* Seuraavan viikon tapahtumat merkitty tähdellä
Miryam Gnazzo
Computing closest singular matrix-valued functions
* Thursday 07 December 2023, 09:15, M2 (M233)
Harri Hakula
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)
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.
Thomas Wasserman (University of Oxford)
TBA
Tuesday 19 December 2023, 10:15, M3 (M234)
mathematical physics seminar (Kytölä, Peltola)
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
Seyma Bodur (U. Valladolid)
Single-server private information retrieval scheme with codes over rings
Thursday 05 October 2023, 14:15, M3 (M234)
A Private Information Retrieval (PIR) scheme allows users to retrieve data from a database without disclosing to the server information about the identity of the data retrieved. A single-server PIR scheme is based on computational privacy and assumes computers have limited power. Therefore, it requires computational difficulty. When a system consists of a single server, it is possible to achieve information-theoretic privacy by transmitting the entire database. However, this approach is not feasible. The first computational PIR scheme based on coding theory is presented [2020 IEEE International Symposium on Information Theory (ISIT), pp. 10651070 (2020] by Holzbaur, Hollanti, and Wachter-Zeh. However, Bordage and Lavauzelle presented an attack that occurs in polynomial time and with high probability [Cryptogr. Commun. 13, 519526 (2020)]. We present a single-server PIR scheme using codes over rings that utilize the coding theory perspective of Holzbaur, Hollanti, and Wachter-Zeh, which provides resistance against the attack described in [Cryptogr. Commun. 13, 519526 (2020)]. This talk is based on a joint work with Edgar Martínez-Moro and Diego Ruano.
ANTA Seminar / Hollanti et al.
Nenad Teofanov (University of Novi Sad, Serbia)
An introduction to localization operators
Wednesday 04 October 2023, 10:15, M3 (M234)
The aim of the lecture is to offer a brief introduction to time-frequency localization operators.
To motivate the talk we first discuss Fourier multiplier operators. Such operators are used for example in the design of frequency filters in signal analysis. However, in some situations it is of interest to treat time-frequency plane as one geometric whole rather than as two separate spaces.
Operators which perform simultaneous localization in time and in frequency arise as a natural extension of Fourier multipliers. Historically, such operators were first observed by Felix Berezin in the context of quantization problem in quantum mechanics in early 1970s. 35 years ago Ingrid Daubechies published an influential paper on localization operators and their applications in optics and signal analysis. A convenient framework for the study of localization operators as short-time Fourier transform multipliers is given by Elena Cordero and Karlheinz Gröchenig in 2003. Feichtingers modulation spaces are used when considering continuity properties of such operators.
The central part of the talk is devoted to some basic properties of localization operators and their connection to pseudodifferential operators. We will also briefly discuss bilinear localization operators.
In the last part of the talk we will reconsider localization operators as continuous frame multipliers defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. Finally, we consider the tensor product setting for continuous frame multipliers. A specific feature in such context is the notion of partial trace. By using the partial trace theorem we will offer an interpretation of tensor product continuous frame multipliers as density operators for bipartite quantum systems in quantum mechanics.
Seminar on analysis and geometry
Shinji Koshida (Aalto University)
Planar algebras for the Young graph and the Khovanov Heisenberg category
Tuesday 03 October 2023, 11:00, M3 (M234)
I will discuss planar algebras of Jones' style associated with the Young graph and harmonic functions on it. In particular, I will explain that, for the harmonic function originating from the Plancherel measure, the associated planar algebra recovers the local relations for the Khovanov Heisenberg category as algebraic relations. We will also see that various functions of Young diagrams including moments, Boolean cumulants, and normalized characters are identified with elements in the planar algebra. These results provide an alternative proof to the Rattan--Sniady conjecture that I proved in the past.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Gaétan Leclerc (Sorbonne Universite)
On oscillatory integrals with Hölder phases
Tuesday 03 October 2023, 10:15, M3 (M234)
It is an understatement to say that oscillatory integrals play a major role in analysis. In usual settings, we are able to understand the behavior of such integrals by using results like the (non)-stationary phase lemma or the Van Der Corput lemma. But for such results to hold, the phase has to be regular enough. What can we say when the phase is only Hölder regular?
This talk aims to explore some results, ideas, and methods for understanding oscillatory integrals in such cases. If the general case is not reachable for now, a particular setting seems to yield some interesting results: when the phase exhibits self-similarity, a recent method introduced by Bourgain and Dyatlov, and generalized by Li, Naud, Pan, Sahlsten, Steven, Jordan, and Baker allows us to prove power decay of the associated oscillatory integral. We will recall some results in the smooth case, discuss some ideas in a probabilistic setting, and finally we will discuss the main tool behind the aforementionned method: the sum-product phenomenon.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Prof. Vitezslav Kala (Charles University)
Universal quadratic forms and Northcott property of infinite number fields
Thursday 28 September 2023, 14:15, M3 (M234)
Universal quadratic forms generalize the sum of four squares about which it is well known that it represents all positive rational integers. In the talk, I'll start by discussing some results on universal quadratic forms over totally real number fields. Then I'll move on to the - markedly different! - situation over infinite degree extensions K of Q. In particular, I'll show that if K doesn't have many small elements (i.e., "K has the Northcott property"), then it admits no universal form. The talk should be broadly accessible, and is based on a very recent joint work with Nicolas Daans and Siu Hang Man.
ANTA Seminar / Hollanti et al.
Aleksi Avela (Aalto University)
On Imbalanced Data and Text Classification
Wednesday 27 September 2023, 13:30, M240
Midterm review talks
Kalle Alaluusua (Aalto University)
Community recovery in sparse random graphs
Wednesday 27 September 2023, 13:00, M240
Midterm review talks
Theo Elenius
Regularity for nonhomogeneous variational problems on metric measure spaces
Wednesday 27 September 2023, 10:15, M3 (M234)
Seminar on analysis and geometry
David Adame-Carrillo (Aalto University)
A logCFT on the lattice: Discrete symplectic fermions on double dimers
Tuesday 26 September 2023, 10:15, M3 (M234)
Recently (past 25 years), there has been interest in the (double-)dimer model because of the conformally invariant properties of its scaling limit. Physicists, on the other hand, have proposed this model to be described by a logarithmic Conformal Field Theory (logCFT) of central charge c=−2. In the first half of this talk, I will introduce a discretization of the symplectic fermions a logCFT at c=−2 as observables on the double dimer model. From these observables, I will explain how to build a space of local fields which carries a Virasoro representation of central charge
−2. On the second half, I will dive into the logarithmic structure of the representation. In particular, I will show that it contains an L_0 Jordan block of primary fields with conformal weight 0.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Neehar Verma and Johan Dinesen
MSc theses introductions by new PhD students
Thursday 21 September 2023, 15:00, M3 (M234)
ANTA Seminar / Hollanti et al.
Selim Virtanen
Application of category theory to the study of biregular LCL-problems and round elimination
Thursday 21 September 2023, 14:15, M3 (M234)
MSc thesis presentation (advisor Jukka Suomela, CS)
ANTA Seminar / Hollanti et al.
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Thursday 21 September 2023, 09:15, M237
Further information
Sari Rogovin
Some remarks on the Gehring-Hayman theorem
Wednesday 20 September 2023, 10:15, M3 (M234)
Seminar on analysis and geometry
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Friday 15 September 2023, 09:15, M3 (M234)
Further information
Olli Herrala (Aalto University)
Scheduling computational jobs on Triton
Wednesday 13 September 2023, 16:00, M3 (M234)
This is a workshop on how to submit demanding computational jobs to Aalto's high-performance computing cluster "Triton".
