cerclé (EPFL)
A probabilistic approach to Toda Conformal Field Theories
Tuesday 27 February 2024, 15:00, M3 (M234)
Toda conformal field theories form a family of two-dimensional quantum field theories initially introduced in the physics literature. They are natural generalizations of Liouville theory that enjoy, in addition to conformal invariance, an enhanced level of symmetry encoded by W-algebras.
In this presentation we will explain how one can study these theories from a mathematically rigorous perspective. For this purpose we will describe a probabilistic framework designed to make sense of these models and provide some insight on how the introduction of this framework can help to understand the model.
To be more specific, we will prove ---we will not enter into much details but rather try to convey the main ideas--- that one can compute some basic correlation functions of the theory based on probabilistic tools. Along the proof of this statement we will shed light on some unexpected interplays between probability theory and conformal field theory such as a generalized Brownian path decomposition.
Yi Tian (University of Bonn)
Permutons, Meanders, and Random Geometry
Tuesday 27 February 2024, 10:15, M3 (M234)
In this talk, we start with an overview of space-filling SLE, the quantum sphere, and the mating of trees theorem. We then define permutons and illustrate their natural construction from SLE-decorated LQG. Focusing on two special cases, Baxter permutons and meandric permutons, we reveal how they arise as limits of Baxter permutations and meanders, respectively. Through this exploration, permutons offer insights into the connection between discrete models and random geometry.
Mathematical Physics Seminar / Kytölä - Peltola
Charles Parker, Oxford
Computing H2-conforming finite element approximations without having to implement C1-elements
Thursday 22 February 2024, 13:15, M2 (M233)
Fourth-order elliptic problems arise in a variety of applications from thin plates to phase separation to liquid crystals. A conforming Galerkin discretization requires a finite dimensional subspace of H2, which in turn means that conforming finite element subspaces are C1-continuous. In contrast to standard H1-conforming C0-elements, C1-elements, particularly those of high order, are less understood from a theoretical perspective and are not implemented in many existing finite element codes. In this talk, we address the implementation of the elements. In particular, we present algorithms that compute C1 finite element approximations to fourth-order elliptic problems and which only require elements with at most C0-continuity. We also discuss solvers for the resulting subproblems and illustrate the method on a number of representative test problems.
Augustin Lafay and Julien Roussillon (Aalto)
W3 conformal blocks at c=2 and Specht polynomials
Tuesday 20 February 2024, 10:15, M3 (M234)
In this two-part talk we will present recent results on W3 conformal blocks. These are solutions of a system of PDEs arising from W3 algebra (an extension of the Virasoro algebra) null-vectors and Ward identities. At c=2, we give an explicit subspace of solutions having the dimension predicted by CFT. The solutions are expressed in terms of Specht polynomials in a simple way. After giving heuristic physical motivations, we will state a conjecture relating these functions to connection probabilities in the triple dimer model, recently computed by Kenyon and Shi. All along the talk, we will present the analogous known results for the Virasoro case.
Antti Hannukainen
Parameter-dependent diffusion equation in layered media
Thursday 15 February 2024, 13:30, M2 (M233)
Tomas Laamanen
On the Impact of Statin Treatment on the Hypoxic Metabolism of In Vitro Grown Prostate Cancer Cells (MSc thesis presentation)
Wednesday 14 February 2024, 15:15, Zoom
The Master's thesis presentation is given in zoom
https://aalto.zoom.us/j/66809637898
Meeting ID: 668 0963 7898
Milla Laurikkala
Performance analysis of complex-valued convolutional neural networks on 5G L1 (MSc thesis presentation)
Wednesday 14 February 2024, 14:15, M3 (M234)
Tuomas Hytönen
Reduced inequalities for vector-valued functions
Wednesday 14 February 2024, 10:15, M3 (M234)
Seminar on analysis and geometry
Prof. Eeva Vilkkumaa (Aalto University)
Supporting the Development of a Robust, Market-Shaping Strategy with Scenario-Based Portfolio Decision Analysis: Case Study with Nordea
Tuesday 13 February 2024, 15:15, U5 (U147)
Strategic decision-making is challenging due to multiple strategic objectives and long planning horizons that make it difficult to assess the future impacts of proposed strategic actions with respect to these objectives. Moreover, strategy work often requires a balance between preparing for alternative scenarios for the future (i.e., developing a robust strategy), and trying to steer the course of change towards a desirable direction (i.e., developing a market-shaping strategy). We present a model-based framework for supporting the development of a robust, market-shaping strategy. For the purposes of this framework, we develop a new portfolio decision analytic model and algorithms to help generate decision recommendations for selecting strategic actions, when (i) the actions scenario- and objective-specific impacts, the baseline values for these impacts, as well as preferences between strategic objectives are incompletely specified, and (ii) information regarding scenario likelihoods is incomplete and may depend on the selected actions. This framework is applied in a high-impact case on supporting the strategy process at the payments unit of Nordea Bank Abp, the largest retail bank in the Nordic countries.
