# Esitelmiä, seminaareja ja väitöksiä

* Seuraavan viikon tapahtumat merkitty tähdellä

Ryosuke Sato (Chuo University)

**CAR algebras and stochastic processes on random point processes**

*** ** Tuesday 25 June 2024, 10:15, M3 (M234)

CAR algebras are fundamental operator algebras that appear in various fields of mathematics and mathematical physics. In this talk, we will focus on its relationship to random point processes, which are mathematical descriptions of random interacting particles. In particular, after discussing the relation between quasi-free states of CAR algebras and determinantal point processes, we will investigate how the operator algebraic framework provides stochastic processes on random point processes.

Toni Annala (IAS)

**Motivic homotopy theory**

*** ** Tuesday 25 June 2024, 14:15, M3 (M234)

Cohomology theories are an integral part of modern algebraic geometry. In algebraic topology, (stable) homotopy theory provides a convenient framework to study various cohomology theories and their interrelations. In algebraic geometry, a similar role should be played by motivic homotopy theory, which strictly generalizes Grothendieck's dream of motives.
In the first part of the talk, I will motivate the necessity of homotopy theory to study cohomology theories in algebraic topology and algebraic geometry. I will also introduce A^1-homotopy theory, defined by Morel and Voevodsky in the late 90s. In the second part of my talk, I will introduce the motivic stable homotopy theory, which is the subject of my long-term project with Marc Hoyois, Ryomei Iwasa, and others. The goal of this theory is to build a framework for studying all cohomology theories in algebraic geometry simultaneously. I will give some sample results, and explain what concrete consequences can be derived from our results.

Algebra & Discrete Math Seminar

**Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)**

*** ** Wednesday 26 June 2024, 09:00, M3 (M234)

Further information

## Past events

Katherine Maxwell (Kavli IPMU)

**Superstring measure extended to supergrassmannian space**

Thursday 20 June 2024, 10:15, M3 (M234)

I will describe an extension of the integration measure for calculating scattering amplitudes in (super)string theory to a large (super)grassmannian space, known as the super Sato grassmannian. In comparison to bosonic string theory, superstring theory provides some simplifications in the properties of the integration measure, which I will highlight in my talk. On the other hand, superstring theory is intrinsically related to the supermoduli space of super Riemann surfaces, which poses challenges because of the supergeometric structure. I will explain why working with supergrassmannian space could be a good solution to these problems. This is based off of joint work with Alexander Voronov.

**Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)**

Wednesday 19 June 2024, 09:00, M3 (M234)

Further information

Okko Makkonen

**Midterm review: Algebraic methods in homomorphic secret sharing**

Thursday 13 June 2024, 11:15, M3 (M234)

ANTA Seminar / Hollanti et al.

Shinji Koshida (Aalto)

**Building Natural Number Game from scratch**

Tuesday 11 June 2024, 10:15, M3 (M234)

I will present a non-expert view on type theory taking formalization of natural numbers as an example. In particular, I will define natural numbers and the operation of addition, prove the unit laws, associativity and commutativity. If time permits, I will also prove Peano's 7th and 8th axioms. The demonstration will go in a proof assistant Agda. (This presentation is not about a conventional topic from mathematical physics.)

**Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)**

Tuesday 11 June 2024, 09:15, M3 (M234)

Further information

Starting time corrected!

Professor Dan Brown, University of Waterloo

**Algorithmic information theory, creativity and communication**

Monday 10 June 2024, 14:00, T3

We build an analysis based on Algorithmic Information Theory of computational creativity and extend it to revisit computational aesthetics. Our approach gives an interesting basis to novelty, value, typicality, and a number of other basic concepts in aesthetics, while also focusing on how information is communicated between creators and audiences. In more recent work, we extend this to considering the process of review, which we present as a task that conveys information among various actors, including creators, audiences and reviewers.

Philine Schiewe

**Optimization - A first look (2x45min)**

Thursday 06 June 2024, 14:15, M2 (M233)

In this seminar, we will revisit various key areas of mathematical
optimization. Starting from linear optimization and classical solution
approaches exploiting the polyhedral feasible sets, we will continue to
mixed-integer linear programming. Here, solution approaches from linear
programming can be transferred in the context of cutting-plane and
branch-and-bound methods striving towards integral polyhedra. As a
special case of mixed-integer linear programs, we consider combinatorial
optimization. Classical combinatorial optimization problems contain both
polynomially solvable problems such as matchings and minimum spanning
trees as well as many famous NP-hard problems such as the traveling
salesperson problem and maximum cut.
As a second generalization of linear programming, we consider
semidefinite optimization. Here, we see how combinatorial optimization
problems can be approximated by semidefinite programs and have a look at
interior-point-based solution approaches.

ANTA Seminar / Hollanti et al.

Prof. Sueli I. R. Costa (Unicamp, Brazil)

**On lattices applied to coding for reliable and secure communications**

Monday 03 June 2024, 13:15, M2 (M233)

This talk aims to present a general approach to some lattice applications in communications emphasizing topics we have been working on recently as well others of interest. Those are related to spherical codes, index coding, multilevel coding/ decoding, Construction Pi-A from Hurwitz quaternions, twisted embeddings in lattice based cryptography and federated learning.

ANTA Seminar / Hollanti et al.

Aada Hakula

**Diffuse Optical Tomography with an Inaccurate Forward Operator in the Linearized Inverse Problem (Master's Thesis Presentation)**

Monday 03 June 2024, 13:00, M3 (M234)

Patricija Sapokaite

**Midterm review: Cycles in hypergraphs and matroids**

Friday 31 May 2024, 13:15, M2 (M233)

Algebra and discrete mathematics seminar

Joonas Vättö

**Segal axioms for the massless, free boson (midterm review presentation)**

Friday 31 May 2024, 10:15, M3 (M234)

After a review of the geometric axiomatisation scheme to two-dimensional conformal field theories (CFTs) in the spirit of Kontsevich and Segal, I will explicitly show how to construct the chiral CFT for the free, massless boson on arbitrary compact Riemann surfaces. The construction provides a rich playground for the interplay of distant areas of mathematics (Kähler spaces, C*-algebras, geometric function theory, etc.). Time permitting, I will sketch connections to Teichmüller theory, global analysis, and the Atiyah-Singer index theory.

Valtteri Lipiäinen, Johan Dinesen, Tuomo Valtonen, Neehar Verma

**Course presentations: Applications of Coding Theory to Security **

Thursday 30 May 2024, 12:00, M2 (M233)

12:00 Valtteri Lipiäinen: CodedPaddedFL and CodedSecAgg: Straggler mitigation and secure aggregation in federated learning.
12:30 Johan Dinesen: McEliece cryptosystem.
13:15 Tuomo Valtonen: Secure distributed matrix multiplication.
13:45 Neehar Verma: Private polynomial computation from Lagrange encoding.

ACTS Course Presentations / Hollanti et al.

Stephen Moore (IMPAN)

**Representations of the Reflection Equation Algebra**

Tuesday 28 May 2024, 10:15, M3 (M234)

The reflection equation was introduced in relation to quantum integrable systems with boundary condition and is closely related to the Yang-Baxter equation. The reflection equation algebra was in turn introduced to allow the algebraic study of solutions of the reflection equation, similar to the connection between quantum groups and the Yang-Baxter equation. We will describe the basic properties of the reflection equation algebra and explain the classification of its bounded *-representations. This is based on joint work with Kenny De Commer.

**Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)**

Friday 24 May 2024, 09:15, M3 (M234)

Further information

Markus Hirvensalo

**Midterm review: Extending the linearized Calderon problem to unbounded perturbations**

Thursday 23 May 2024, 09:15, M2 (M233)

Heikki Kettunen

**TBA (Master's Thesis Presentation)**

Wednesday 22 May 2024, 14:15, M2 (M233)

Diplomityöesitelmä / Hakula

Meri Aho

**On the quality of mathematical writing produced by ChatGPT and Gemini (MSc thesis presentation)**

Wednesday 22 May 2024, 11:15, M240

Thilini Panagoda

**On Temperature changes in Finland (MSc thesis presentation)**

Monday 20 May 2024, 09:30,

Kalle Kytölä

**Introduction to formalized mathematics with convergence in distribution as an example**

Thursday 16 May 2024, 16:15, M3 (M234)

Rolf Stenberg

**Courant vs. Nitsche**

Thursday 16 May 2024, 09:15, M2 (M233)

Kai Hippi

**Quantum ergodicity of a surface with a weak point scatterer**

Wednesday 15 May 2024, 14:15, M3 (M234)

Seminar on analysis and geometry

Lauri Särkiö

**Regularity of parabolic double-phase equations (Midterm review)**

Wednesday 15 May 2024, 11:15, M3 (M234)

Prof. Alberto Ravagnani (Eindhoven University of Technology)

**The Service Rate Region Polytope**

Tuesday 14 May 2024, 15:15, M1 (M232)

In distributed data storage, information is distributed across multiple servers with redundancy, in such a way that multiple users can access it at the same time. The access requests that a distributed data storage system can support are described by a convex polytope, called the service rate region of the system. This talk is about the properties of the service rate region, and about how the algebra of the system determines the geometry of the corresponding polytope.

Lilja Metsälampi

**Midterm review**

Monday 13 May 2024, 16:15, M3 (M234)

Algebra and discrete mathematics seminar

Dr. Benjamin Jany (TU Eindhoven)

**Bounds and field size for locally recoverable codes**

Monday 13 May 2024, 14:15, M2 (M233)

In the last decade, Locally Recoverable Codes (LRC) have been a critical topic in communication and distributed storage. In addition to the minimum distance, dimension and length of a code, LRCs also consider the locality parameter, i.e. the minimum number of entries needed to recover a given entry for any codeword. The parameters of LRCs are subject to a general Singleton bound and codes achieving the bound are called optimal LRCs. Constructions are known when the underlying field size of the code is larger than the length of the code. However, still little is known about the existence of optimal LRCs over small underlying field sizes. In this talk, I will show how we established new bounds that depend on locality and the field size of code using a duality theory of LRCs and
the combinatorial structure of the code. This talk is based on joint work with A. Gruica and A. Ravagnani.

ANTA Seminar / Hollanti et al.

Dmitrii Vasilev

**Performance analysis of neural likelihood approximation methods for decision making models**

Wednesday 08 May 2024, 16:15, M3 (M234)

Rodrigo Martín Sánchez-Ledesma (Complutense U. Madrid / INDRA)

**Overview and extension of root-based attacks against PLWE instances**

Tuesday 07 May 2024, 15:15, M2 (M233)

The Polynomial Learning With Errors problem (PLWE) serves as the background of two of the four cryptosystems standardised in July 2022 by the National Institute of Standards and Technology to replace non-quantum resistant current primitives like those based on RSA, finite field based Diffie-Hellman and its elliptic curve analogue. Although PLWE is highly believed to be quantum resistant, unlike other post-quantum proposals like multivariate and some code based ones, this fact has not yet been established. Moreover, several vulnerabilities have been encountered for a number of specific instances. In a search for more flexibility, it becomes fully relevant to study the robustness of PLWE based on other polynomials, not necessarily cyclotomic. In 2015, Lauter et al. found a good number of attacks based on different features of the roots of the polynomial. In the present talk we present an overview of the approximations made against PLWE derived from these work, along with several new attacks which refine those by Lauter exploiting the order of the trace of roots over finite extensions of the finite field under the three scenarios laid out by Lauter et al, allowing to generalize the setting in which the attacks can be carried out. This is joint work with I. Blanco-Chacón and R. Durán.

ANTA Seminar / Hollanti et al.

Teemu Mäki

**MSc thesis presentation: Side-channel attacks in digital forensics**

Tuesday 07 May 2024, 14:15, M2 (M233)

Advisors: Lassi Helanti (National Bureau of Investigation Forensic Laboratory) and Estuardo Alpirez Bock (Xiphera)

ANTA Seminar / Hollanti et al.

Oula Kekäläinen

**MSc thesis presentation: Generalization of Descartes' rule of signs to multivariate polynomials with real exponents**

Monday 29 April 2024, 16:15, M3 (M234)

Algebra and discrete mathematics seminar

Joonas Laaksonen

**MSc thesis presentation**

Monday 29 April 2024, 14:15, M3 (M234)

Diplomityöesitelmä

Diplomityöesitelmä / Hakula

Tunç Köse (Aalto University)

**Community recovery with variational inference and stochastic block models (MSc presentation)**

Monday 29 April 2024, 14:15, M222 (Kappa)

Lasse Leskelä

Lauri Nyman

**Distance to singularity for matrix pencils via Riemannian optimization**

Thursday 25 April 2024, 09:15, M2 (M233)

Lauri Nyman

**Distance to singularity for matrix pencils via Riemannian optimization**

Thursday 25 April 2024, 09:15, M2 (M233)

Lauri Nyman

**Distance to singularity for matrix pencils via Riemannian optimization**

Thursday 25 April 2024, 09:15, M2 (M233)

Leevi Kaukonen

**MSc thesis presentation**

Wednesday 24 April 2024, 14:15, M3 (M234)

Diplomityöesitelmä

Diplomityöesitelmä / Hakula

Anna-Mariya Otsetova

**Axisymmetric capillary water waves with vorticity and swirl connecting to static unduloid configurations**

Wednesday 24 April 2024, 10:15, M3 (M234)

We study steady axisymmetric water waves with general vorticity and swirl, subject to the influence of surface tension. Explicit solutions to such a water wave problem are static configurations where the surface is an unduloid, that is, a periodic surface of revolution with constant mean curvature. We prove that to any such configuration there connects a global continuum of non-static solutions by means of a global implicit function theorem and topological degree theory. To prove this, the key is strict monotonicity of a certain function describing the mean curvature of an unduloid and involving complete elliptic integrals. From this point of view, this paper is an interesting interplay between water waves, geometry, and properties of elliptic integrals.
This is a joint work with Jörg Weber (University of Vienna) and Erik Wahlén (Lund University).

Seminar on analysis and geometry

Gerald Williams (University of Essex)

**Incidence graphs of generalized polygons and star graphs of group presentations with cyclic symmetry**

Monday 22 April 2024, 16:15, M3 (M234)

A generalized polygon is a point-line incidence structure that includes projective planes (generalized 3-gons). Incidence graphs of generalized m-gons are connected bipartite graphs of diameter m and girth 2m. Associated to any group presentation is a graph called the star graph, which encodes structural information about the group defined by the presentation. Transitional behaviour can occur for groups defined by presentations whose star graph components are incidence graphs of generalized polygons; such presentations are called special. A cyclic presentation of a group is a type of group presentation that admits a cyclic symmetry. In this talk I will discuss joint work with Ihechukwu Chinyere in which we classify the special cyclic presentations.

Algebra and discrete mathematics seminar

Ivy Woo

**Partial Lattice Trapdoors: How to Split Lattice Trapdoors, Literally**

Monday 22 April 2024, 13:30, Väre Q203

We introduce a natural technique for sharing lattice trapdoors: splitting them into partial trapdoors of smaller dimensions. We define security properties for these objects and prove these properties for a simple construction. Our proofs are based on the k-MSIS and k-MLWE assumptions together with the following conjecture: sampling two matrices with entries following discrete Gaussian distributions of width \sigma_0 or \sigma_1 and then sampling a matrix with entries following a discrete Gaussian distribution of width \sigma > \poly \cdot \max(\sigma_0, \sigma_1) from the lattices spanned by these two matrices leads to two distributions that are statistically close. We construct simple threshold signatures and IBE schemes from this primitive to illustrate its utility.

Cryptography seminar

prof. Samuli Siltanen (University of Helsinki)

**The magic of math: three-dimensional X-ray vision (FMS colloquium)**

Wednesday 17 April 2024, 16:15, M1 (M232)

Further information

In the 1970s, a new X-ray based innovation was introduced. Tomography, or slice imaging, revealed the inner structure of a patient point by point as a three-dimensional map of tissues. This opened up a new world for doctors as they could do precise diagnosing based on these "CAT-scans."
Tomography is based on recording X-ray images of the patient along many directions, and then using mathematics in a clever way for combining the information into a 3D image. This talk explains that process in simple terms. An important research topic in modern mathematics is to look for a way to do tomographic imaging with the least possible amount of radiation dose to the patient. Or to compensate for incomplete measurements caused by restrictions in the imaging arrangement. This is based on a process called regularisation, also illustrated in the talk in an easy-to-understand way.
Also: there is a fun quiz revealing natural tomographers among the audience.