Gamma-optinars - Seminars on the Group of Applied Mathematical Modelling and Optimisation (GAMMA-OPT))
Aleksis Koski
Sobolev homeomorphic extensions
Wednesday 13 September 2023, 10:15, Y346
One of the most fundamental results in complex analysis is the Riemann Mapping Theorem, which provides a way to express domains in the plane as conformal images of the unit disk. Much in the same spirit, one can ask which properties of a fixed boundary map allow for a homeomorphic extension with specific geometric and analytic properties. In Nonlinear Elasticity, the existence of a Sobolev homeomorphism between two given shapes constitutes an axiomatic property for the associated minimization problems to be well-defined. Classical results such as the Beurling-Ahlfors extension theorem or the Radó-Kneser-Choquet theorem provide the basic building blocks to address these questions in the 2D case, but do not extend well to irregular domains or to higher dimensions. In this talk, I will review these problems starting from the basics and introduce the methods we have developed in recent years together with Jani Onninen and Stanislav Hencl to address both 2D and 3D extension problems.
Seminar on analysis and geometry
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Thursday 31 August 2023, 09:15, M3 (M234)
Further information
Carsten Peterson (Aalto)
Quantum ergodicity on Bruhat-Tits buildings
Wednesday 30 August 2023, 11:00, M3 (M234)
Originally, quantum ergodicity concerned equidistribution properties of Laplacian eigenfunctions with large eigenvalue on manifolds for which the geodesic flow is ergodic, such as hyperbolic surfaces. More recently, several authors have investigated quantum ergodicity for sequences of spaces which ``converge'' in the sense of Benjamini-Schramm to their common universal cover, such as a sequence of hyperbolic surfaces whose injectivity radii go to infinity, and when one restricts to eigenfunctions with eigenvalues in a fixed range. Previous authors have considered this type of quantum ergodicity in the settings of regular graphs (Anantharaman-Le Masson '15, Brooks-Le Masson-Lindenstrauss '16), rank one symmetric spaces (Le Masson-Sahlsten '17, Abert-Bergeron-Le Masson '18), and some higher rank symmetric spaces (Brumley-Matz '21). We prove analogous results in the case when the underlying common universal cover is the Bruhat-Tits building associated to $PGL(3, F)$ where $F$ is a non-archimedean local field. This may be seen as both a higher rank analogue of the regular graphs setting as well as a non-archimedean analogue of the symmetric space setting.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Henrik Ueberschär (Sorbonne, Paris)
Multifractality for periodic solutions of certain PDE
Wednesday 30 August 2023, 10:00, M3 (M234)
Many dynamical systems are in a state of transition between two regimes. Examples are firing patterns of neurons, disordered quantum systems or pseudo-integrable systems. A common feature which is often observed for critical states of such systems is a multifractal self-similarity in a certain scaling regime which cannot be captured by a single fractal exponent but only by a spectrum of fractal exponents.
I will discuss a proof of multifractality of solutions for certain stationary Schrödinger equations with a singular potential on the square torus (joint with Jon Keating). Towards the end of the talk, I will allude to some new work on multifractal scaling and solutions to nonlinear PDE in fluid dynamics on cubic tori.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Ewain Gwynne (University of Chicago)
The Liouville quantum gravity metric
Monday 28 August 2023, 14:00, M3 (M234)
This is a 5-lecture mini-course (Mon-Fri 14-16).
Abstract: Liouville quantum gravity (LQG) is a universal one-parameter family of random fractal surfaces. These surfaces have connections to string theory, conformal field theory, and statistical mechanics, and are expected to describe the scaling limits of various types of random planar maps. Recent works have shown that one can endow an LQG surface with a metric (distance function). This metric has many interesting geometric properties. For example, it induces the same topology as the Euclidean metric, but its Hausdorff dimension is strictly greater than two and its geodesics merge into each other to form a tree-like structure. I will discuss the definition of and motivation for LQG, the construction and properties of the metric, and some of the techniques for proving things about it.
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Friday 25 August 2023, 09:00, M3 (M234)
Further information
Anatole Dedecker (Université Paris-Saclay)
What does formalized mathematics look like, and why do we care about it?
Wednesday 23 August 2023, 15:00, M3 (M234)
While computer formalization of mathematics is by no means a new idea, it has seen a significant increase in popularity in the past five years, to a point that a consequent proportion of the mathematical community has heard of it. During this talk, I will try to convey, in very practical terms, what it feels like to "formalize mathematics" using the Lean theorem prover. I will also discuss why we care about it (it's not just checking proofs!), as well as related questions. This will all be told from the perspective of someone who learnt maths and formalization at the same time, which I hope will bring an interesting light on this fascinating new tool.
seminar on computer formalized mathematics
Joel Hakavuori (Aalto)
Subadditivity of shifts, Eilenberg-Zilber shuffle products and cohomology of lattices
Wednesday 23 August 2023, 12:00, M203
We show that the maximal shifts in the minimal free resolution of a monomial ideal form a subadditive sequence, answering a conjecture of Avramov, Conca and Iyengar. To do so, we study different models for the cohomology rings of posets and lattices, introduce the Eilenberg-Zilber shuffle product for lattices and use it to establish vanishing theorems and models for homology for lattices. The talk is based on joint work with Karim Adiprasito, Minas Margaritis and Eran Nevo.
Algebra and Discrete Mathematics Seminar
Rodrigo Martín Sánchez-Ledesma (Complutense University of Madrid and INDRA)
KEM protocols over unauthenticated channels: Overview of Post-Quantum Cryptography, migration and challenges
Tuesday 15 August 2023, 14:15, M3 (M234)
This talk is a brief introduction to the Post-Quantum Cryptography (PQC) standardization process and its two current competitions. Within this setting, the notion of Key Encapsulation Mechanism (KEM) is critical to the development of key establishment on PQC, as an alternative to traditional key establishment mechanisms. We will focus on PQC protocols based on this concept over unauthenticated channels. A number of KEM-based protocols between two parties are proposed, and their resistance over unauthenticated channels is studied. This means analyzing the security of the protocol itself, and its robustness against Man-in-the-Middle attacks. A comparison with their KEX-based counterparts is made in terms of the protocol itself and the types of attacks they are subject to. Finally, a number of go-to KEM-based protocol instances to migrate to, based on the conditions of currently-in-use KEX-based protocols, are proposed.
ANTA Seminar / Hollanti et al.
Muhammad Ardiyansyah
Statistical Modeling with Hidden Variables (Doctoral defence)
Friday 11 August 2023, 12:00, M1 (M232)
Altti Jääskeläinen
Edge-promoting Bayesian experimental design for electrical impedance tomography
Thursday 10 August 2023, 10:15, M3 (M234)
Kasper Rantamägi
Zero-shot classifier based on robust ellipsoid optimization (Bachelor's thesis presentation)
Friday 21 July 2023, 10:15, M3 (M234)
Olga Kuznetsova
The structure and complexity of optimization problems in statistics and algebra (Doctoral defence)
Wednesday 19 July 2023, 12:00, M1 (M232)
Dr. Amin Sakzad (Monash University)
Private Re-Randomization for Module LWE and Applications to Quasi-Optimal ZK-SNARKs
Wednesday 12 July 2023, 15:15, M3 (M234)
We introduce the first candidate lattice-based Designated Verifier (DV) ZK-SNARK protocol with \emph{quasi-optimal proof length} (quasi-linear in the security/privacy parameter), avoiding the use of the exponential smudging technique. Our ZK-SNARK also achieves significant improvements in proof length in practice, with proofs length below KB for 128-bit security/privacy level.
Our main technical result is a new regularity theorem for `private' re-randomization of Module LWE (MLWE) samples using discrete Gaussian randomization vectors, also known as a lattice-based leftover hash lemma with leakage, which applies with a discrete Gaussian re-randomization parameter that is polynomial in the statistical privacy parameter.