Hamid Al-Saqban (Paderborn University)
Unique Ergodicity for Foliations of Generic Abelian Differentials, Revisited
Tuesday 13 February 2024, 10:15, M3 (M234)
In Teichmuller theory, a theorem due to H. Masur and W. Veech states that for generic Abelian differentials, the leaves of the horizontal foliation are uniquely ergodic. Said differently, the orbits of the horizontal straight-line flow on a generic translation surface are uniquely ergodic. Subsequently, G. Forni proved an effective form of this statement, establishing in particular precise power-laws for the deviations of ergodic averages of smooth functions from the power law (as predicted by the ergodic theorem). The main goal of this talk is to introduce and motivate translation surfaces, and to explain the main ideas behind an analytic approach (via anisotropic Banach spaces) to effective unique ergodicity for straight-line flows on a generic translation surface. This is a joint work in progress with D. Galli (University of Zurich).
Mathematical Physics Seminar / Radnell
Teemu Lundström
f-vector inequalities for order and chain polytopes
Thursday 08 February 2024, 13:15, M237
Midterm review talks / Algebra and discrete mathematics seminar
Antti Autio
Comparing reduced basis models for electrical impedance tomography
Thursday 08 February 2024, 09:15, M2 (M233)
Petteri Kaski
The Asymptotic Rank Conjecture and the Set Cover Conjecture are not Both True
Wednesday 07 February 2024, 16:15, M2 (M233)
Strassen's asymptotic rank conjecture [Progr. Math. 120 (1994)] claims a strong submultiplicative upper bound on the rank of a three-tensor obtained as an iterated Kronecker product of a constant-size base tensor. The conjecture, if true, most notably would put square matrix multiplication in quadratic time. We note here that some more-or-less unexpected algorithmic results in the area of exponential-time algorithms would also follow. Specifically, we study the so-called set cover conjecture, which states that for any ε>0 there exists a positive integer constant k such that no algorithm solves the k-Set Cover problem in worst-case time O((2-ε)^n|F|poly(n)). The k-Set Cover problem asks, given as input an n-element universe U, a family F of size-at-most-k subsets of U, and a positive integer t, whether there is a subfamily of at most t sets in F whose union is U. The conjecture was formulated by Cygan, Fomin, Kowalik, Lokshtanov, Marx, Pilipczuk, Pilipczuk, and Saurabh in the monograph Parameterized Algorithms [Springer, 2015], but was implicit as a hypothesis already in Cygan, Dell, Lokshtanov, Marx, Nederlof, Okamoto, Paturi, Saurabh, and Wahlström [CCC 2012, TALG 2016], there conjectured to follow from the Strong Exponential Time Hypothesis. We prove that if the asymptotic rank conjecture is true, then the set cover conjecture is false. Using a reduction by Krauthgamer and Trabelsi [STACS 2019], in this scenario we would also get an O((2-δ)^n)-time randomized algorithm for some constant δ>0 for another well-studied problem for which no such algorithm is known, namely that of deciding whether a given -vertex directed graph has a Hamiltonian cycle.
This is joint work with Andreas Björklund (ITU Copenhagen).
ANTA Seminar / Hollanti et al.
Mr Aufa Biahdillah (Aalto University)
Master's thesis presentation: An Overview of the Quantum Fourier Transform and Its Application in Machine Learning
Wednesday 07 February 2024, 14:15, M3 (M234)
The field of quantum physics has ushered in a new era of scientific discovery. Most research today is focused on this field, including computer science, which has given rise to quantum computing. The Fourier transform, which has been adapted to this trend, has resulted in the quantum Fourier transform. This is essentially a Fourier transform performed on a quantum state, which is a key element of quantum computing. One of the most significant outcomes of this transformation is quantum phase estimation, a subroutine algorithm that is useful when combined with other algorithms. Some of the key algorithms that can be combined with quantum phase estimation include the quantum principal component analysis, the Harrow-Hassidim-Lloyd algorithm, and the quantum singular value thresholding, which will be studied in this thesis. Additionally, a comparison to classical computing will be provided to highlight the advantages and disadvantages of the quantum version.