SMY kollokvio

Kim Myyryläinen

**Parabolic Muckenhoupt weights**

Wednesday 17 April 2024, 10:15, M3 (M234)

Seminar on analysis and geometry

Ivy Woo

**Obfuscation from Lattice-Based Equivocal Assumption**

Tuesday 16 April 2024, 15:15, M2 (M233)

The Learning with Errors (LWE) problem w.r.t. a matrix B asks to recover the secret-error tuple (s,e) given the sample c = sB+e mod q. In typical settings, e.g. when B mod q is uniformly random, the solution (s,e) is uniquely determined by (B,c). In lattice terminology, this is due to the non-existence of short vectors in the lattice spanned by the rows of B modulo q.
We propose the notion of "primal lattice trapdoors", a suit of algorithms which generates a matrix B together with a trapdoor, such that the lattice of B contains hidden exceptionally short vectors, allowing LWE samples w.r.t. B to admit multiple solutions, whereas the trapdoor allows to sample from the solution space. We provide a construction and prove that it satisfies a set of desirable properties, either unconditionally or computationally based on the NTRU assumption.
Leveraging our tool, we construct a lattice-based indistinguishability obfuscator, a powerful cryptographic primitive known to imply most in cryptography.

ANTA Seminar / Hollanti et al.

Joaquín de la Barra

**Decision models for reinforcing critical infrastructures (Mid-term evaluation)**

Tuesday 16 April 2024, 14:30, M3 (M234)

Sampo Niemelä

**MSc thesis presentation: Coding theory for federated learning**

Tuesday 16 April 2024, 11:15, M2 (M233)

Advisors: Okko Makkonen and Serge Kas Hanna

ANTA MSc thesis presentation / Hollanti

Ville Havu

**ELSI Software interface for electronic structure solvers**

Thursday 11 April 2024, 09:15, M2 (M233)

Kevin Nguyen

**On sales lead optimization of personal insurance covers with multi-armed bandit algorithms (MSc thesis presentation)**

Wednesday 10 April 2024, 15:15, M2 (M233)

Lauri Särkiö

**Very weak solutions to parabolic p-Laplace systems**

Wednesday 10 April 2024, 10:15, M3 (M234)

Seminar on analysis and geometry

Prof. Paul Van Dooren (UCLouvain)

**Assigning Stationary Distributions to Stochastic Matrices**

Tuesday 09 April 2024, 15:15, M1 (M232)

The target stationary distribution problem (TSDP) is the following: given an
irreducible stochastic matrix G and a target stationary distribution μ^, construct
a minimum norm perturbation, ∆, such that G^ = G + ∆ is also stochastic and
has the prescribed target stationary distribution, μ^. We first consider rank-1
perturbations ∆ and show how to efficiently minimize their norm when such a
solution is feasible. But sparsity and/or connectivity of the graph of G + ∆ may
then get lost. We then impose a constraint on the support of ∆, that is, on the
set of non-zero entries of ∆. This is particularly meaningful in practice since
one cannot typically modify all entries of G. We first show how to construct
a feasible solution G^ that has essentially the same support as the matrix G.
Then we show how to compute globally optimal and sparse solutions using
the component-wise l_1 norm and linear optimization. We propose an efficient
implementation that relies on a column-generation approach which allows us to
solve sparse problems of size up to 10^5 × 10^5 in a few minutes.

Jonas Tölle

**Nonlinear (stochastic) PDEs with singular diffusivity**

Tuesday 09 April 2024, 10:15, M140

In this talk, we shall discuss properties of solutions to parabolic deterministic (and stochastic) partial differential equations with singular nonlinear divergence-type diffusivity with zero Dirichlet boundary conditions on a bounded Euclidean domain. As these kinds of equations usually lack good coercivity estimates in higher spatial dimensions, we choose to address the general well-posedness question by variational weak energy methods.
Examples include the (stochastic) singular $p$-Laplace equation, the multi-valued (stochastic) total variation flow and the (stochastic) curve shortening flow.
We shall present improved pathwise regularity results and decay estimates for a general class of singular divergence-type PDEs. We shall also address the stochastic case, where the equation is perturbed by additive Gaussian noise.
Based on joint works with Benjamin Gess (Leipzig and Bielefeld), Wei Liu (Xuzhou), Florian Seib (Berlin), and Wilhelm Stannat (Berlin).

Seminar on analysis and geometry

**Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)**

Tuesday 09 April 2024, 09:00, M203

Further information

Paul Van Dooren

**Perfect shifts and the QR algorithm**

Thursday 04 April 2024, 09:15, M2 (M233)

Tuomas Hytönen (Aalto)

**True and fake generalized eigenvectors of infinite matrices**

Tuesday 02 April 2024, 10:15, M3 (M234)

In von Neumann's formulation of Quantum Mechanics, physical observables are represented by self-adjoint operators in some Hilbert space. The spectrum of the operator is interpreted as the set of possible outcomes of a measurement of the observable, which is perhaps the most important physical prediction of this mathematical model. In Physics literature, especially on the introductory level, a somewhat heuristic approach to studying the spectrum is sometimes employed: "generalized eigenvectors" outside the original Hilbert space are acceptable, unless they are too wild to be "physical". The aim of the talk is to provide a rigorous justification of such heuristics under certain conditions, but also to show that these heuristics may miserably fail in some situations.

Thomas Wasserman (Oxford)

**Functorial Field Theory and Defects**

Tuesday 26 March 2024, 10:15, M3 (M234)

I will give an overview of functorial field theories, a mathematical formalisation of quantum field theories as functors out of some (higher) category of bordisms between manifolds. It is particularly well suited for describing topological quantum field theories. In the first half of this talk I will explain the Cobordism Hypothesis: a classification result for topological quantum field theories. In the second half, I will explain how one thinks about defects (interfaces between different quantum field theories) in this formalism, and how this relates to the bulk-boundary correspondence between three-dimensional topological quantum field theories and two-dimensional conformal field theories. I will aim to make this talk accessible to a broad audience.

mathematical physics seminar

Toni Karvonen

**The relation between asymptotic and worst-case settings in numerical integration**

Thursday 21 March 2024, 09:15, M2 (M233)

Jani Onninen (Syracuse University)

**Quasiregular values**

Wednesday 20 March 2024, 10:15, M3 (M234)

Quasiregular maps form a higher-dimensional class of maps with many similar properties to holomorphic maps, such as continuity, openness, discreteness, and versions of the Liouville and Picard theorems. In this talk, we give a pointwise definition of quasiregularity. We show that this condition yields counterparts to many fundamental properties of quasiregular maps at a single point. The studied maps have already shown to play a key part in various important 2D results. Joint work with Ilmari Kangasniemi.

Seminar on analysis and geometry

Luis Brummet (Aalto)

**Survey on complex driven Loewner chains**

Tuesday 19 March 2024, 10:15, M3 (M234)

In this talk we provide some basic facts about Loewner chains driven by both deterministic functions and stochastic processes. In the second half of the talk we provide some insights about the current development on Loewner chains driven by deterministic complex-valued functions and complex Brownian motion.

Aapo Laukkarinen

**Convex body domination and its applications to matrix-weighted norm inequalities**

Wednesday 13 March 2024, 10:15, M3 (M234)

Seminar on analysis and geometry

Prof. Henrik Garde (Aarhus University)

**Obstacles in Calderóns inverse conductivity problem**

Tuesday 12 March 2024, 15:15, U6 KONECRANES (U149)

I will discuss the inverse conductivity problem on recovering interior information about the electrical conductivity of a body from exterior electrical measurements. I will show how one can reconstruct the exact shape and position (called obstacles/inclusions) of inhomogeneities, using energy-comparisons with Neumann-to-Dirichlet maps.
The method is at the same time both simple and surprisingly general, allowing inhomogeneities with parts that are finite positive and negative perturbations, parts that are superconducting or insulating, and parts originating from a Muckenhoupt weight (leading to degenerate/singular problems). The method can also recover collections of cracks in the form of hypersurfaces.
If time permits it, I will also discuss how to handle more practical electrode models and noisy measurements in a rigorous way.