To obtain this result, we obtain bounds on the smoothing parameter of an intersection of a random -ary SIS module lattice, Gadget SIS module lattice, and Gaussian orthogonal module lattice over standard power of 2 cyclotomic rings, and a bound on the minimum of module gadget lattices. We then introduce a new candidate \emph{linear-only} homomorphic encryption scheme called Module Half-GSW (HGSW), which is a variant of the GSW somewhat homomorphic encryption scheme over modules, and apply our regularity theorem to provide smudging-free circuit-private homomorphic linear operations for Module HGSW. The talk is based on https://eprint.iacr.org/2022/1690.
ANTA Seminar / Hollanti et al.
Yunseon Lee
Comparison of Monte Carlo and diffusion approximation simulations in optical tomography
Friday 30 June 2023, 08:15, M2 (M233)
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Thursday 29 June 2023, 09:15, M1 (M232)
Further information
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Tuesday 27 June 2023, 09:15, M1 (M232)
Further information
Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Friday 16 June 2023, 09:30, Riihi (Y225a)
Further information
Dr. Ali Abbas (University of Southern California)
Ethical Decision Quality: Avoiding Common Pitfalls in Organizational Decision-Making
Thursday 08 June 2023, 16:00, M1 (M232)
Further information
This talk first demonstrates numerous examples of situations where business organizations and government agencies did the right thing in terms of gathering information or conducting some analyses, but then ended up making bad decisions. By examining a sequence of decisions from publicly available sources in business and government enterprises, the talk characterizes 11 elements to be considered when making "Good" organizational decisions. We refer to those elements as the Elements of Ethical Decision Quality. The talk then presents specific examples of decisions where the Elements of Ethical Decision Quality created value by either improving the quality of the decisions or by providing awareness to policymakers about the implications of the current decision-making process. These examples include work with the U.S. Transportation and Security Administration (TSA), U.S. Customs and Border Protection (CBP), and NASA.
The event can also be attended remotely on Zoom here: https://aalto.zoom.us/j/68625209279
Aalto Systems Forum / Ahti Salo (Systems Analysis Laboratory)
Prof. Marcus Greferath (University College Dublin)
On current work in Group Testing with Error-Correction Capabilities
Wednesday 07 June 2023, 16:15, M3 (M234)
During the years of the COVID19 pandemic my collaborators and I have tried to revisit and possibly remodel the discipline of group testing in such a way, that it can be seen as a finite linear algebra over the binary semifield. Residuation Theory as presented in a textbook by T. S. Blyth and M. F. Janowitz plays a prominent role in our account on this topic, and we will also attempt to address the error-prone part. The presentation will be complemented by a number of examples.
ANTA Seminar / Hollanti et al.
Younis Bouzar
Sparse Grid Interpolation (Bachelor thesis talk)
Monday 05 June 2023, 13:15, M3 (M234)
Dr. Alberto Pedrouzo Ulloa (U. Vigo)
Disrespectfully playing with Homomorphic Encryption, Federated Learning and Multivariate Rings
Wednesday 31 May 2023, 10:15, M3 (M234)
In this talk we will discuss some of the benefits and shortcomings of using Homomorphic Encryption (HE) for two very different types of practical applications. Firstly, we will talk about Federated Learning, and how to tailor HE for the efficient execution of secure average aggregation. In the last part of the talk, we will modify current HE schemes with the objective of better dealing with privacy-sensitive multidimensional signals (e.g., images). In particular, we will explore the possibility of substituting the more conventional power-of-two cyclotomic rings for different types of multivariate rings.
ANTA Seminar / Hollanti et al.
Prof. Gunnar Fløystad (University of Bergen)
Polarizations of artin monomial ideals define triangulated balls
Monday 29 May 2023, 15:15, Zoom
We show that any polarization of an artin monomial ideal
defines a triangulated ball, via the Stanley-Reisner correspondence.
This proves a conjecture of A.Almousa, H.Lohne and the speaker.
Geometrically, polarizations of ideals containing the ideal (x_1^{a_1}, ...., x_n^{a_n})
define full-dimensional triangulated balls on the sphere which is the join of boundaries of simplices of dimensions a_1-1, ... , a_n-1.
Combinatorially, these triangulated balls derive from subsets T of products of finite sets A_1 x A_2 x ... x A_n which we call bitight. The subset T and its complement fulfill exchange conditions similar to that of matroids.
Zoom link: https://aalto.zoom.us/j/64355991428
Algebra and Discrete Mathematics Seminar
Ville Turunen
Diophantine equation (n+1)x^2-ny^2 = 1 in time-frequency analysis
Wednesday 24 May 2023, 16:15, Y307
We introduce and study Diophantine equation (n+1)x^2-ny^2 = 1. It resembles the more complicated Lagrange's theory of Pell's equation x^2-ny^2=1. Positive n \in Z is called P-smooth if its prime factors belong to a subset P of the primes. In tonal music, the melodic intervals n: (n+1) are nearly always {2,3,5,7}-smooth. In 1897, Størmer used Pell's equation to find the P-smooth pairs (n,n+1). We give a simple well-motivated method for Størmer's problem.
ANTA Seminar / Hollanti et al.
Petteri Kaski (Aalto)
Constructive and nonconstructive enumeration
Monday 22 May 2023, 15:15, M2 (M233)
This talk will be a primer to combinatorial constructive and nonconstructive enumeration up to isomorphism and will consist of two parts (a) a recall/primer of finite groups and group actions to capture pertinent isomorphism relations and (b) an introduction to algorithmic isomorph-free exhaustive generation techniques, in particular to Brendan McKay's [J Algorithms 1998] influential canonical construction path technique.
Algebra and discrete mathematics seminar
Anton Vavilov (Aalto University)
Implementing Electrical Impedance Tomography for Real-World Stroke Monitoring (Doctoral Midterm Review)
Wednesday 17 May 2023, 13:30, M203
Tuomas Kelomäki (Aalto University)
Discrete Morse theory for Khovanov homology (Doctoral Midterm Review)
Wednesday 17 May 2023, 13:00, M203
Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Tuesday 16 May 2023, 09:30, Riihi (Y225a)
Further information
Irene Heinrich (TU Darmstadt)
Colored highly regular graphs
Monday 15 May 2023, 15:15, M2 (M233)
A coloured graph is k-ultrahomogeneous if every isomorphism between two induced subgraphs of order at most k extends to an automorphism. A coloured graph is t-tuple regular if the number of vertices adjacent to every vertex in a set S of order at most k depends only on the isomorphism type of the subgraph induced by S. We classify the finite vertex-coloured k-ultrahomogeneous graphs and the finite vertex-coloured l-tuple regular graphs for k at least 4 and l at least 5, respectively. Our theorem in particular classifies finite vertex-coloured ultrahomogeneous graphs, where ultrahomogeneous means the graph is simultaneously k-ultrahomogeneous for all k.
Algebra and discrete mathematics seminar
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Friday 12 May 2023, 09:00, M3 (M234)
Further information
Prof. Giacomo Micheli (U. South Florida)
On a proof of a conjecture on Arboreal Galois Representations
Thursday 11 May 2023, 16:15, M3 (M234)
In this talk we first recall the notion of arboreal Galois representation and then we develop a method to effectively determine the set of primes p for which certain arboreal Galois representations are surjective modulo p.
Our method is based on a combination of height bounds on integral points on elliptic curves over function fields in positive characteristic and the ABC theorem for function fields.
Using this technique we prove Jones' conjecture on the surjectivity of the arboreal Galois representation attached to f=x^2+t [Conjecture 6.7, Compositio Math. 43 (5) (2007)].
This is a joint work with Andrea Ferraguti.
ANTA Seminar / Hollanti et al.