(Advisor: Ville Turunen)
Maija Löyskä
Cryptocurrency Limit Order Books: On predicting price movements using neural network (MSc thesis presentation)
Wednesday 07 February 2024, 12:00,
Mikhail Basok (University of Helsinki)
Dimers on a Riemann surface and compactified free field
Tuesday 06 February 2024, 10:15, M3 (M234)
Consider the dimer model sampled on a general Riemann surface. In this setup, the dimer height function becomes additively multivalued with a random monodromy. Given a sequence of graphs approximating the conformal structure of the surface in a suitable way, the underlying sequence of height functions is expected to converge to the compactified free field on the surface. Recently, this problem was addressed by Berestycki, Laslier and Ray in the case of Temperley graphs. Using various probabilistic methods, they obtained the following universal result: given that a sequence of graphs satisfies certain set of probabilistic conditions (which link it with the conformal structure of the surface), the limit of height functions exists, is conformally invariant and does not depend on a particular sequence of graphs. However, the identification of the limit with the compactified free field was missing in this result. In my recent work I fill this gap by studying the same problem from the perspective of discrete complex analysis. For this purpose, I consider graphs embedded into locally flat Riemann surfaces with conical singularities and satisfying certain local geometric conditions. In this setup I obtain an analytic description of the limit which allows to identify it with a suitable version of the compactified free field; I also prove the convergence in some non-Temperlian cases when the surface is generic. A core part of this approach is the regularity theory on t-embeddings recently developed by Chelkak, Laslier and Russkikh.
In this talk we discuss the aforementioned results, in particular, how the methods of discrete complex analysis are generalized to the case of a Riemann surface, and how the geometry of the surface affects the limit.
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Friday 02 February 2024, 09:00, M3 (M234)
Further information
https://aalto.zoom.us/j/62767998708
Olavi Nevanlinna
Power series for piecewise constant holomorphic functions. How and Why?
Thursday 01 February 2024, 09:15, M2 (M233)
Prof. Pedro Munari (Universidade Federal de São Carlos, Brazil)
The Robust Bike Sharing Rebalancing Problem under Demand Uncertainty
Wednesday 31 January 2024, 15:00, M2 (M233)
Bike Sharing Systems (BSSs) are an excellent solution to improve urban mobility, offering a mode of transportation that is both economical and environmentally friendly. These systems are spread worldwide and help alleviate heavy traffic and reduce pollution, yielding direct and indirect benefits to the local population. Nonetheless, effectively managing these systems can pose practical challenges, as some stations often experience fluctuations in bike availability, resulting in surpluses or shortages and, occasionally, becoming full or empty. Rebalancing operations need to be regularly performed to restore the desired inventory levels at each station, and they are significantly affected by the unpredictable demand at stations. To aid decision-making in such situations, we introduce the Robust Bike Sharing Rebalancing Problem (RBRP), which combines the Vehicle Routing Problem with robust optimization techniques to enhance rebalancing operations in BSSs. We present two novel mixed-integer programming formulations and a tailored branch-and-cut algorithm for the RBRP. The first formulation is compact and based on the linearization of recursive equations, while the second relies on robust rounded capacity inequalities and feasibility cuts. Computational results using benchmark instances based on real-world data indicate the effectiveness of our approaches and highlight the benefits of using robust solutions to support decision-making in BSSs.
Gamma-optinars - Seminars of the Group of Applied Mathematical Modelling and Optimisation (GAMMA-OPT))
Haiqing Xu
From the Riemann Mapping Theorem to a Sobolev Homeomorphism
Wednesday 31 January 2024, 10:15, M3 (M234)
Seminar on analysis and geometry
Mikko Närhi (Aalto)
Censored Regression Models with Autoregressive Errors (MSc thesis presentation)
Wednesday 31 January 2024, 10:15, M237
In time series analysis, addressing censored data poses a significant challenge. This thesis focuses on censored data in radio access networks, where high user density and limited infrastructure lead to incomplete observations of data traffic demand. We propose a Censored Linear Regression model with autoregressive errors to estimate the censored data, employing Gaussian imputation on the premise that the complete data follows a multivariate normal distribution. This model was applied to historical data from a country-wide cellular network, imputing censored observations to enhance forecast accuracy. While the model is effective in estimating censored data, its impact on improving forecast accuracy varies, rendering its overall benefit in such contexts inconclusive.
Mehr Rai
Geometry of Numbers and Exterior Algebras: Towards Bombieri-Vaaler's Version of Siegel's Lemma (MSc thesis presentation)
Tuesday 30 January 2024, 15:15, M2 (M233)
Advisor Tapani Matala-aho.
ANTA Seminar / Hollanti et al.