Osama Abuzaid (Aalto)

**Random matrices, multiple SLEs and large deviations**

Tuesday 12 March 2024, 10:15, M3 (M234)

A fundamental goal in random matrix theory is to understand the eigenvalues of a given random matrix model. Schramm-Loewner evolution SLE(κ) is a one-parameter family of random curves arising from two-dimensional conformal geometry. In this talk I will show how the evolution of eigenvalues of certain Itô-diffused random matrices coincide with the driving functions of multiple interacting SLE(κ) curves of some special values of κ. If time permits, in the end I will present a large deviation principle which quantifies the exponential rate of convergence of SLE(κ)-curves to deterministic SLE(0) in the limit κ->0.

Prof. Francesco De Pretis (University of Modena )

**Making decisions with evidential probability and objective Bayesian calibration inductive logics**

Monday 11 March 2024, 15:15, Y225a

Calibration inductive logics are based on accepting estimates of relative frequencies, which are used to generate imprecise probabilities. In turn, these imprecise probabilities are intended to guide beliefs and decisions a process called calibration. Two prominent examples are Henry E. Kyburg's system of Evidential Probability and Jon Williamson's version of Objective Bayesianism. There are many unexplored questions about these logics. How well do they perform in the short-run? Under what circumstances do they do better or worse? What is their performance relative to traditional Bayesianism? In this article, we develop an agent-based model of a classic binomial decision problem, including players based on variations of Evidential Probability and Objective Bayesianism. We compare the performances of these players, including against a benchmark player who uses standard Bayesian inductive logic. We find that the calibrated players can match the performance of the Bayesian player, but only with particular acceptance thresholds and decision rules. Among other points, our discussion raises some challenges for characterising cautious reasoning using imprecise probabilities. Thus, we demonstrate a new way of systematically comparing imprecise probability systems, and we conclude that calibration inductive logics are surprisingly promising for making decisions.

Marko Huhtanen

**Non-Hermitian quantum mechanics eigenvalue problem**

Thursday 07 March 2024, 08:59, M2 (M233)

Wontae Kim

**Hölder regularity of the parabolic double phase equation**

Wednesday 06 March 2024, 10:15, M3 (M234)

Seminar on analysis and geometry

Tuukka Himanka

**Physics-Informed Neural Networks in Probabilistic Spatio-Temporal Modelling**

Friday 01 March 2024, 14:15, M3 (M234)

Diplomityöesitelmä / Hakula

Jalo Nousiainen

**Machine learning and inverse problems in extreme adaptive optics**

Thursday 29 February 2024, 09:15, M2 (M233)

Timo Takala

**Preserving Besov energy in sphericalization and flattening**

Wednesday 28 February 2024, 10:15, M3 (M234)

Seminar on analysis and geometry

Baptiste Cerclé (EPFL)

**A probabilistic approach to Toda Conformal Field Theories**

Tuesday 27 February 2024, 15:00, M3 (M234)

Toda conformal field theories form a family of two-dimensional quantum field theories initially introduced in the physics literature. They are natural generalizations of Liouville theory that enjoy, in addition to conformal invariance, an enhanced level of symmetry encoded by W-algebras.
In this presentation we will explain how one can study these theories from a mathematically rigorous perspective. For this purpose we will describe a probabilistic framework designed to make sense of these models and provide some insight on how the introduction of this framework can help to understand the model.
To be more specific, we will prove ---we will not enter into much details but rather try to convey the main ideas--- that one can compute some basic correlation functions of the theory based on probabilistic tools. Along the proof of this statement we will shed light on some unexpected interplays between probability theory and conformal field theory such as a generalized Brownian path decomposition.

Yi Tian (University of Bonn)

**Permutons, Meanders, and Random Geometry**

Tuesday 27 February 2024, 10:15, M3 (M234)

In this talk, we start with an overview of space-filling SLE, the quantum sphere, and the mating of trees theorem. We then define permutons and illustrate their natural construction from SLE-decorated LQG. Focusing on two special cases, Baxter permutons and meandric permutons, we reveal how they arise as limits of Baxter permutations and meanders, respectively. Through this exploration, permutons offer insights into the connection between discrete models and random geometry.

Mathematical Physics Seminar / Kytölä - Peltola

Charles Parker, Oxford

**Computing H2-conforming finite element approximations without having to implement C1-elements**

Thursday 22 February 2024, 13:15, M2 (M233)

Fourth-order elliptic problems arise in a variety of applications from thin plates to phase separation to liquid crystals. A conforming Galerkin discretization requires a finite dimensional subspace of H2, which in turn means that conforming finite element subspaces are C1-continuous. In contrast to standard H1-conforming C0-elements, C1-elements, particularly those of high order, are less understood from a theoretical perspective and are not implemented in many existing finite element codes. In this talk, we address the implementation of the elements. In particular, we present algorithms that compute C1 finite element approximations to fourth-order elliptic problems and which only require elements with at most C0-continuity. We also discuss solvers for the resulting subproblems and illustrate the method on a number of representative test problems.

Augustin Lafay and Julien Roussillon (Aalto)

**W3 conformal blocks at c=2 and Specht polynomials**

Tuesday 20 February 2024, 10:15, M3 (M234)

In this two-part talk we will present recent results on W3 conformal blocks. These are solutions of a system of PDEs arising from W3 algebra (an extension of the Virasoro algebra) null-vectors and Ward identities. At c=2, we give an explicit subspace of solutions having the dimension predicted by CFT. The solutions are expressed in terms of Specht polynomials in a simple way. After giving heuristic physical motivations, we will state a conjecture relating these functions to connection probabilities in the triple dimer model, recently computed by Kenyon and Shi. All along the talk, we will present the analogous known results for the Virasoro case.

Antti Hannukainen

**Parameter-dependent diffusion equation in layered media**

Thursday 15 February 2024, 13:30, M2 (M233)

Tomas Laamanen

**On the Impact of Statin Treatment on the Hypoxic Metabolism of In Vitro Grown Prostate Cancer Cells (MSc thesis presentation)**

Wednesday 14 February 2024, 15:15, Zoom

The Master's thesis presentation is given in zoom
https://aalto.zoom.us/j/66809637898
Meeting ID: 668 0963 7898

Milla Laurikkala

**Performance analysis of complex-valued convolutional neural networks on 5G L1 (MSc thesis presentation)**

Wednesday 14 February 2024, 14:15, M3 (M234)

Tuomas Hytönen

**Reduced inequalities for vector-valued functions**

Wednesday 14 February 2024, 10:15, M3 (M234)

Seminar on analysis and geometry

Prof. Eeva Vilkkumaa (Aalto University)

**Supporting the Development of a Robust, Market-Shaping Strategy with Scenario-Based Portfolio Decision Analysis: Case Study with Nordea**

Tuesday 13 February 2024, 15:15, U5 (U147)

Strategic decision-making is challenging due to multiple strategic objectives and long planning horizons that make it difficult to assess the future impacts of proposed strategic actions with respect to these objectives. Moreover, strategy work often requires a balance between preparing for alternative scenarios for the future (i.e., developing a robust strategy), and trying to steer the course of change towards a desirable direction (i.e., developing a market-shaping strategy). We present a model-based framework for supporting the development of a robust, market-shaping strategy. For the purposes of this framework, we develop a new portfolio decision analytic model and algorithms to help generate decision recommendations for selecting strategic actions, when (i) the actions scenario- and objective-specific impacts, the baseline values for these impacts, as well as preferences between strategic objectives are incompletely specified, and (ii) information regarding scenario likelihoods is incomplete and may depend on the selected actions. This framework is applied in a high-impact case on supporting the strategy process at the payments unit of Nordea Bank Abp, the largest retail bank in the Nordic countries.