Zichan Xie (Aalto University)
District heating system - dynamic simulation and optimization (Doctoral Midterm Review)
Thursday 11 May 2023, 13:30, M203
Jaakko Pere (Aalto University)
On extreme behavior of multivariate and infinite dimensional observations (Doctoral Midterm Review)
Thursday 11 May 2023, 13:00, M203
Prof. Federico Poloni (University of Pisa)
Centrality measures on Markov chains, with applications to roads and infection models
Tuesday 09 May 2023, 15:15, M1 (M232)
We describe a couple of centrality measures on graphs that can be obtained from certain Markov chain models associated to them, and their computation with methods taken from numerical linear algebra.
The Kemeny constant is a quantity that measures the connectedness of a Markov chain by studying certain properties of the random walk associated to it. The variation in the Kemeny constant can be used to identify edges whose removal would alter the connectivity of a network; this is useful information, for instance, in planning urban and regional road networks.
For problems based on "spreading" on a graph, such as news propagation and infectious disease modelling, instead models based on a single random walker fall short: they are unable to capture characteristics of the model such as the time to saturation. We study this phenomenon, and propose an alternative way to treat computationally the full model, which can be interpreted as another Markov chain with an exponential
number of states. The resulting metric can once again be interpreted as a measure of the centrality of the vertices / agents in the network in the propagation.
Lasse Leskelä
Information-theoretic limits in inhomogeneous random hypergraphs
Tuesday 09 May 2023, 10:30, M3 (M234)
The hypergraph stochastic block model is a statistical model for sampling inhomogeneous random hypergraphs associated with a partition of the vertex set. In this talk I will discuss fundamental concepts and recent developments on the statistical analysis of hypergraph stochastic block models. The focus is on universal information-theoretic bounds and phase transitions that help to understand requirements on data sparsity and model dimensions under which consistent learning of the underlying vertex partition is possible.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Prof. Emer. Brendan D McKay (Australian National University)
A scientist's adventure into pseudoscience: the strange case of the Bible Codes
Thursday 04 May 2023, 15:15, M2 (M233)
Further information
Over the centuries, many claims have been made of numerical patterns of miraculous nature hidden within the text of sacred writings, including the Jewish, Christian and Islamic scriptures. Usually the patterns involve counting of letters and words, or calculations involving numerical equivalents of the letters.
Until recently, all such claims were made by people with little mathematical understanding and were easily explained. This situation changed when a highly respected Israeli mathematician Eliyahu Rips and two others published a paper in the academic journal Statistical Science claiming to prove that information about medieval Jewish rabbis was encoded in the Hebrew text of the Book of Genesis. The journal reported that its reviewers were "baffled".
The paper in Statistical Science spawned a huge "Bible Codes" industry, complete with best selling books, TV documentaries, and even a romance movie.
The talk will reveal the inside story of the Codes and the people behind them, from their inception through to their refutation.
Aalto Stochastics & Statistics Seminar / Leskelä
David Adame-Carrillo
Virasoro structure of the discrete GFF: basic techniques and some results
Tuesday 02 May 2023, 10:15, M3 (M234)
I will discuss the basic tools of discrete complex analysis on
Z
2
that we use to construct a Virasoro representation on the space of local fields of the discrete Gaussian Free Field. I will also go over some recent results we obtained with Delara Behzad and Kalle Kytölä.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Asadollah Aghajani
Semilinear elliptic equations with sublinear first order terms (Part 2)
Friday 28 April 2023, 10:15, M3 (M234)
Seminar on analysis and geometry
Hannukainen, Antti (Aalto)
TBA
Thursday 27 April 2023, 14:15, U7
Aalto-Helsinki Applied Mathematics Seminar
Asadollah Aghajani
Semilinear elliptic equations with sublinear first order terms (Part 1)
Wednesday 26 April 2023, 10:15, M3 (M234)
Seminar on analysis and geometry
Sung-Chul Park (Korea Institute for Advanced Study)
Scaling Limit of Planar Ising Model through Discrete Complex Analysis
Tuesday 25 April 2023, 10:15, M3 (M234)
In this expository talk, I will give an outline of the developments in the field of critical and massive scaling limits in the Ising model in two dimensions starting from the breakthrough work of Smirnov, which defined the notion of s-holomorphicity. Emphasis will be placed on explaining the steps and techniques used to relate this discrete complex analytic notion to analysis in continuum, yielding conformal invariance of the model in the critical case.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Miika Hannula (University of Helsinki)
On database dependencies and information inequalities
Monday 24 April 2023, 15:15, M2 (M233)
In databases, notions of dependence and independence play a crucial role. For instance, every database relation typically has a key, which is a set of attributes that functionally determines the remaining attributes in the relation. By taking a uniform distribution over the database relation, these dependency notions can be recast using Shannons information measures. Consequently, logical implication between database dependencies can (sometimes) be reconceptualized as an information inequality, that is, a linear inequality over entropies. In this talk we review these connections and also consider information inequalities from a computational perspective. Unlike logical implication in database theory, not much seems to be known about the exact computational complexity of decision problems associated with information inequalities.
Algebra and discrete mathematics seminar
Pattanun Chanpiwat (University of Maryland & Aalto University)
The policy graph decomposition of multistage stochastic programming problems
Thursday 20 April 2023, 16:15, M203
Further information
We start at 16.00h with coffee & pulla. The talk starts at 16.15h.
Gamma-optinars - Seminars of the Group of Applied Mathematical Modelling and Optimisation (GAMMA-OPT))
Serge Kas Hanna
Error-correcting codes for DNA storage
Wednesday 19 April 2023, 16:15, M3 (M234)
DNA storage is a promising candidate for next-generation storage systems due to its compactness, high durability, and energy efficiency. However, the process of storing digital data in synthetic DNA suffers from deletion and insertion errors that may affect the sequence of nucleotides during synthesis, sequencing, and storage. The reliability of the DNA storage can be improved by integrating codes that correct deletions and insertions within the storage system. This talk will give a general overview of deletion/insertion correcting codes and discuss the specific encoding and decoding constraints imposed by the technologies used in DNA storage systems.
ANTA Seminar / Hollanti et al.
Konstantin Izyurov (University of Helsinki)
BPZ equations and OPE for the critical Ising correlations.
Tuesday 18 April 2023, 10:15, M3 (M234)
The correlation functions in conformal field theories, in particular, in minimal models, enjoy a number of properties. Among them are, in particular, Belavin-Polyakov-Zamolodchikov equations, which are second order partial differential equations, and the Operator product expansion (OPE) hypothesis concerning the asymptotic expansions of correlations to all orders.
The correlations in scaling limit of the critical the Ising model have been recently computed rigorously. However, the program of relating them on mathematical level to correlations in a minimal CFT is not completed, and deriving the BPZ equations and the OPE from the explicit expressions is not straightforward. In this talk, I will discuss our recent results in this direction. This is a joint work with Christian Webb.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Olga Kuznetsova (Aalto University)
Weak maximum likelihood threshold of coloured Gaussian graphical models
Monday 17 April 2023, 15:15, M2 (M233)
Colored Gaussian graphical models are linear concentration models arising from undirected graphs with a coloring in its vertices and edges. Given a coloured Gaussian graphical models, one may be interested to know how many observations are necessary for a maximum likelihood estimate to exist with positive probability. This is called the weak maximum likelihood threshold of a graph. We discuss computational and algebraic methods for studying the weak maximum likelihood threshold of a graph.