Dissertation
Juha-Pekka Puska
Bayesian Optimal Experimental Design in Imaging
Friday 26 January 2024, 12:00, M1 (M232)
Tom Gustafsson
Inequality constraints and the finite element method
Thursday 25 January 2024, 09:15, M2 (M233)
David Karpuk
The sphere-packing density of unit lattices
Tuesday 23 January 2024, 15:15, M2 (M233)
Lattices, that is, discrete subgroups of Euclidean space, are a fundamental object in mathematics with connections to Lie Group Theory, Cryptography, and Algebraic Number Theory. The sphere-packing density of a lattice roughly measures how efficiently its points are packed into Euclidean space. The search for the optimal lattice packing in n-dimensional space is a long-standing problem, with known solutions only for certain small n. On the other hand, certain lattices arising naturally from Algebraic Number Theory have natural properties that make them especially suitable for applications in communications. In this talk, we will discuss an apparently new class of lattices, which we deem R_n-lattices, whose properties attempt to capture those coming from Number Theoretic lattices while also yielding efficient sphere packing. Falling into this class of lattices are unit lattices coming from totally real Galois number fields, and we apply our results to understand the sphere-packing densities of some well-known classes of unit lattices. This is joint work with Jose Cruz of the University of Calgary.
ANTA Seminar / Hollanti et al.
Liam Hughes (Aalto)
Mated-CRT maps
Tuesday 23 January 2024, 10:15, M3 (M234)
For gamma in (0,2), the gamma-mated-CRT map is a random triangulation in the plane encoded by a pair of Brownian motions with correlation depending on gamma. It can be obtained as a discretized version of the infinite-volume peanosphere construction that glues together two continuum random trees to get a sphere-homeomorphic surface decorated by a space-filling path, or alternatively as the adjacency graph of cells filled in by a space-filling Schramm--Loewner evolution parametrized by Liouville quantum gravity volume.
Many other models of random planar maps (RPMs) can be encoded by 2D random walks, which can be approximated by Brownian motion using Skorokhod-type embeddings to allow statements about these RPMs to be reduced to statements about mated-CRT maps. For instance, one can understand graph distances in uniform infinite planar triangulations by studying the embedding of the mated-CRT map into the plane given by the SLE construction. In this talk I will give an introduction to mated-CRT maps and suggest directions for future work.
Suzuki Yuya
Numerical integration and function approximation in Gaussian-weighted Sobolev space
Thursday 18 January 2024, 09:15, M2 (M233)
Kieran Ryan (Aalto)
The mirror model
Tuesday 16 January 2024, 10:15, M3 (M234)
Abstract: Consider the Lorentz mirror model on the 2d lattice: at each lattice site, independently place a mirror at 45 degrees to the lattice with some probability p. The orientation of the mirror is chosen independently, say north-west with probability q in (0,1). Loops can then be formed which bounce off the mirrors, or pass straight through lattice sites with no mirror. What is the probability that the loop through some given edge is infinite? For p=1 it is known to be zero, but for p in (0,1) the problem is open.
We study this model where we re-weigh the measure by n^#loops. We discuss a form of breaking of translation invariance, where for n large, almost all the loops are trivial loops surrounding black faces, or trivial loops surrounding the white faces. We can see that the method applied also works for a model of loops coming from O(n)-invariant quantum spin chains, where the breaking of translation invariance is known as dimerisation.
Joint work with Jakob Björnberg.
Marko Huhtanen
Image compression techniques
Thursday 11 January 2024, 09:15, M2 (M233)
Prof. Guillermo Mantilla-Soler (Universidad Nacional de Colombia)
Analogies between classic arithmetic and function fields
Tuesday 09 January 2024, 15:15, U6 KONECRANES (U149)
In his talk I will explain how similarities between the integers and the polynomial ring over a field allow us to find, and prove, connections between objects that at first glance seem to be quite different. As an example of this I will show how Lagranges interpolation theorem is nothing else but a particular case of the Chinese reminder theorem. If time allows I will show how a simple result on polynomials leads to the statement of the famous ABC conjecture.
Thomas Wasserman (University of Oxford)
The Landau-Ginzburg / Conformal Field Theory Correspondence
Tuesday 19 December 2023, 10:15, M3 (M234)
In the first half of this talk I will give an introduction to the Landau-Ginzburg (LG) / Conformal Field Theory (CFT) correspondence, which predicts a relationship between certain categories of matrix factorisations (for the ``LG potential'') and modular tensor categories (on the CFT side). This prediction has its origin in physics, and comes from observations about 2-dimensional N=2 supersymmetric quantum field theory. I will explain how this prediction is to be interpreted mathematically and what difficulties one encounters in doing this. In the second half of the talk I will discuss joint work with Ana Ros Camacho in which we realise the LG/CFT correspondence for the potentials x^d. The main ingredient in this is an enriched category theoretical versions of the classical Temperley-Lieb/Jones-Wenzl construction of the representation category of quantum su(2).
mathematical physics seminar (Kytölä, Peltola)
Aapo Pajala (Aalto)
Shapiro Conjecture for rational functions
Monday 18 December 2023, 14:15, M3 (M234)
The Shapiro Conjecture (Theorem of Mukhin, Tarasov and Varchenko as of 2009) is a statement about subspaces of univariate complex polynomials. It gives a sufficient condition for the existence of a real basis in terms of the Wronski polynomial of the subspace.