Hamid Al-Saqban (Paderborn University)

**Unique Ergodicity for Foliations of Generic Abelian Differentials, Revisited**

Tuesday 13 February 2024, 10:15, M3 (M234)

In Teichmuller theory, a theorem due to H. Masur and W. Veech states that for generic Abelian differentials, the leaves of the horizontal foliation are uniquely ergodic. Said differently, the orbits of the horizontal straight-line flow on a generic translation surface are uniquely ergodic. Subsequently, G. Forni proved an effective form of this statement, establishing in particular precise power-laws for the deviations of ergodic averages of smooth functions from the power law (as predicted by the ergodic theorem). The main goal of this talk is to introduce and motivate translation surfaces, and to explain the main ideas behind an analytic approach (via anisotropic Banach spaces) to effective unique ergodicity for straight-line flows on a generic translation surface. This is a joint work in progress with D. Galli (University of Zurich).

Mathematical Physics Seminar / Radnell

Teemu Lundström

**f-vector inequalities for order and chain polytopes**

Thursday 08 February 2024, 13:15, M237

Midterm review talks / Algebra and discrete mathematics seminar

Antti Autio

**Comparing reduced basis models for electrical impedance tomography**

Thursday 08 February 2024, 09:15, M2 (M233)

Petteri Kaski

**The Asymptotic Rank Conjecture and the Set Cover Conjecture are not Both True**

Wednesday 07 February 2024, 16:15, M2 (M233)

Strassen's asymptotic rank conjecture [Progr. Math. 120 (1994)] claims a strong submultiplicative upper bound on the rank of a three-tensor obtained as an iterated Kronecker product of a constant-size base tensor. The conjecture, if true, most notably would put square matrix multiplication in quadratic time. We note here that some more-or-less unexpected algorithmic results in the area of exponential-time algorithms would also follow. Specifically, we study the so-called set cover conjecture, which states that for any ε>0 there exists a positive integer constant k such that no algorithm solves the k-Set Cover problem in worst-case time O((2-ε)^n|F|poly(n)). The k-Set Cover problem asks, given as input an n-element universe U, a family F of size-at-most-k subsets of U, and a positive integer t, whether there is a subfamily of at most t sets in F whose union is U. The conjecture was formulated by Cygan, Fomin, Kowalik, Lokshtanov, Marx, Pilipczuk, Pilipczuk, and Saurabh in the monograph Parameterized Algorithms [Springer, 2015], but was implicit as a hypothesis already in Cygan, Dell, Lokshtanov, Marx, Nederlof, Okamoto, Paturi, Saurabh, and Wahlström [CCC 2012, TALG 2016], there conjectured to follow from the Strong Exponential Time Hypothesis. We prove that if the asymptotic rank conjecture is true, then the set cover conjecture is false. Using a reduction by Krauthgamer and Trabelsi [STACS 2019], in this scenario we would also get an O((2-δ)^n)-time randomized algorithm for some constant δ>0 for another well-studied problem for which no such algorithm is known, namely that of deciding whether a given -vertex directed graph has a Hamiltonian cycle.
This is joint work with Andreas Björklund (ITU Copenhagen).

ANTA Seminar / Hollanti et al.

Mr Aufa Biahdillah (Aalto University)

**Master's thesis presentation: An Overview of the Quantum Fourier Transform and Its Application in Machine Learning**

Wednesday 07 February 2024, 14:15, M3 (M234)

The field of quantum physics has ushered in a new era of scientific discovery. Most research today is focused on this field, including computer science, which has given rise to quantum computing. The Fourier transform, which has been adapted to this trend, has resulted in the quantum Fourier transform. This is essentially a Fourier transform performed on a quantum state, which is a key element of quantum computing. One of the most significant outcomes of this transformation is quantum phase estimation, a subroutine algorithm that is useful when combined with other algorithms. Some of the key algorithms that can be combined with quantum phase estimation include the quantum principal component analysis, the Harrow-Hassidim-Lloyd algorithm, and the quantum singular value thresholding, which will be studied in this thesis. Additionally, a comparison to classical computing will be provided to highlight the advantages and disadvantages of the quantum version.

(Advisor: Ville Turunen)

Maija Löyskä

**Cryptocurrency Limit Order Books: On predicting price movements using neural network (MSc thesis presentation)**

Wednesday 07 February 2024, 12:00,

Mikhail Basok (University of Helsinki)

**Dimers on a Riemann surface and compactified free field**

Tuesday 06 February 2024, 10:15, M3 (M234)

Consider the dimer model sampled on a general Riemann surface. In this setup, the dimer height function becomes additively multivalued with a random monodromy. Given a sequence of graphs approximating the conformal structure of the surface in a suitable way, the underlying sequence of height functions is expected to converge to the compactified free field on the surface. Recently, this problem was addressed by Berestycki, Laslier and Ray in the case of Temperley graphs. Using various probabilistic methods, they obtained the following universal result: given that a sequence of graphs satisfies certain set of probabilistic conditions (which link it with the conformal structure of the surface), the limit of height functions exists, is conformally invariant and does not depend on a particular sequence of graphs. However, the identification of the limit with the compactified free field was missing in this result. In my recent work I fill this gap by studying the same problem from the perspective of discrete complex analysis. For this purpose, I consider graphs embedded into locally flat Riemann surfaces with conical singularities and satisfying certain local geometric conditions. In this setup I obtain an analytic description of the limit which allows to identify it with a suitable version of the compactified free field; I also prove the convergence in some non-Temperlian cases when the surface is generic. A core part of this approach is the regularity theory on t-embeddings recently developed by Chelkak, Laslier and Russkikh.
In this talk we discuss the aforementioned results, in particular, how the methods of discrete complex analysis are generalized to the case of a Riemann surface, and how the geometry of the surface affects the limit.

**Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)**

Friday 02 February 2024, 09:00, M3 (M234)

Further information

https://aalto.zoom.us/j/62767998708

Olavi Nevanlinna

**Power series for piecewise constant holomorphic functions. How and Why?**

Thursday 01 February 2024, 09:15, M2 (M233)

Prof. Pedro Munari (Universidade Federal de São Carlos, Brazil)

**The Robust Bike Sharing Rebalancing Problem under Demand Uncertainty**

Wednesday 31 January 2024, 15:00, M2 (M233)

Bike Sharing Systems (BSSs) are an excellent solution to improve urban mobility, offering a mode of transportation that is both economical and environmentally friendly. These systems are spread worldwide and help alleviate heavy traffic and reduce pollution, yielding direct and indirect benefits to the local population. Nonetheless, effectively managing these systems can pose practical challenges, as some stations often experience fluctuations in bike availability, resulting in surpluses or shortages and, occasionally, becoming full or empty. Rebalancing operations need to be regularly performed to restore the desired inventory levels at each station, and they are significantly affected by the unpredictable demand at stations. To aid decision-making in such situations, we introduce the Robust Bike Sharing Rebalancing Problem (RBRP), which combines the Vehicle Routing Problem with robust optimization techniques to enhance rebalancing operations in BSSs. We present two novel mixed-integer programming formulations and a tailored branch-and-cut algorithm for the RBRP. The first formulation is compact and based on the linearization of recursive equations, while the second relies on robust rounded capacity inequalities and feasibility cuts. Computational results using benchmark instances based on real-world data indicate the effectiveness of our approaches and highlight the benefits of using robust solutions to support decision-making in BSSs.

Gamma-optinars - Seminars of the Group of Applied Mathematical Modelling and Optimisation (GAMMA-OPT))

Mikko Närhi (Aalto)

**Censored Regression Models with Autoregressive Errors (MSc thesis presentation)**

Wednesday 31 January 2024, 10:15, M237

In time series analysis, addressing censored data poses a significant challenge. This thesis focuses on censored data in radio access networks, where high user density and limited infrastructure lead to incomplete observations of data traffic demand. We propose a Censored Linear Regression model with autoregressive errors to estimate the censored data, employing Gaussian imputation on the premise that the complete data follows a multivariate normal distribution. This model was applied to historical data from a country-wide cellular network, imputing censored observations to enhance forecast accuracy. While the model is effective in estimating censored data, its impact on improving forecast accuracy varies, rendering its overall benefit in such contexts inconclusive.

Haiqing Xu

**From the Riemann Mapping Theorem to a Sobolev Homeomorphism**

Wednesday 31 January 2024, 10:15, M3 (M234)

Seminar on analysis and geometry

Mehr Rai

**Geometry of Numbers and Exterior Algebras: Towards Bombieri-Vaaler's Version of Siegel's Lemma (MSc thesis presentation)**

Tuesday 30 January 2024, 15:15, M2 (M233)

Advisor Tapani Matala-aho.

