Matematiikan ja systeemianalyysin laitos

# Esitelmiä, seminaareja ja väitöksiä

* Seuraavan viikon tapahtumat merkitty tähdellä

Asadollah Aghajani
Regularity of stable solutions to elliptic PDEs and Gelfand-type problems II
* Today * Wednesday 01 February 2023,   12:15,   M3 (M234)
Seminar on analysis and geometry

Rahinatou Yuh Njah
Ring/Polynomial learning with errors (RLWE/PLWE): Equivalence and attacks
* Today * Wednesday 01 February 2023,   16:15,   M3 (M234)
ANTA Seminar

Petri Laarne (University of Helsinki)
Almost sure solution of nonlinear wave equation: from donut to plane
* Tuesday 07 February 2023,   10:15,   M2 (M233)
I discuss the recent preprint [arXiv:2211.16111] of Nikolay Barashkov and I, where we show the almost sure well-posedness of a deterministic nonlinear wave equation (cubic Klein-Gordon equation) on the plane. Here "almost sur" is in respect to the \\\\phi^4 quantum field theory. I briefly introduce the invariant measure argument and outline the solution on 2D torus due to Oh and Thomann. I then explain our main contributions: extension of periodic solutions to infinite volume, and a weaker result for nonlinear Schrödinger equation. The viewpoint is functional-analytic with a dash of probability.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Wontae Kim
TBA
Wednesday 08 February 2023,   12:15,   M3 (M234)
Seminar on analysis and geometry

Prof. William Mance, University of Adam Mickiewicz in Poznan
Normal numbers
Wednesday 08 February 2023,   16:15,   M3 (M234)
Informally, a real number is normal in base b if in its b-ary expansion all digits and blocks of digits occur as often as one would expect them to uniformly at random. Borel introduced normal numbers in 1909 and proved that Lebesgue-almost every real number is normal in all bases b \geq 2. Even though this shows that, in some sense, normal numbers are "typical," no example of a number normal in all bases was given until 1939 by Turing. In the last 100 years, the study of normal numbers has spread over a wide breadth of seemingly unrelated disciplines. Normality is closely related to number theory, ergodic theory, theoretical computer science, probability theory, fractal geometry, descriptive set theory, and others areas of math. We will explore the basic properties of normal numbers and surprising connections they have, depending on the interest of the audience.
ANTA Seminar

Prof. Anita Schöbel (RPTU Kaiserslautern and Fraunhofer ITWM)
Robust multi-objective optimization
Tuesday 14 February 2023,   15:15,   U6 (U149)
Most real-world optimization problems contain parameters which are not known at the time a decision is to be made. In robust optimization one specifies the uncertainty in a scenario set and tries to hedge against the worst case. Classical robust optimization aims at finding a solution which is best in the worst-case scenario. It is a well-studied concept but it is known to be very conservative: A robust solution comes with a high price in its nominal objective function value. This motivated researchers to introduce less conservative robustness concepts in the last decade. Moreover, many real-world problems involve not only one, but multiple criteria. While robust single-objective optimization has been investigated for 25 years, robust multi-objective optimization is a new field in which already the definition of "robust" is a challenge. In the talk, several robustness concepts will be discussed and illustrated at applications from public transport.

Panu Lahti (Chinese Academy of Sciences)
TBA
Wednesday 22 February 2023,   12:15,   M3 (M234)
Seminar on analysis and geometry

Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Monday 06 March 2023,   09:30,   Riihi (Y225a)
Further information

Stephen Moore (Institute of Mathematics Polish Academy of Sciences)
TBA
Tuesday 07 March 2023,   10:15,   M2 (M233)
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Ethan Sussman (MIT)
TBA
Tuesday 07 March 2023,   11:15,   M2 (M233)
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Ethan Sussman (MIT)
TBA
Tuesday 14 March 2023,   10:15,   M2 (M233)
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Dr. David Karpuk, WithSecure
Recent progress in secure distributed computation
Wednesday 15 March 2023,   16:15,   M3 (M234)
ANTA Seminar

Peter Kristel (Bonn)
TBA
Tuesday 11 April 2023,   10:15,   M2 (M233)
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Monday 17 April 2023,   09:30,   Riihi (Y225a)
Further information

Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Tuesday 16 May 2023,   09:30,   Riihi (Y225a)
Further information

Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Friday 16 June 2023,   09:30,   Riihi (Y225a)
Further information

## Past events

Tuomas Kelomäki
Using discrete Morse theory algebraically Part 2
Tuesday 31 January 2023,   14:00,   M237
Algebra and discrete mathematics seminar

Kalle Koskinen (University of Helsinki)
Infinite volume states of the mean-field spherical model in a random external field
Tuesday 31 January 2023,   10:15,   M2 (M233)
One method of introducing external randomness to a Gibbs state, as opposed to the internal randomness of the Gibbs state itself, is to perturb the Hamiltonian with a term corresponding to the coupling of a random external field to the system. For the mean-field spherical model, the corresponding perturbed model can be exactly solved, in some sense, in the infinite volume limit. In this talk, we will introduce, motivate, and present some constructions and results concerning the so-called infinite volume metastases of the mean-field spherical model in a random external field. The aim of this talk is to present the general theory of disordered systems as it pertains to this particular model, and highlight the particular aspects of this model which lead to its curious behaviour as a disordered system. This talk is based on work in a recently accepted paper to appear in the Journal of Statistical Physics.
Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Petri Laarne (University of Helsinki)
Almost sure solution of nonlinear wave equation: from donut to plane
Wednesday 25 January 2023,   20:19,   M2 (M233)