In the case of 2-dimensional subspaces, the conjecture becomes a statement about rational functions and their critical points. This presentation outlines an "elementary" proof for this special case presented by A. Eremenko and A. Gabrielov in 2005. The main tools of the proof are combinatorial invariants called nets for rational functions. Eremenko and Gabrielov then show that the statement holds for particular rational functions, and use the nets to argue that analytic continuation can be used to obtain a complete proof.
mathematical physics seminar (Kytölä, Peltola)
Prof. Ting Xue (University of Melbourne)
Springer theory and finite groups of Lie type
Tuesday 12 December 2023, 15:15, U6 KONECRANES (U149)
Springer theory for reductive algebraic groups plays an important role in determining irreducible characters of finite groups of Lie type. We discuss its generalisation to the setting of graded Lie algebras. We explain how level-rank dualities arise from unipotent irreducible characters and their connections with the graded Springer theory. If time permits, we discuss a conjectural realisation of these dualities using affine Springer fibers.
Alexis Langlois-Rémillard (University of Bonn)
Uncoiled periodic and affine Temperley-Lieb algebras, Jones-Wenzl projectors and their trace
Tuesday 12 December 2023, 10:15, M3 (M234)
The affine and periodic Temperley-Lieb algebras are families of infinite-dimensional algebras with a diagrammatic presentation. They have been studied in the last 30 years, mostly for their physical applications in statistical mechanics, where the diagrammatic presentation encodes the connectivity property of the models. Most of the relevant representations for physics are finite-dimensional.
In the first part of the talk, we will present the diagrammatic calculus related to these algebras and define finite-dimensional quotients of these algebras, which we name uncoiled algebras in reference to the diagrammatic interpretation. Afterwards, we construct a family of Jones-Wenzl idempotents, each of which projects onto one of the one-dimensional modules these algebras admit.
The second part of the talk will go in depth on the construction of the Jones-Wenzl idempotents and present some of their applications, mainly looking at their trace.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Miryam Gnazzo
Computing closest singular matrix-valued functions
Thursday 07 December 2023, 09:15, M2 (M233)
Harri Hakula
Johanna Immonen (Helsinki University)
Percolation and Modular Invariance
Tuesday 05 December 2023, 10:15, M3 (M234)
The talk will consider modular forms and crossing probabilities. In particular, I will review how Cardy's formula can be expressed in terms of the modular Eta function, and further, that Cardys function is the unique function that satisfies f(r)+f(1/r)=1 and has an expansion in form e−2παr times a power series in e−2πr for some α∈R. The first property is implied by a symmetry of the problem, but there is no physical argument for the latter.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Jukka Kohonen (Aalto)
Decorating lattices for the season, featuring: SageMath
Thursday 30 November 2023, 16:15, M2 (M233)
I will demonstrate SageMath, the free open-source mathematics software, from the viewpoint of my recent work with modular lattices (in order theory). A virtual listing of 40-element modular lattices is created, seemingly numbering 3 trillion (3 * 10^12). From a user's viewpoint, the lattices can be accessed at will -- sequentially, by ordinal index, or randomly. But in reality only 740 million smaller lattices are listed: from them, a SageMath class creates bigger lattices on the fly. To do this properly, we need graphs and their automorphism groups; classical "balls into boxes" combinatorics; and data abstraction. All this we find in SageMath. We also see how modular lattices are decorated with shiny trinkets for the season.
computer mathematics seminar / ForAlli
Dr. Thomas Westerbäck (Mälardalen University)
A matroid generalization and associations with modules and information theory
Thursday 30 November 2023, 14:15, M3 (M234)
There is a direct connection between linear codes over fields and matroids, commonly referred to as representable matroids. Specifically, a generator matrix for a linear code over a field not only serves as a coding tool but also as a representation for a representable matroid. Exploiting this connection, matroid theory has proven important in establishing numerous results in information theory, for example, in the areas of distributed storage, field linear codes with Hamming weights, network coding, index coding, and caching. Representable matroids also constitute an intriguing class in their own right, with connections to various areas within mathematics.
In this talk, I will present a generalization of matroids and how this generalization can be associated with modules. I will also illustrate how this connection can be used to establish results in information theory, especially in scenarios where algebraic structures other than vector spaces are considered.
ANTA Seminar / Hollanti et al.