ANTA Seminar / Hollanti et al.

Dissertation

Juha-Pekka Puska

**Bayesian Optimal Experimental Design in Imaging**

Friday 26 January 2024, 12:00, M1 (M232)

Tom Gustafsson

**Inequality constraints and the finite element method**

Thursday 25 January 2024, 09:15, M2 (M233)

David Karpuk

**The sphere-packing density of unit lattices**

Tuesday 23 January 2024, 15:15, M2 (M233)

Lattices, that is, discrete subgroups of Euclidean space, are a fundamental object in mathematics with connections to Lie Group Theory, Cryptography, and Algebraic Number Theory. The sphere-packing density of a lattice roughly measures how efficiently its points are packed into Euclidean space. The search for the optimal lattice packing in n-dimensional space is a long-standing problem, with known solutions only for certain small n. On the other hand, certain lattices arising naturally from Algebraic Number Theory have natural properties that make them especially suitable for applications in communications. In this talk, we will discuss an apparently new class of lattices, which we deem R_n-lattices, whose properties attempt to capture those coming from Number Theoretic lattices while also yielding efficient sphere packing. Falling into this class of lattices are unit lattices coming from totally real Galois number fields, and we apply our results to understand the sphere-packing densities of some well-known classes of unit lattices. This is joint work with Jose Cruz of the University of Calgary.

ANTA Seminar / Hollanti et al.

Liam Hughes (Aalto)

**Mated-CRT maps**

Tuesday 23 January 2024, 10:15, M3 (M234)

For gamma in (0,2), the gamma-mated-CRT map is a random triangulation in the plane encoded by a pair of Brownian motions with correlation depending on gamma. It can be obtained as a discretized version of the infinite-volume peanosphere construction that glues together two continuum random trees to get a sphere-homeomorphic surface decorated by a space-filling path, or alternatively as the adjacency graph of cells filled in by a space-filling Schramm--Loewner evolution parametrized by Liouville quantum gravity volume.
Many other models of random planar maps (RPMs) can be encoded by 2D random walks, which can be approximated by Brownian motion using Skorokhod-type embeddings to allow statements about these RPMs to be reduced to statements about mated-CRT maps. For instance, one can understand graph distances in uniform infinite planar triangulations by studying the embedding of the mated-CRT map into the plane given by the SLE construction. In this talk I will give an introduction to mated-CRT maps and suggest directions for future work.

Suzuki Yuya

**Numerical integration and function approximation in Gaussian-weighted Sobolev space**

Thursday 18 January 2024, 09:15, M2 (M233)

Kieran Ryan (Aalto)

**The mirror model**

Tuesday 16 January 2024, 10:15, M3 (M234)

Abstract: Consider the Lorentz mirror model on the 2d lattice: at each lattice site, independently place a mirror at 45 degrees to the lattice with some probability p. The orientation of the mirror is chosen independently, say north-west with probability q in (0,1). Loops can then be formed which bounce off the mirrors, or pass straight through lattice sites with no mirror. What is the probability that the loop through some given edge is infinite? For p=1 it is known to be zero, but for p in (0,1) the problem is open.
We study this model where we re-weigh the measure by n^#loops. We discuss a form of breaking of translation invariance, where for n large, almost all the loops are trivial loops surrounding black faces, or trivial loops surrounding the white faces. We can see that the method applied also works for a model of loops coming from O(n)-invariant quantum spin chains, where the breaking of translation invariance is known as dimerisation.
Joint work with Jakob Björnberg.

Marko Huhtanen

**Image compression techniques**

Thursday 11 January 2024, 09:15, M2 (M233)

Prof. Guillermo Mantilla-Soler (Universidad Nacional de Colombia)

**Analogies between classic arithmetic and function fields**

Tuesday 09 January 2024, 15:15, U6 KONECRANES (U149)

In his talk I will explain how similarities between the integers and the polynomial ring over a field allow us to find, and prove, connections between objects that at first glance seem to be quite different. As an example of this I will show how Lagranges interpolation theorem is nothing else but a particular case of the Chinese reminder theorem. If time allows I will show how a simple result on polynomials leads to the statement of the famous ABC conjecture.

Thomas Wasserman (University of Oxford)

**The Landau-Ginzburg / Conformal Field Theory Correspondence**

Tuesday 19 December 2023, 10:15, M3 (M234)

In the first half of this talk I will give an introduction to the Landau-Ginzburg (LG) / Conformal Field Theory (CFT) correspondence, which predicts a relationship between certain categories of matrix factorisations (for the ``LG potential'') and modular tensor categories (on the CFT side). This prediction has its origin in physics, and comes from observations about 2-dimensional N=2 supersymmetric quantum field theory. I will explain how this prediction is to be interpreted mathematically and what difficulties one encounters in doing this. In the second half of the talk I will discuss joint work with Ana Ros Camacho in which we realise the LG/CFT correspondence for the potentials x^d. The main ingredient in this is an enriched category theoretical versions of the classical Temperley-Lieb/Jones-Wenzl construction of the representation category of quantum su(2).

mathematical physics seminar (Kytölä, Peltola)

Aapo Pajala (Aalto)

**Shapiro Conjecture for rational functions**

Monday 18 December 2023, 14:15, M3 (M234)

The Shapiro Conjecture (Theorem of Mukhin, Tarasov and Varchenko as of 2009) is a statement about subspaces of univariate complex polynomials. It gives a sufficient condition for the existence of a real basis in terms of the Wronski polynomial of the subspace.
In the case of 2-dimensional subspaces, the conjecture becomes a statement about rational functions and their critical points. This presentation outlines an "elementary" proof for this special case presented by A. Eremenko and A. Gabrielov in 2005. The main tools of the proof are combinatorial invariants called nets for rational functions. Eremenko and Gabrielov then show that the statement holds for particular rational functions, and use the nets to argue that analytic continuation can be used to obtain a complete proof.

mathematical physics seminar (Kytölä, Peltola)

Prof. Ting Xue (University of Melbourne)

**Springer theory and finite groups of Lie type**

Tuesday 12 December 2023, 15:15, U6 KONECRANES (U149)

Springer theory for reductive algebraic groups plays an important role in determining irreducible characters of finite groups of Lie type. We discuss its generalisation to the setting of graded Lie algebras. We explain how level-rank dualities arise from unipotent irreducible characters and their connections with the graded Springer theory. If time permits, we discuss a conjectural realisation of these dualities using affine Springer fibers.

Alexis Langlois-Rémillard (University of Bonn)

**Uncoiled periodic and affine Temperley-Lieb algebras, Jones-Wenzl projectors and their trace**

Tuesday 12 December 2023, 10:15, M3 (M234)

The affine and periodic Temperley-Lieb algebras are families of infinite-dimensional algebras with a diagrammatic presentation. They have been studied in the last 30 years, mostly for their physical applications in statistical mechanics, where the diagrammatic presentation encodes the connectivity property of the models. Most of the relevant representations for physics are finite-dimensional.
In the first part of the talk, we will present the diagrammatic calculus related to these algebras and define finite-dimensional quotients of these algebras, which we name uncoiled algebras in reference to the diagrammatic interpretation. Afterwards, we construct a family of Jones-Wenzl idempotents, each of which projects onto one of the one-dimensional modules these algebras admit.
The second part of the talk will go in depth on the construction of the Jones-Wenzl idempotents and present some of their applications, mainly looking at their trace.

Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Miryam Gnazzo

**Computing closest singular matrix-valued functions**

Thursday 07 December 2023, 09:15, M2 (M233)

Harri Hakula

Johanna Immonen (Helsinki University)

**Percolation and Modular Invariance**

Tuesday 05 December 2023, 10:15, M3 (M234)

The talk will consider modular forms and crossing probabilities. In particular, I will review how Cardy's formula can be expressed in terms of the modular Eta function, and further, that Cardys function is the unique function that satisfies f(r)+f(1/r)=1 and has an expansion in form e−2παr times a power series in e−2πr for some α∈R. The first property is implied by a symmetry of the problem, but there is no physical argument for the latter.

Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Jukka Kohonen (Aalto)

**Decorating lattices for the season, featuring: SageMath**

Thursday 30 November 2023, 16:15, M2 (M233)

I will demonstrate SageMath, the free open-source mathematics software, from the viewpoint of my recent work with modular lattices (in order theory). A virtual listing of 40-element modular lattices is created, seemingly numbering 3 trillion (3 * 10^12). From a user's viewpoint, the lattices can be accessed at will -- sequentially, by ordinal index, or randomly. But in reality only 740 million smaller lattices are listed: from them, a SageMath class creates bigger lattices on the fly. To do this properly, we need graphs and their automorphism groups; classical "balls into boxes" combinatorics; and data abstraction. All this we find in SageMath. We also see how modular lattices are decorated with shiny trinkets for the season.

computer mathematics seminar / ForAlli

Dr. Thomas Westerbäck (Mälardalen University)

**A matroid generalization and associations with modules and information theory**

Thursday 30 November 2023, 14:15, M3 (M234)

There is a direct connection between linear codes over fields and matroids, commonly referred to as representable matroids. Specifically, a generator matrix for a linear code over a field not only serves as a coding tool but also as a representation for a representable matroid. Exploiting this connection, matroid theory has proven important in establishing numerous results in information theory, for example, in the areas of distributed storage, field linear codes with Hamming weights, network coding, index coding, and caching. Representable matroids also constitute an intriguing class in their own right, with connections to various areas within mathematics.
In this talk, I will present a generalization of matroids and how this generalization can be associated with modules. I will also illustrate how this connection can be used to establish results in information theory, especially in scenarios where algebraic structures other than vector spaces are considered.

ANTA Seminar / Hollanti et al.

Dissertation

Matteo Allaix

**Quantum private information retrieval from coded storage systems (PhD defence)**

Wednesday 29 November 2023, 14:00, H304

Opponent Prof. Alberto Ravagnani (Eindhoven), Custos Camilla Hollanti

ANTA PhD Defence

Augustin Lafay (Aalto University)

**Integrability of O(N) loop models and web models.**

Tuesday 28 November 2023, 10:15, M3 (M234)

I will review how one can obtain integrable local transfer matrices for the O(N) loop model from the relevant evaluation representation of the appropriate quantum affine algebra. After motivating the definition of a recently introduced rank 2 counterpart, the G_2 web models, I will show how to use similar ideas to obtain integrable transfer matrices in this context.

Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Ivy Woo

**Class Groups of Imaginary Quadratic Fields and Applications to Cryptography (short talk)**

Thursday 23 November 2023, 16:30, M2 and Zoom

Further information

For a number field K, its class group measures the extent that unique factorisation fails in the ring of integers of K. When K is an imaginary quadratic field such that unique factorisation fails miserably, its class group turns out to exhibit nice properties which are found useful in cryptographic constructions.
In this short talk, I will briefly recall some background on class groups, focused on the case of imaginary quadratic fields, and highlight some reasons for their uses in cryptography. For example, assuming certain computational problems are hard over class groups, we shall see that class groups imply encryption schemes that are more space-efficient than the well-known RSA encryption, and there exist cryptographic primitives with desirable properties that are, as of today, only known to be achievable from class groups.

ANTA Seminar / Hollanti et al.

Nadja Aoutouf (INRIA Paris)

**Leakage of secret sharing schemes**

Thursday 23 November 2023, 14:15, M3 and Zoom

Further information

In this talk, I will give an introduction to my PhD project, which focuses on privacy-preserving techniques.
As technology enables more powerful collection and curation of data, it has become a relevant need to assure the privacy of individuals and their associated data. An information-theoretic approach offers unconditional privacy guarantees without relying on the hardness of certain computational problems, i.e., the system cannot be broken even if the adversary has unlimited computing power. There are a variety of security tasks for which information-theoretic security is a meaningful and useful requirement, such as secret sharing, secure multiparty computation, and private information retrieval.
For instance, against side-channel attacks on systems and hardware, to protect one single crucial value (like a byte of a key), one of the most common, not hardware, countermeasures is masking, which applies a secret sharing scheme to expand this single value into a set of several random values. This forces an attacker to target all these random values (instead of a single value) to extract any meaningful secret information, making the attack more difficult.
This presentation, focusing on privacy-preserving techniques with information-theoretic approaches (i.e. secret sharing schemes), gives insights over the planned research during my PhD project. In this project, the results of Venkatesan Guruswami and Mary Wootters, which show that Reed-Solomon codes with evaluation points in the whole (finite) field, a failed evaluation point can be recovered using information from the remaining functional nodes. Due to the close connection between RS-code and Shamirs secret-sharing scheme vulnerabilities with respect to leakage can be concluded, which set the starting point for the doctoral research project. For instance, if a smaller, incomplete, amount of information is obtained by the adversary from each share (instead of the whole share) the secret can still be recovered. Finally, one of the major goals within the doctoral project is to find the minimal amount of leakage that can be tolerated while preserving the secrecy.

ANTA Seminar / Hollanti et al.

Anna-Mariya Otsetova

**The Amari neural field model**

Wednesday 22 November 2023, 10:15, M3 (M234)

Seminar on analysis and geometry

Oscar Kivinen (Aalto University)

**HOMFLY-PT homology and mathematical physics**

Tuesday 21 November 2023, 10:15, M3 (M234)

The HOMFLY-PT homology of links in the three-sphere was defined by Khovanov-Rozansky, following various earlier constructions and conjectures. Many of these were motivated by string and gauge theories, in addition to questions in low-dimensional topology. HOMFLY-PT homology is a link invariant valued in triply graded vector spaces (or modules over certain polynomial rings) which categorifies the HOMFLY-PT polynomial. In the first part of the talk, I will introduce the mathematical construction of HOMFLY-PT homology. In the second part, I will try to explain some of our current understanding of its physical underpinnings, which continues to develop in parallel with the mathematical theory.

Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Kim Myyryläinen

** Two weight strong type estimates for parabolic maximal function**

Wednesday 15 November 2023, 10:15, M3 (M234)

Seminar on analysis and geometry

Prof. Yuji Nakatsukasa (University of Oxford)

**Numerical Linear Algebra: direct, iterative, and randomized methods**

Tuesday 14 November 2023, 15:15, Hall E (Y124)

In many scientific computing and machine learning problems, we expend the majority of our computational resources in solving large-scale linear algebra problems, typically linear systems Ax = b, eigenvalue problems Ax = λx, or the singular value decomposition A = USV'. Numerical linear algebra (NLA) is a research field that attempts to devise practical algorithms for solving these problems.
Broadly, methods in NLA can be divided into three categories: direct, iterative, and randomized. In this talk I will give a whistle-stop tour of these classes of methods, highlighting the incredible robustness of classical (direct) methods, and the exciting speed and advances in randomized methods.

Joonas Vättö (Aalto University)

**Free, massless boson; an expressionistic view**

Tuesday 14 November 2023, 10:15, M3 (M234)

I will review some ongoing work on constructing the conformal field theory (d'après G. Segal) of the massless, free boson.

Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)

**Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)**

Thursday 09 November 2023, 09:15, M2 (M233)

Further information

Lauri Särkiö

**Higher integrability for singular parabolic double phase problems**

Wednesday 08 November 2023, 10:15, M3 (M234)

Seminar on analysis and geometry

Niklas Miller

**Difference sets and methods to study their existence**

Thursday 02 November 2023, 14:15, M3 (M234)

Some of the main methods for deciding whether or not a difference set of given parameters exists are the self-conjugacy test developed by Turyn in 1965, the field descent and its variations developed by Schmidt et al. in late 1990's, and importantly, the multiplier theorems by Hall, which date back to 1950's. All of these methods are based on knowledge about the decomposition groups in certain cyclotomic fields. In this talk I show that the multiplier groups of cyclic groups G, where v=|G| is non-squarefree, cannot contain a large set of residues. Together with a small "multiplier lemma" this gives a new existence test that can be used to rule out cyclic difference sets.

ANTA Seminar / Hollanti et al.