Algebra and discrete mathematics seminar
Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Monday 17 April 2023, 09:30, Riihi (Y225a)
Further information
Heikki Myllykoski (FMI)
Sparse Bayesian learning for interpolation of radar volumes
Friday 14 April 2023, 09:15, M3 (M234)
Eetu Haavisto (SpectroCor)
Model optimization for diffuse reflection spectroscopy
Thursday 13 April 2023, 12:15, M203
Kash Barker, Ph.D., (University of Oklahoma, USA)
Two-Stage Stochastic Program for Environmental Refugee Displacement Planning
Tuesday 11 April 2023, 15:15, M1 (M232)
Forced displacement is a global problem that requires planning for the relocation and integration of displaced people. Most studies focus on conflict-driven forced displacement, and hence the refugee resettlement problem. These studies generally focus on short-term planning and assume that demand within the fixed time interval is given. However, forced displacement, including environmental displacement as well as conflict-driven displacement, is not a one-time event. On the contrary, it is an ongoing and long-term process with dynamic parameters. We are interested in the long-term displacement problem, especially for climate-driven cases in which people will be forced to leave uninhabitable regions in to escape slow-onset climate change impacts such as water stress, crop failure, and sea level rise. To reflect the long-term planning requirements of the climate-driven displacement problem in the parameters and the model, we propose a two-stage stochastic program where demand uncertainty is represented with various demand scenarios, demand and capacity are managed dynamically, and integration outcomes and related costs are optimized.
Peter Kristel (Bonn)
Extending the free fermion Segal CFT
Tuesday 11 April 2023, 10:15, M3 (M234)
The free fermion was one of Segal's original examples of a theory satisfying his Conformal Field Theory (CFT) axioms. This was made fully rigorous relatively recently by James Tener. I will review Segal's definition of a CFT, and then describe the free fermion. Then, I will report on some of my ongoing work attempting to extend the free fermion, following Stolz and Teichner.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Ivàn Blanco Chacón
Twin primes in quadratic sequences and a partial answer to a conjecture by Sun
Wednesday 05 April 2023, 15:15, M3 (M234)
The following conjecture was made in the 2016 Ireland BT Young Scientist Competition: every prime number q>3 can be expressed as q=p+n(n+1), with p a twin prime and n>0. This conjecture was satisfactorily tested for the first 100 millions of primes, and puzzled by such phenomenon, Gary McGuire asked me to think about a possible proof (or disproof) of the conjecture. The first result I came across is the proof that the validity of the conjecture would easily yield the existence of infinitely many twin primes. The conjecture remains open, but we proved that for each prime q of a set of primes of density 1, can be written as q=p+n(n+1), with p < q also prime (not necessarily twin), which is a weak version of a conjecture by Sun. In the present talk we give a sketch of this proof.
ANTA Seminar / Hollanti et al.
Yu Liu (Aalto University)
Modeling design and control problems involving neural network surrogates
Thursday 30 March 2023, 16:15, M203
Further information
We start at 16.00h with coffee & pulla. The talk starts at 16.15h.
Gamma-optinars - Seminars of the Group of Applied Mathematical Modelling and Optimisation (GAMMA-OPT))
Liam Hughes (University of Cambridge)
Metric gluing of Liouville quantum gravity surfaces
Tuesday 28 March 2023, 11:15, M3 (M234)
Introduced by Polyakov in the 1980s, Liouville quantum gravity (LQG) is in some sense the canonical model of a random fractal Riemannian surface, constructed using the Gaussian free field. Sheffield showed that when a certain type of LQG surface, called a quantum wedge, is decorated by an appropriate independent SLE curve, the wedge is cut into two independent surfaces which are themselves quantum wedges, and that these resulting wedges uniquely determine the original surface as well as the SLE interface. We prove that the original surface can in fact be obtained as a metric space quotient of the LQG metrics on the two wedges. This was proven by Gwynne and Miller in the special case $\gamma = \sqrt{8/3}$, for which $\gamma$-LQG surfaces are equivalent to Brownian surfaces, allowing an explicit description of the metric in terms of Brownian motion that is not available in general. I will explain how our work uses GFF techniques to extend their results to the whole subcritical regime $\gamma \in (0,2)$, while establishing new estimates describing the boundary behaviour of LQG. Joint work with Jason Miller.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Félix Lequen (CY Cergy Paris)
Bourgain's construction of finitely supported measures with regular Furstenberg measure
Tuesday 28 March 2023, 10:15, M3 (M234)
The possible asymptotic distributions of a random dynamical system are described by stationary measures, and in this talk we will be interested in the properties of these measures - in particular, whether they are absolutely continuous. First, I will quickly describe the case of Bernoulli convolutions, which can be seen as generalisations of the Cantor middle third set, and then the case of random iterations of matrices in SL(2, R) acting on the real projective line, where the stationary measure is unique under certain conditions, and is called the Furstenberg measure. It had been conjectured that the Furstenberg measure is always singular when the random walk has a finite support. There have been several counter-examples, and the aim of the talk will be to describe that of Bourgain, where the measure even has a very regular density. I will explain why the construction works for any simple Lie group, using the work of Boutonnet, Ioana, and Salehi Golsefidy on local spectral gaps in simple Lie groups.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Tobias Boege (Aalto University)
Matroids in information theory
Monday 27 March 2023, 15:15, M2 (M233)
Matroids capture combinatorial properties of independence in linear algebra and graph theory. It is less well-known that (poly)matroidal structures also appear as entropy functions of discrete random variables. We give an introduction to this point of view and survey relevant results and examples.
Algebra and discrete mathematics seminar
Dr. David Karpuk, WithSecure
Recent progress in secure distributed computation
Wednesday 22 March 2023, 16:15, M3 (M234)
In this talk we will explore some recent results in Secure Distributed Computation, in which a user distributes a computational task across several worker nodes while protecting sensitive aspects of the computation from potential adversaries with access to the worker nodes. This presentation will focus on the case of matrix multiplication, but we will discuss generalizations with potential applications to decentralized machine learning. Many of our results represent joint work with Razan Tajeddine.
ANTA Seminar
Masashi Misawa (Kumamoto University)
Expansion of positivity and Hölder regularity for doubly nonlinear parabolic type equations
Wednesday 22 March 2023, 12:15, M3 (M234)
Seminar on analysis and geometry
Kieran Ryan (TU Vienna)
Fermionic and Bosonic features of the Double Dimer model and Gaussian free field
Tuesday 21 March 2023, 10:15, M3 (M234)
The double dimer model (DDM) on a planar graph is a model of random loops, and the Gaussian free field (GFF) is a model of a height function. The two models are linked by a conjecture that the DDM loops converge in the scaling limit to loops in the continuum, which are level lines of the GFF.
I will introduce these two models and outline two results. First, certain 2n-point correlation functions in the DDM are known to be determinants in the 2-point functions; we give a new proof of this, which in particular we show can be extended to the GFF. Second, it is known that the GFF exhibits a "height gap": if one sets the boundary height to be +\lambda on one half of the boundary, and -\lambda on the other, then if \lambda = \sqrt(pi/8), the zero level line actually exhibits a sharp "jump" of 2\lambda. We give a simple derivation of this special value of the height gap, using the determinental result.
Joint work with Marcin Lis (TU Vienna)
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Nikita Belyak (Aalto University)
Optimal Classification Trees
Thursday 16 March 2023, 16:15, M203
Further information
We start at 16.00h with coffee & pulla. The talk starts at 16.15h.
Gamma-optinars - Seminars of the Group of Applied Mathematical Modelling and Optimisation (GAMMA-OPT))
Hiroshi Isozaki (University of Tsukuba) , Yuya Suzuki (Aalto University)
Wave scattering in the Penrose diagram / Numerical integration and function approximation on Rd using equispaced points and lattice points
Thursday 16 March 2023, 14:15, U7
Hiroshi Isozaki (University of Tsukuba, isozakih@math.tsukuba.ac.jp): Wave scattering in the Penrose diagram
Yuya Suzuki (Aalto University, yuya.suszuki@aalto.fi): Numerical integration and function approximation on Rd using equispaced points and lattice points
Aalto-Helsinki Applied Mathematics Seminar
Dr. Özgür Ceyhan, CritiX, University of Luxembourg
From fault tolerance to combinatorial geometry and more
Wednesday 15 March 2023, 16:15, M3 (M234)
Nonlinear dynamical systems pose a significant challenge when it comes to controlling them. The challenge raises to another level if we require fault tolerance. In this talk, I introduce Byzantine fault tolerance (BFT) protocols that aim at resiliency by guaranteeing consistency. I will discuss the essential combinatorial geometry behind BFT, which it shares with seemingly distant areas in math, such as Cantor's work on cardinality of reals and Turing's Halting problem. Finally, if time permits (i.e., when the eyes start rolling), I will discuss how the Diagonal Argument (from category theory) provides a unifying framework to discuss all. I assume no prior knowledge of these subjects and will try to introduce and discuss the basics.