Dissertation
Matteo Allaix
Quantum private information retrieval from coded storage systems (PhD defence)
Wednesday 29 November 2023, 14:00, H304
Opponent Prof. Alberto Ravagnani (Eindhoven), Custos Camilla Hollanti
ANTA PhD Defence
Augustin Lafay (Aalto University)
Integrability of O(N) loop models and web models.
Tuesday 28 November 2023, 10:15, M3 (M234)
I will review how one can obtain integrable local transfer matrices for the O(N) loop model from the relevant evaluation representation of the appropriate quantum affine algebra. After motivating the definition of a recently introduced rank 2 counterpart, the G_2 web models, I will show how to use similar ideas to obtain integrable transfer matrices in this context.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Ivy Woo
Class Groups of Imaginary Quadratic Fields and Applications to Cryptography (short talk)
Thursday 23 November 2023, 16:30, M2 and Zoom
Further information
For a number field K, its class group measures the extent that unique factorisation fails in the ring of integers of K. When K is an imaginary quadratic field such that unique factorisation fails miserably, its class group turns out to exhibit nice properties which are found useful in cryptographic constructions.
In this short talk, I will briefly recall some background on class groups, focused on the case of imaginary quadratic fields, and highlight some reasons for their uses in cryptography. For example, assuming certain computational problems are hard over class groups, we shall see that class groups imply encryption schemes that are more space-efficient than the well-known RSA encryption, and there exist cryptographic primitives with desirable properties that are, as of today, only known to be achievable from class groups.
ANTA Seminar / Hollanti et al.
Nadja Aoutouf (INRIA Paris)
Leakage of secret sharing schemes
Thursday 23 November 2023, 14:15, M3 and Zoom
Further information
In this talk, I will give an introduction to my PhD project, which focuses on privacy-preserving techniques.
As technology enables more powerful collection and curation of data, it has become a relevant need to assure the privacy of individuals and their associated data. An information-theoretic approach offers unconditional privacy guarantees without relying on the hardness of certain computational problems, i.e., the system cannot be broken even if the adversary has unlimited computing power. There are a variety of security tasks for which information-theoretic security is a meaningful and useful requirement, such as secret sharing, secure multiparty computation, and private information retrieval.
For instance, against side-channel attacks on systems and hardware, to protect one single crucial value (like a byte of a key), one of the most common, not hardware, countermeasures is masking, which applies a secret sharing scheme to expand this single value into a set of several random values. This forces an attacker to target all these random values (instead of a single value) to extract any meaningful secret information, making the attack more difficult.
This presentation, focusing on privacy-preserving techniques with information-theoretic approaches (i.e. secret sharing schemes), gives insights over the planned research during my PhD project. In this project, the results of Venkatesan Guruswami and Mary Wootters, which show that Reed-Solomon codes with evaluation points in the whole (finite) field, a failed evaluation point can be recovered using information from the remaining functional nodes. Due to the close connection between RS-code and Shamirs secret-sharing scheme vulnerabilities with respect to leakage can be concluded, which set the starting point for the doctoral research project. For instance, if a smaller, incomplete, amount of information is obtained by the adversary from each share (instead of the whole share) the secret can still be recovered. Finally, one of the major goals within the doctoral project is to find the minimal amount of leakage that can be tolerated while preserving the secrecy.
ANTA Seminar / Hollanti et al.
Anna-Mariya Otsetova
The Amari neural field model
Wednesday 22 November 2023, 10:15, M3 (M234)
Seminar on analysis and geometry
Oscar Kivinen (Aalto University)
HOMFLY-PT homology and mathematical physics
Tuesday 21 November 2023, 10:15, M3 (M234)
The HOMFLY-PT homology of links in the three-sphere was defined by Khovanov-Rozansky, following various earlier constructions and conjectures. Many of these were motivated by string and gauge theories, in addition to questions in low-dimensional topology. HOMFLY-PT homology is a link invariant valued in triply graded vector spaces (or modules over certain polynomial rings) which categorifies the HOMFLY-PT polynomial. In the first part of the talk, I will introduce the mathematical construction of HOMFLY-PT homology. In the second part, I will try to explain some of our current understanding of its physical underpinnings, which continues to develop in parallel with the mathematical theory.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Kim Myyryläinen
Two weight strong type estimates for parabolic maximal function
Wednesday 15 November 2023, 10:15, M3 (M234)
Seminar on analysis and geometry
Prof. Yuji Nakatsukasa (University of Oxford)
Numerical Linear Algebra: direct, iterative, and randomized methods
Tuesday 14 November 2023, 15:15, Hall E (Y124)
In many scientific computing and machine learning problems, we expend the majority of our computational resources in solving large-scale linear algebra problems, typically linear systems Ax = b, eigenvalue problems Ax = λx, or the singular value decomposition A = USV'. Numerical linear algebra (NLA) is a research field that attempts to devise practical algorithms for solving these problems.