Wontae Kim

**Calderon-Zygmund type estimate for the parabolic double phase problem**

Wednesday 01 November 2023, 10:15, M3 (M234)

Seminar on analysis and geometry

Ulrik Hansen (University of Fribourg)

**Universality of Large-Scale Geometry for Planar Critical Random-Cluster Models**

Tuesday 31 October 2023, 10:15, M3 (M234)

Conformal invariance of general critical planar lattice models was conjectured by Belavin, Polyakov and Zamolodchikov in the early 80s. Using the (non-rigorous) renormalisation group flow, they deduced that any scaling limit of such a model must be rotationally invariant. Since any such limit must also be translation and scale invariant, the argument goes that it will also be invariant under the action of the group of transformations which are locally a composition of these three types of transformations. This is exactly the conformal group, which, in the planar case, is infinite-dimensional and therefore, particularly rich as a symmetry group. Another conjecture of theoretical physics going back to Griffiths and Kadanoff is that of universality: That the scaling limits of various models with different microscopic details, e.g. the graph on which it is defined, turn out to be the same across so-called universality classes.
During the last 25 years, the first conjecture has received immense attention from the probabilistic community after Schramm's introduction of the SLE. In this talk, however, we shall turn our attention to the second question. Building on work by Duminil-Copin, Kozlowski, Krachun, Manolescu and Oulamara, we prove that the critical random-cluster models each satisfy a universality property across a large class of planar graphs including the hexagonal and triangular lattices. A consequence thereof will be that any scaling limit in one of these universality classes is rotationally invariant and thus, this may also be thought of as a stepping stone towards proving conformal invariance for all critical random-cluster models.
Based on joint work with Ioan Manolescu.

Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Nyberg Fest (invited talks)

**Nyberg fest celebrates and honors Prof. emerita Kaisa Nyberg's work in the field of cryptography and cybersecurity. **

Friday 27 October 2023, 13:00, Dipoli, Lumituuli

Further information

Nyberg fest celebrates and honors Prof. emerita Kaisa Nyberg's work in the field of cryptography and cybersecurity. We organize a research seminar where the speakers will be Nyberg's former colleagues and doctoral students.
Prof. emerita Kaisa Nyberg is a distinguished scholar renowned for her significant contributions to the field of cryptography. With a career spanning several decades across academia, industry, and military, Nyberg has made groundbreaking advancements in the development of cryptanalysis and cryptographic protocols. She is most notably recognized for her pioneering work in linear and differential cryptanalysis, which are nowadays fundamental concepts in provable security and the design of cryptographic algorithms. Nyberg's expertise and dedication have had a lasting impact on the world of cryptography, a testament to her prominence in the field.

Dr. Maxwell Forst (U. Minnesota-Duluth)

**On the Geometry of Lattice Extensions (zoom talk, M3 for audience)**

Thursday 26 October 2023, 15:15, M3 (M234)

Further information

Given a lattice L, an extension of L is a lattice M of strictly greater rank such that the intersection of M and the subspace spanned by L is equal to L. In this talk we will discuss constructions of such lattice extensions where particular geometric invariants of M, such as the determinant, covering radius and successive minima, are related the corresponding geometric invariants of L. This talk is based on joint work with Lenny Fukshansky. Zoom: https://aalto.zoom.us/j/62956597693

ANTA Seminar / Hollanti et al.

Sakari Niemelä

**Higher integrability of metric double phase minimizers**

Wednesday 25 October 2023, 10:15, M3 (M234)

Seminar on analysis and geometry

Tuomas Kelomäki (Aalto University)

**Planar algebra structure of Khovanov homology**

Tuesday 24 October 2023, 10:15, M3 (M234)

The powerful knot invariant Jones polynomial is defined by local skein relations and normalisation. On the other hand, the original categorification of the Jones polynomial was defined on a global scale - Khovanov homology takes whole knots and links as an input. It was later realized, by Bar-Natan, that Khovanov's construction can be defined locally and that these local pieces can be composed by a planar algebra structure. We take a look at Bar-Natan's framework and how it can be used to obtain new results about the original Khovanov homology.

Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Dr. Jacques Benatar (U. Helsinki)

**Polynomials with multiplicative coefficients, and related questions**

Thursday 19 October 2023, 14:15, M3 (M234)

I will discuss some recent work, joint with Alon Nishry and Brad Rodgers, concerning the distribution of Dirichlet and trigonometric polynomials generated by multiplicative coefficients f(n). In the first part of the talk we will explore some old and new results for deterministic sequences f(n) (Möbius, Legendre symbol,...), stopping along our journey to marvel at a variety of wild and thorny conjectures. The second half of the talk will be devoted to Steinhaus random multiplicative coefficients f(n) = X(n). These considerations give rise to a couple of intriguing arithmetic problems.

ANTA Seminar / Hollanti et al.

Heather Macbeth (Fordham University)

**Making mathematics computer-checkable**

Wednesday 18 October 2023, 16:15, M1 (M232)

Further information

In the last thirty years, computer proof verification became a mature technology, with successes including the checking of the Four-Colour Theorem, the Odd Order Theorem, and Hales' proof of the Kepler Conjecture. Recent advances such as the "Liquid Tensor Experiment" verifying a recent theorem of Scholze have provided further momentum, as likewise have promising experiments integrating this technology with machine learning.
I will briefly describe some of these developments. I will then try to describe, more generally, what it feels like to carry out research-level computer verifications of mathematics proofs: the level of expression one has access to, the ways one finds oneself interrogating and reorganizing a paper proof, the kinds of arguments which are more tedious (or less tedious!) than on paper.
[This is a Finnish Mathematical Society online colloquium. Colloquium watch events are organized at Finnish universities' mathematics departments. The physical location of the Aalto event will be announced later.]

Finnish Mathematical Society online colloquium

Xavier Poncini (Aalto University)

**Planar-algebraic models: statistical mechanics and knot theory**

Tuesday 17 October 2023, 10:15, M3 (M234)

V.F.R. Jones initially introduced planar algebras to describe the standard invariant of a subfactor. Since then, planar algebras have found many applications in mathematics and physics. Informally, a planar algebra describes the interaction of elements of a graded vector space in the plane. The 'two-dimensional' structure of planar algebras makes them natural objects to describe planar statistical-mechanical models. In this talk, I will focus on the role played by planar algebras in relating statistical mechanics and knot theory. In particular, I will introduce a notion of YangBaxter integrability and show that statistical-mechanical models with this property give rise to polynomial link invariants. If time permits, I will report on recent results (joint with J. Rasmussen) classifying all singly generated planar algebras admitting a YangBaxter integrable model.

Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Afrin Hossain (MSc thesis presentation, Aalto/VTT)

**Torus-based Fully Homomorphic Encryption in Federated Learning**

Thursday 12 October 2023, 15:15, M3 (M234)

Advisors: Wilmar Bolanos, Visa Vallivaara

ANTA Seminar / Hollanti et al.

Matilde Costa

**BV capacity and Hausdorff content**

Wednesday 11 October 2023, 10:15, M3 (M234)

Seminar on analysis and geometry

Érika Roldán, Ph.D. (Max Planck Institute for Mathematics in the Sciences)

**Topology and Geometry of Random Cubical Complexes**

Tuesday 10 October 2023, 15:15, U6 (U149)

In this talk, we explore the expected topology (measured via homology) and local geometry of two different models of random subcomplexes of the regular cubical grid: percolation clusters, and the Eden Cell Growth model. We will also compare the expected topology that these average structures exhibit with the topology of the extremal structures that it is possible to obtain in the entire set of these cubical complexes. You can look at some of these random structures here (https://skfb.ly/6VINC) and start making some guesses about their topological behavior.

Mikhail Basok (University of Helsinki)

** Double-dimer nesting field: local statistics and convergence to the nesting field of CLE(4)**

Tuesday 10 October 2023, 10:15, M3 (M234)

Given a random loop ensemble in some domain on the plane, we can define the corresponding nesting field at a point by computing the number of loops surrounding this point and subtracting its mean. If the number of loops in all samples of the loop ensemble is bounded by some constant, then we get a well-defined random variable pointwise. Miller, Watson and Wilson have shown that, applying a suitable regularization procedure, one can extend this definition to the conformal loop ensemble with parameter k (CLE(k)) for all 8/3Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)

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

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