ANTA Seminar
Anna-Mariya Otsetova (Lund University)
Axisymmetric capillary waves on cylindrical fluid jets
Wednesday 15 March 2023, 14:15, M203
Seminar / Tölle
Kim Myyryläinen
Two weight norm inequalities for parabolic maximal function
Wednesday 15 March 2023, 12:15, M3 (M234)
Seminar on analysis and geometry
Iván Blanco Chacón (University of Alcalá, Madrid )
From Number Theory to postquantum Cryptography. Ten years (at least) of travel.
Tuesday 14 March 2023, 15:15, U6 (U149)
Euler didn't conceive his notorious theorem as an efficient manner to cipher messages, but two centuries later, his result backs the omnipresent RSA cryptosystem. Neither Abel, nor Poincaré were specially concerned on how to communicate messages in a secure manner when they tackled elliptic integrals and still, elliptic curves are at the basis of the SSL and TLS Internet protocols.
With the frantic development of quantum computing (IBM announced Osprey three months ago, a 433 qbits processor, beating its already commercialised 21 qbits QSystem1 ), we must set ourselves en guard as soon as possible. This is the reason why the NIST launched a public contest to standardise postquantum cryptographic primitives in 2017, recently resolved in July 2022. However, the mathematical tools backing these new proposals are, if no more complicated, at least more challenging than the previous ones.
The goal of my talk is to mention my research lines developed since 2011 until now, a journey which started in Barcelona with such ethereal topics as Shimura curves, modularity and p-adic L-functions and led me to questions as designing efficient codes, crypto-analysing postquantum primitives while still working in more mystic maths in my free time.
Riina Hakkarainen
Drift detection methods for data streams
Tuesday 14 March 2023, 12:15, M3 (M234)
Ethan Sussman (MIT)
Towards a rigorous Coulomb-gas formalism for the minimal models (contd.)
Tuesday 14 March 2023, 10:15, M3 (M234)
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Dissertation
Topi Kuutela. Opponent: Bastian von Harrach (Goethe University Frankfurt)
Computational and theoretical models in diffuse imaging
Friday 10 March 2023, 12:00, A2
Ethan Sussman (MIT)
Towards a rigorous Coulomb-gas formalism for the minimal models, part 2
Thursday 09 March 2023, 10:15, Y307
In the late 80's, the physicists Dotsenko and Fateev used the Coulomb-gas formalism to solve for the structure constants of Belavin--Polyakov--Zamolodchikov's minimal models of 2D CFT. To this day, their analysis has not been made mathematically rigorous. In this talk, we will discuss progress towards a rigorous Coulomb-gas formalism, along with its application to the construction of the minimal models.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Timo Takala
Vanishing subspaces of the John-Nirenberg space
Wednesday 08 March 2023, 12:15, M3 (M234)
Seminar on analysis and geometry
Ethan Sussman (MIT)
Towards a rigorous Coulomb-gas formalism for the minimal models
Tuesday 07 March 2023, 11:15, M3 (M234)
In the late 80's, the physicists Dotsenko and Fateev used the Coulomb-gas formalism to solve for the structure constants of Belavin--Polyakov--Zamolodchikov's minimal models of 2D CFT. To this day, their analysis has not been made mathematically rigorous. In this talk, we will discuss progress towards a rigorous Coulomb-gas formalism, along with its application to the construction of the minimal models.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Stephen Moore (Institute of Mathematics Polish Academy of Sciences)
Limits of traces for Temperley-Lieb algebras
Tuesday 07 March 2023, 10:15, M3 (M234)
In recent decades, there have been interesting connections made between a number of areas of mathematics, including statistical mechanics, knot theory, quantum groups, and subfactors. The Temperley-Lieb algebras are a family of finite dimensional algebras that were the original source of these connections. In this talk we review the representation theory of the finite Temperley-Lieb algebras. We then discuss extremal traces, their classification, and applications to the representation theory of an infinite dimensional generalization of the Temperley-Lieb algebra.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Ethan Sussman (MIT)
Towards a rigorous Coulomb-gas formalism for the minimal models.
Tuesday 07 March 2023, 10:00,
Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Monday 06 March 2023, 09:30, Riihi (Y225a)
Further information
Joonatan Bergholm
Gauss-Newton menetelmä (Kandiesitelmä)
Friday 03 March 2023, 10:15, M2 (M233)
Paula Weller (Aalto University)
Finite Adaptability in Multistage Linear Optimization
Thursday 02 March 2023, 16:15, M203
Further information
We start at 16.00h with coffee & pulla. The talk starts at 16.15h.
Gamma-optinars - Seminars on the Group of Applied Mathematical Modelling and Optimisation (GAMMA-OPT))
Lauri Särkiö
Lipschitz truncation for parabolic double phase equations
Wednesday 01 March 2023, 12:15, M3 (M234)
Seminar on analysis and geometry
Xavier Poncini (University of Queensland)
A planar-algebraic universe
Tuesday 28 February 2023, 10:15, M3 (M234)
Conformal nets provide a rigorous mathematical framework for conformal field theory, assigning an algebra of observables to each region of the underlying spacetime manifold. Here, we consider so-called discrete conformal nets whereby the spacetime is not a smooth manifold but instead has an 'atomic' structure. It turns out that planar algebras can be used to construct 'almost' examples of discrete conformal nets. In this talk, I will review this business and detail recent efforts to construct fully-fledged examples of discrete conformal nets. Inspired by the statistical mechanics literature, I will also introduce some integrable operators that act on the spacetime and detail some of their algebraic structure.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Panu Lahti (Chinese Academy of Sciences)
Alberti's rank one theorem and quasiconformal mappings in metric measure spaces
Wednesday 22 February 2023, 12:15, M3 (M234)
We investigate a version of Albertis rank one theorem in Ahlfors regular
metric spaces, as well as a connection with quasiconformal mappings. More precisely, we give a proof of the rank one theorem that partially follows along the usual steps, but the most crucial step consists in showing for a BV mapping f that at |Df|^s-a.e. point in X, the mapping f behaves non-quasiconformally.
Seminar on analysis and geometry
Janne Junnila (University of Helsinki)
Decompositions of log-correlated Gaussian fields
Tuesday 21 February 2023, 10:15, M3 (M234)
Log-correlated Gaussian fields such as the Gaussian free field are random Schwartz distributions whose covariances have a logarithmic singularity on their diagonal. They appear for instance in Liouville quantum gravity, characteristic polynomials of random matrices, the dimer model etc. In this talk I will present ways to decompose general log-correlated fields into a sum of a canonical log-correlated field with a particularly nice covariance structure and a Hölder-continuous error term. I will also discuss applications to the study of the Gaussian multiplicative chaos of the field. The talk is based on joint works with Eero Saksman and Christian Webb as well as Juhan Aru and Antoine Jego.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Tomas Eklund
Impact of air passengers on COVID-19 transmission (MSc presentation)
Friday 17 February 2023, 14:15, M3 (M234)
Video stream at https://aalto.zoom.us/j/65615277822
MSc presentation / Lasse Leskelä
Fausto Barbero (University of Helsinki)
Expressivity of languages for probabilistic causal reasoning
Friday 17 February 2023, 13:00, Y229c
Causal reasoning, as developed e.g. in the works of J. Pearl and of Spirtes, Glymour & Scheines, is a collection of effective but rather disorganized mathematical techniques and ad hoc formalisms. With Gabriel Sandu, we proposed a semantic framework (causal multiteam semantics) by means of which many of the statements typical of causal reasoning (concerning e.g. conditional probabilities, "do expressions", Pearl's "counterfactuals") can be decomposed into three simpler elements: (marginal) probability statements, and two distinct conditionals, which describe the effects, respectively, of an action and of an increase in information.