Broadly, methods in NLA can be divided into three categories: direct, iterative, and randomized. In this talk I will give a whistle-stop tour of these classes of methods, highlighting the incredible robustness of classical (direct) methods, and the exciting speed and advances in randomized methods.
Joonas Vättö (Aalto University)
Free, massless boson; an expressionistic view
Tuesday 14 November 2023, 10:15, M3 (M234)
I will review some ongoing work on constructing the conformal field theory (d'après G. Segal) of the massless, free boson.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Thursday 09 November 2023, 09:15, M2 (M233)
Further information
Lauri Särkiö
Higher integrability for singular parabolic double phase problems
Wednesday 08 November 2023, 10:15, M3 (M234)
Seminar on analysis and geometry
Niklas Miller
Difference sets and methods to study their existence
Thursday 02 November 2023, 14:15, M3 (M234)
Some of the main methods for deciding whether or not a difference set of given parameters exists are the self-conjugacy test developed by Turyn in 1965, the field descent and its variations developed by Schmidt et al. in late 1990's, and importantly, the multiplier theorems by Hall, which date back to 1950's. All of these methods are based on knowledge about the decomposition groups in certain cyclotomic fields. In this talk I show that the multiplier groups of cyclic groups G, where v=|G| is non-squarefree, cannot contain a large set of residues. Together with a small "multiplier lemma" this gives a new existence test that can be used to rule out cyclic difference sets.
ANTA Seminar / Hollanti et al.
Wontae Kim
Calderon-Zygmund type estimate for the parabolic double phase problem
Wednesday 01 November 2023, 10:15, M3 (M234)
Seminar on analysis and geometry
Ulrik Hansen (University of Fribourg)
Universality of Large-Scale Geometry for Planar Critical Random-Cluster Models
Tuesday 31 October 2023, 10:15, M3 (M234)
Conformal invariance of general critical planar lattice models was conjectured by Belavin, Polyakov and Zamolodchikov in the early 80s. Using the (non-rigorous) renormalisation group flow, they deduced that any scaling limit of such a model must be rotationally invariant. Since any such limit must also be translation and scale invariant, the argument goes that it will also be invariant under the action of the group of transformations which are locally a composition of these three types of transformations. This is exactly the conformal group, which, in the planar case, is infinite-dimensional and therefore, particularly rich as a symmetry group. Another conjecture of theoretical physics going back to Griffiths and Kadanoff is that of universality: That the scaling limits of various models with different microscopic details, e.g. the graph on which it is defined, turn out to be the same across so-called universality classes.
During the last 25 years, the first conjecture has received immense attention from the probabilistic community after Schramm's introduction of the SLE. In this talk, however, we shall turn our attention to the second question. Building on work by Duminil-Copin, Kozlowski, Krachun, Manolescu and Oulamara, we prove that the critical random-cluster models each satisfy a universality property across a large class of planar graphs including the hexagonal and triangular lattices. A consequence thereof will be that any scaling limit in one of these universality classes is rotationally invariant and thus, this may also be thought of as a stepping stone towards proving conformal invariance for all critical random-cluster models.
Based on joint work with Ioan Manolescu.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Nyberg Fest (invited talks)
Nyberg fest celebrates and honors Prof. emerita Kaisa Nyberg's work in the field of cryptography and cybersecurity.
Friday 27 October 2023, 13:00, Dipoli, Lumituuli
Further information
Nyberg fest celebrates and honors Prof. emerita Kaisa Nyberg's work in the field of cryptography and cybersecurity. We organize a research seminar where the speakers will be Nyberg's former colleagues and doctoral students.
Prof. emerita Kaisa Nyberg is a distinguished scholar renowned for her significant contributions to the field of cryptography. With a career spanning several decades across academia, industry, and military, Nyberg has made groundbreaking advancements in the development of cryptanalysis and cryptographic protocols. She is most notably recognized for her pioneering work in linear and differential cryptanalysis, which are nowadays fundamental concepts in provable security and the design of cryptographic algorithms. Nyberg's expertise and dedication have had a lasting impact on the world of cryptography, a testament to her prominence in the field.
Dr. Maxwell Forst (U. Minnesota-Duluth)
On the Geometry of Lattice Extensions (zoom talk, M3 for audience)
Thursday 26 October 2023, 15:15, M3 (M234)
Further information
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. Zoom: https://aalto.zoom.us/j/62956597693
ANTA Seminar / Hollanti et al.