In this talk I will present part of a joint work with Jonni Virtema. We gave abstract characterizations of the expressive power of a number of candidate languages for probabilistic causal reasoning; these characterizations involve identifying three special classes of linear inequalities.
By analyzing the geometry of these inequalities as interpreted in standard n-simplexes, we used the characterization results to prove that the languages form a proper hierarchy (i.e., that distinct levels of generality of the syntax correspond to distinct levels of expressivity) and to prove some further undefinability result.
Algebra and Discrete Mathematics Seminar (Boege, Orlich)
Prof. Anita Schöbel (RPTU Kaiserslautern and Fraunhofer ITWM)
Robust multi-objective optimization
Tuesday 14 February 2023, 15:15, U6 (U149)
Most real-world optimization problems contain parameters which are not known at the time a decision is to be made. In robust optimization one specifies the uncertainty in a scenario set and tries to hedge against the worst case.
Classical robust optimization aims at finding a solution which is best in the worst-case scenario. It is a well-studied concept but it is known to be very conservative: A robust solution comes with a high price in its nominal objective function value. This motivated researchers to introduce less conservative robustness concepts in the last decade. Moreover, many real-world problems involve not only one, but multiple criteria. While robust single-objective optimization has been investigated for 25 years, robust multi-objective optimization is a new field in which already the definition of "robust" is a challenge.
In the talk, several robustness concepts will be discussed and
illustrated at applications from public transport.
Eemil Halonen (Matematiikan kandidaattiseminaari )
Friday 10 February 2023, 09:00, M3 (M234)
Further information
Performance comparison of 3D wind Anemometers
Prof. William Mance, University of Adam Mickiewicz in Poznan
Normal numbers
Wednesday 08 February 2023, 16:15, M3 (M234)
Informally, a real number is normal in base b if in its b-ary expansion all digits and blocks of digits occur as often as one would expect them to uniformly at random. Borel introduced normal numbers in 1909 and proved that Lebesgue-almost every real number is normal in all bases b \geq 2. Even though this shows that, in some sense, normal numbers are "typical," no example of a number normal in all bases was given until 1939 by Turing. In the last 100 years, the study of normal numbers has spread over a wide breadth of seemingly unrelated disciplines. Normality is closely related to number theory, ergodic theory, theoretical computer science, probability theory, fractal geometry, descriptive set theory, and others areas of math. We will explore the basic properties of normal numbers and surprising connections they have, depending on the interest of the audience.
ANTA Seminar
Wontae Kim
Whitney decomposition for the parabolic double phase problem
Wednesday 08 February 2023, 12:15, M3 (M234)
Seminar on analysis and geometry
Sándor Kisfaludi-Bak (Aalto)
On geometric variants of the traveling salesman problem
Tuesday 07 February 2023, 14:00, M237
In the classic Euclidean traveling salesman problem, we are given n points in the Euclidean plane, and the goal is to find the shortest round trip that visits all the points. We will briefly discuss how modern algorithmic and lower bound tools allowed us to find (conditionally) optimal exact and approximation algorithms for this problem, while the closely related Steiner tree problem seems to resist many similar attempts. We will then turn to the traveling salesman or Steiner tree with "neighborhoods". Here instead of points, we are given a set of affine subspaces, and the goal is to find the shortest round trip or tree that intersects each subspace. It turns out that these problems have a different computational complexity than the classic problems with points: they require a completely novel approach for the hyperplane case, while the other cases remain largely mysterious.
Algebra and Discrete Mathematics Seminar (Boege, Orlich)
Petri Laarne (University of Helsinki)
Almost sure solution of nonlinear wave equation: from donut to plane
Tuesday 07 February 2023, 10:15, M2 (M233)
I discuss the recent preprint [arXiv:2211.16111] of Nikolay Barashkov and I, where we show the almost sure well-posedness of a deterministic nonlinear wave equation (cubic Klein-Gordon equation) on the plane. Here "almost sur" is in respect to the \\\\phi^4 quantum field theory. I briefly introduce the invariant measure argument and outline the solution on 2D torus due to Oh and Thomann. I then explain our main contributions: extension of periodic solutions to infinite volume, and a weaker result for nonlinear Schrödinger equation. The viewpoint is functional-analytic with a dash of probability.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Rahinatou Yuh Njah
Ring/Polynomial learning with errors (RLWE/PLWE): Equivalence and attacks
Wednesday 01 February 2023, 16:15, M3 (M234)
ANTA Seminar
Asadollah Aghajani
Regularity of stable solutions to elliptic PDEs and Gelfand-type problems II
Wednesday 01 February 2023, 12:15, M3 (M234)
Seminar on analysis and geometry
Tuomas Kelomäki
Using discrete Morse theory algebraically Part 2
Tuesday 31 January 2023, 14:00, M237
Algebra and discrete mathematics seminar
Kalle Koskinen (University of Helsinki)
Infinite volume states of the mean-field spherical model in a random external field
Tuesday 31 January 2023, 10:15, M2 (M233)
One method of introducing external randomness to a Gibbs state, as opposed to the internal randomness of the Gibbs state itself, is to perturb the Hamiltonian with a term corresponding to the coupling of a random external field to the system. For the mean-field spherical model, the corresponding perturbed model can be exactly solved, in some sense, in the infinite volume limit. In this talk, we will introduce, motivate, and present some constructions and results concerning the so-called infinite volume metastases of the mean-field spherical model in a random external field. The aim of this talk is to present the general theory of disordered systems as it pertains to this particular model, and highlight the particular aspects of this model which lead to its curious behaviour as a disordered system. This talk is based on work in a recently accepted paper to appear in the Journal of Statistical Physics.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Petri Laarne (University of Helsinki)
Almost sure solution of nonlinear wave equation: from donut to plane
Wednesday 25 January 2023, 20:19, M2 (M233)
Prof. Alexandru Paler
Graph states and the challenges for efficient quantum circuit compilation
Wednesday 25 January 2023, 16:15, M3 (M234)
Graphs can be used as a diagrammatic representation of entangled states: vertices represent qubits, and edges are the entangling gates performed between the qubits. Arbitrary quantum circuits can be compiled into a fault-tolerant gate set, and the resulting circuit can be reformulated as a graph state. Such graphs can be manipulated by local operations (single qubit/vertex gates) such that edges are added and removed in a well defined manner during a process called local complementation. The latter might have interesting applications for the optimisation of (fault-tolerant) quantum circuits, quantum communication networks and in general whenever, either: a) there is a need to minimize the number of edges (entangling gates) without affecting the functionality of the state, or b) the state has to be embedded into a quantum hardware architecture that has a different connectivity. This talk is partially based on the work from https://arxiv.org/abs/2209.07345
ANTA Seminar
Asadollah Aghajani
Regularity of stable solutions to elliptic PDEs and Gelfand-type problems I
Wednesday 25 January 2023, 12:15, M3 (M234)
Seminar on analysis and geometry
Tuomas Kelomäki
Using discrete Morse theory algebraically
Tuesday 24 January 2023, 14:00, M237
This is an introductory talk on discrete Morse theory and especially on Sköldberg's algebraic formulation of it. The goal is to learn the method through several examples. If the time permits, we will also derive finite versions of several classical results in homological algebra from the theory.