Sakari Niemelä
Higher integrability of metric double phase minimizers
Wednesday 25 October 2023, 10:15, M3 (M234)
Seminar on analysis and geometry
Tuomas Kelomäki (Aalto University)
Planar algebra structure of Khovanov homology
Tuesday 24 October 2023, 10:15, M3 (M234)
The powerful knot invariant Jones polynomial is defined by local skein relations and normalisation. On the other hand, the original categorification of the Jones polynomial was defined on a global scale - Khovanov homology takes whole knots and links as an input. It was later realized, by Bar-Natan, that Khovanov's construction can be defined locally and that these local pieces can be composed by a planar algebra structure. We take a look at Bar-Natan's framework and how it can be used to obtain new results about the original Khovanov homology.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Dr. Jacques Benatar (U. Helsinki)
Polynomials with multiplicative coefficients, and related questions
Thursday 19 October 2023, 14:15, M3 (M234)
I will discuss some recent work, joint with Alon Nishry and Brad Rodgers, concerning the distribution of Dirichlet and trigonometric polynomials generated by multiplicative coefficients f(n). In the first part of the talk we will explore some old and new results for deterministic sequences f(n) (Möbius, Legendre symbol,...), stopping along our journey to marvel at a variety of wild and thorny conjectures. The second half of the talk will be devoted to Steinhaus random multiplicative coefficients f(n) = X(n). These considerations give rise to a couple of intriguing arithmetic problems.
ANTA Seminar / Hollanti et al.
Heather Macbeth (Fordham University)
Making mathematics computer-checkable
Wednesday 18 October 2023, 16:15, M1 (M232)
Further information
In the last thirty years, computer proof verification became a mature technology, with successes including the checking of the Four-Colour Theorem, the Odd Order Theorem, and Hales' proof of the Kepler Conjecture. Recent advances such as the "Liquid Tensor Experiment" verifying a recent theorem of Scholze have provided further momentum, as likewise have promising experiments integrating this technology with machine learning.
I will briefly describe some of these developments. I will then try to describe, more generally, what it feels like to carry out research-level computer verifications of mathematics proofs: the level of expression one has access to, the ways one finds oneself interrogating and reorganizing a paper proof, the kinds of arguments which are more tedious (or less tedious!) than on paper.
[This is a Finnish Mathematical Society online colloquium. Colloquium watch events are organized at Finnish universities' mathematics departments. The physical location of the Aalto event will be announced later.]
Finnish Mathematical Society online colloquium
Xavier Poncini (Aalto University)
Planar-algebraic models: statistical mechanics and knot theory
Tuesday 17 October 2023, 10:15, M3 (M234)
V.F.R. Jones initially introduced planar algebras to describe the standard invariant of a subfactor. Since then, planar algebras have found many applications in mathematics and physics. Informally, a planar algebra describes the interaction of elements of a graded vector space in the plane. The 'two-dimensional' structure of planar algebras makes them natural objects to describe planar statistical-mechanical models. In this talk, I will focus on the role played by planar algebras in relating statistical mechanics and knot theory. In particular, I will introduce a notion of YangBaxter integrability and show that statistical-mechanical models with this property give rise to polynomial link invariants. If time permits, I will report on recent results (joint with J. Rasmussen) classifying all singly generated planar algebras admitting a YangBaxter integrable model.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Afrin Hossain (MSc thesis presentation, Aalto/VTT)
Torus-based Fully Homomorphic Encryption in Federated Learning
Thursday 12 October 2023, 15:15, M3 (M234)
Advisors: Wilmar Bolanos, Visa Vallivaara
ANTA Seminar / Hollanti et al.
Matilde Costa
BV capacity and Hausdorff content
Wednesday 11 October 2023, 10:15, M3 (M234)
Seminar on analysis and geometry
Érika Roldán, Ph.D. (Max Planck Institute for Mathematics in the Sciences)
Topology and Geometry of Random Cubical Complexes
Tuesday 10 October 2023, 15:15, U6 (U149)
In this talk, we explore the expected topology (measured via homology) and local geometry of two different models of random subcomplexes of the regular cubical grid: percolation clusters, and the Eden Cell Growth model. We will also compare the expected topology that these average structures exhibit with the topology of the extremal structures that it is possible to obtain in the entire set of these cubical complexes. You can look at some of these random structures here (https://skfb.ly/6VINC) and start making some guesses about their topological behavior.
Mikhail Basok (University of Helsinki)
Double-dimer nesting field: local statistics and convergence to the nesting field of CLE(4)
Tuesday 10 October 2023, 10:15, M3 (M234)
Given a random loop ensemble in some domain on the plane, we can define the corresponding nesting field at a point by computing the number of loops surrounding this point and subtracting its mean. If the number of loops in all samples of the loop ensemble is bounded by some constant, then we get a well-defined random variable pointwise. Miller, Watson and Wilson have shown that, applying a suitable regularization procedure, one can extend this definition to the conformal loop ensemble with parameter k (CLE(k)) for all 8/3
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