Algebra and Discrete Mathematics Seminar (Boege, Orlich)
Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Friday 20 January 2023, 09:30, Riihi (Y225a)
Further information
Wilmar Bolanos
The trace form over cyclic number fields
Wednesday 18 January 2023, 16:15, M3 (M234)
For a given number field K, the integral trace form of K is the quadratic form defined by the trace operator Tr_K/Q(x^2) over the ring of integers of K. In the mid 80's Conner and Perlis showed that for cyclic number fields of prime degree p the isometry class of integral trace is completely determined by the discriminant. The main objective of this talk is to discuss the principal aspects of Conner and Perlis' work and a completed generalization for tame cyclic number fields of arbitrary degree. Furthermore, for such fields, we give an explicit description of a Gram matrix of the integral trace in terms of the discriminant of the field.
ANTA Seminar
Tuomas Sahlsten
PDEs and dynamics
Wednesday 18 January 2023, 12:15, M3 (M234)
In these talks we will discuss various methods how the theory of dynamical systems can be used to study PDEs such as wave- or Schrödinger equation on planar domains or manifolds. The talks are more an introduction to the ideas, and we try not to assume any background knowledge on the concepts discussed. In the first talk we will focus on 2D surfaces without boundary, where the dynamics is given by the geodesic flow. Here a pre-trace formula due to Selberg allows us to connect eigenfunctions of the Laplacian and the lengths of the periodic orbits of the dynamics. We then outline how number theoretic assumptions on the surface or randomly sampling the surfaces helps to control the complicated periodic orbit structure.
Seminar on analysis and geometry
Camilla Hollanti
Capacity of private information retrieval from coded and colluding servers (online talk at the Technion Coding Theory Seminar)
Wednesday 11 January 2023, 16:30, Zoom
Further information
Private information retrieval (PIR) addresses the question of how to retrieve data items from a database or cloud without disclosing information about the identity of the data items retrieved. The area has received renewed attention in the context of PIR from coded storage. Here, the files are distributed over the servers according to a storage code instead of mere replication. Alongside with the basic principles of PIR, we will review recent capacity results and demonstrate the usefulness of the so-called star product PIR scheme.
The talk is based on joint work with Ragnar Freij-Hollanti, Oliver Gnilke, Lukas Holzbaur, David Karpuk, and Jie Li.
Technion Coding Theory Seminar/ANTA Seminar
René Langøen (University of Bergen)
The direct monodromy problem and isomonodromic deformations for the Rabi model
Tuesday 10 January 2023, 10:15, M2 (M233)
We discuss the local and global solutions of the Rabi model in Garnier form, a linear system of first order differential equations, with complex rational coefficients. The analytic continuation of the local solutions are described by a monodromy group, which gives a matrix representation of the fundamental group of the punctured Riemann sphere. A detailed geometric description of linear systems of first order differential equations is given, in terms of a local family of connection forms on a principal bundle. The geometric description reveals the Frobenius integrability conditions, which are used to obtain necessary and sufficient conditions for an isomonodromic deformation of the Rabi model.
mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Emil Verkama
Repairing the universality theorem for 4-polytopes
Monday 09 January 2023, 11:00, M2 (M233)
Master's thesis presentation
Jarno Maaninen
Bayesian experimental design for magnetorelaxometry imaging
Thursday 05 January 2023, 11:00, M3 (M234)
Master's thesis presentation
Saara Vestola
Enhancement of data veracity for preamble signature ID classification in PRACH, Master thesis talk
Tuesday 20 December 2022, 11:00, M237
Oscar Kivinen (EPFL, Lausanne)
Plane curves: a bridge between number theory, knots, and physics
Friday 16 December 2022, 15:30, M237
Plane curves are some of the simplest classical algebro-geometric objects, that most of us encounter in middle school (over the real numbers). Especially their singularity theory remains a source of many interesting discoveries. For example, it turns out many moduli spaces of sheaves on singular plane curves are related to 1) arithmetic problems arising in the Langlands program 2) physics of some 3d/4d supersymmetric gauge theories.
On the other hand, in most cases a lot of data about the singularities is controlled by the knots arising as their links, and one may ask how the relevant knot theory is reflected in the themes 1) and 2) above. I will give an introduction to plane curves and discuss the relation to 1) and possibly 2), highlighting a recent result about "orbital integrals on p-adic groups (obtained by myself and Tsai) where the topology of the singularities informs the arithmetic. Little background knowledge will be required, apart from knowing what knots, finite fields, and the general linear group are.
Algebra and Discrete Mathematics Seminar
Toni Annala (Institute for Advanced Study)
Topologically protected tricolorings
Friday 16 December 2022, 14:00, M237
Topological vortices are codimension-one topological defects that arise in various physical systems, such as liquid crystals, Bose--Einstein condensates, and vacuum structures of Yang--Mills theories. I will explain how, under certain homotopical assumptions that are satisfied in many realistic systems, topological vortex configurations admit faithful presentations in terms of colored link diagrams. The most well-known coloring scheme of links is given by tricolorings: each arc of the link diagram is colored by one of three possible colors (red, green, or blue) in such a way that, in each crossing, either all arcs have the same color, or all arcs have a different color. A tricolored link is topologically protected if it cannot be transformed into a disjoint union of unlinked simple loops by a sequence of color-respecting isotopies and color-respecting local cut-and-paste operations. The latter operations are referred to as allowed local surgeries. We use equivariant bordism groups of three-manifolds to construct invariants of colored links that are conserved in allowed local surgeries, and employ the invariant to classify all tricolored links up to local surgeries. The talk is based on joint work with Hermanni Rajamäki, Roberto Zamora Zamora, and Mikko Möttönen.
Algebra and Discrete Mathematics Seminar
Tuomas Tuukkanen (Princeton & Aalto)
Fermionic Fock Spaces in Conformal Field Theory (MSc thesis presentation)
Friday 16 December 2022, 11:00, M3 (M234)
mathematical physics seminar (Kytölä / Peltola / Sahlsten)
Vivian Healey (Texas State University)
Loewner evolution, Dyson Brownian motion, and tree embeddings
Thursday 15 December 2022, 10:15, M3 (M234)
The Loewner equation gives a correspondence between curves in the upper half-plane (or disk) and continuous real functions (called the driving function for the equation). When the driving function is Brownian motion, the result is Schramm-Loewner Evolution (SLE). In this talk, we will discuss links between multiple Loewner evolution and Dyson Brownian motion. First, we show that multiple radial SLE is generated by Dyson Brownian motion on the circle. Second, we show that in the chordal case, scaling the Brownian term to 0 in a branching Dyson Brownian motion generates tree embeddings in the halfplane. If time allows, we will also discuss the Dyson superprocess, which is the scaling limit of this driving measure when the branching structure is conditioned to converge to the continuum random tree. (Joint work with Gregory Lawler and Govind Menon)
mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Anne Schreuder (Cambridge University)
On Lévy-driven Loewner Evolutions
Thursday 08 December 2022, 10:15, Y405
This talk is about the behaviour of Loewner evolutions driven by a Lévy process. Schramm's celebrated version (Schramm-Loewner evolution), driven by standard Brownian motion, has been a great success for describing critical interfaces in statistical physics. Loewner evolutions with other random drivers have been proposed, for instance, as candidates for finding extremal multifractal spectra, and some tree-like growth processes in statistical physics. Questions on how the Loewner trace behaves, e.g., whether it is generated by a (discontinuous) curve, whether it is locally connected, tree-like, or forest-like, have been partially answered in the symmetric alpha-stable case. We consider the case of general Levy drivers. Joint work with Eveliina Peltola (Aalto and Bonn).
mathematical physics seminar (Kytölä, Peltola, Sahlsten)
Sivusta vastaa: webmaster-math [at] list [dot] aalto [dot] fi