Prof. Alexandru Paler
Graph states and the challenges for efficient quantum circuit compilation
Wednesday 25 January 2023,   16:15,   M3 (M234)
Graphs can be used as a diagrammatic representation of entangled states: vertices represent qubits, and edges are the entangling gates performed between the qubits. Arbitrary quantum circuits can be compiled into a fault-tolerant gate set, and the resulting circuit can be reformulated as a graph state. Such graphs can be manipulated by local operations (single qubit/vertex gates) such that edges are added and removed in a well defined manner during a process called local complementation. The latter might have interesting applications for the optimisation of (fault-tolerant) quantum circuits, quantum communication networks and in general whenever, either: a) there is a need to minimize the number of edges (entangling gates) without affecting the functionality of the state, or b) the state has to be embedded into a quantum hardware architecture that has a different connectivity. This talk is partially based on the work from https://arxiv.org/abs/2209.07345
ANTA Seminar

Asadollah Aghajani
Regularity of stable solutions to elliptic PDEs and Gelfand-type problems I
Wednesday 25 January 2023,   12:15,   M3 (M234)
Seminar on analysis and geometry

Tuomas Kelomäki
Using discrete Morse theory algebraically
Tuesday 24 January 2023,   14:00,   M237
This is an introductory talk on discrete Morse theory and especially on Sköldberg's algebraic formulation of it. The goal is to learn the method through several examples. If the time permits, we will also derive finite versions of several classical results in homological algebra from the theory.
Algebra and Discrete Mathematics Seminar (Boege, Orlich)

Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Friday 20 January 2023,   09:30,   Riihi (Y225a)
Further information

Wilmar Bolanos
The trace form over cyclic number fields
Wednesday 18 January 2023,   16:15,   M3 (M234)
For a given number field K, the integral trace form of K is the quadratic form defined by the trace operator Tr_K/Q(x^2) over the ring of integers of K. In the mid 80's Conner and Perlis showed that for cyclic number fields of prime degree p the isometry class of integral trace is completely determined by the discriminant. The main objective of this talk is to discuss the principal aspects of Conner and Perlis' work and a completed generalization for tame cyclic number fields of arbitrary degree. Furthermore, for such fields, we give an explicit description of a Gram matrix of the integral trace in terms of the discriminant of the field.
ANTA Seminar

Tuomas Sahlsten
PDEs and dynamics
Wednesday 18 January 2023,   12:15,   M3 (M234)
In these talks we will discuss various methods how the theory of dynamical systems can be used to study PDEs such as wave- or Schrödinger equation on planar domains or manifolds. The talks are more an introduction to the ideas, and we try not to assume any background knowledge on the concepts discussed. In the first talk we will focus on 2D surfaces without boundary, where the dynamics is given by the geodesic flow. Here a pre-trace formula due to Selberg allows us to connect eigenfunctions of the Laplacian and the lengths of the periodic orbits of the dynamics. We then outline how number theoretic assumptions on the surface or randomly sampling the surfaces helps to control the complicated periodic orbit structure.
Seminar on analysis and geometry

Camilla Hollanti
Capacity of private information retrieval from coded and colluding servers (online talk at the Technion Coding Theory Seminar)
Wednesday 11 January 2023,   16:30,   Zoom
Further information
Private information retrieval (PIR) addresses the question of how to retrieve data items from a database or cloud without disclosing information about the identity of the data items retrieved. The area has received renewed attention in the context of PIR from coded storage. Here, the files are distributed over the servers according to a storage code instead of mere replication. Alongside with the basic principles of PIR, we will review recent capacity results and demonstrate the usefulness of the so-called star product PIR scheme. The talk is based on joint work with Ragnar Freij-Hollanti, Oliver Gnilke, Lukas Holzbaur, David Karpuk, and Jie Li.
Technion Coding Theory Seminar/ANTA Seminar

René Langøen (University of Bergen)
The direct monodromy problem and isomonodromic deformations for the Rabi model
Tuesday 10 January 2023,   10:15,   M2 (M233)
We discuss the local and global solutions of the Rabi model in Garnier form, a linear system of first order differential equations, with complex rational coefficients. The analytic continuation of the local solutions are described by a monodromy group, which gives a matrix representation of the fundamental group of the punctured Riemann sphere. A detailed geometric description of linear systems of first order differential equations is given, in terms of a local family of connection forms on a principal bundle. The geometric description reveals the Frobenius integrability conditions, which are used to obtain necessary and sufficient conditions for an isomonodromic deformation of the Rabi model.
mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Emil Verkama
Repairing the universality theorem for 4-polytopes
Monday 09 January 2023,   11:00,   M2 (M233)
Master's thesis presentation

Jarno Maaninen
Bayesian experimental design for magnetorelaxometry imaging
Thursday 05 January 2023,   11:00,   M3 (M234)
Master's thesis presentation

Saara Vestola
Enhancement of data veracity for preamble signature ID classification in PRACH, Master thesis talk
Tuesday 20 December 2022,   11:00,   M237

Oscar Kivinen (EPFL, Lausanne)
Plane curves: a bridge between number theory, knots, and physics
Friday 16 December 2022,   15:30,   M237
Plane curves are some of the simplest classical algebro-geometric objects, that most of us encounter in middle school (over the real numbers). Especially their singularity theory remains a source of many interesting discoveries. For example, it turns out many moduli spaces of sheaves on singular plane curves are related to 1) arithmetic problems arising in the Langlands program 2) physics of some 3d/4d supersymmetric gauge theories. On the other hand, in most cases a lot of data about the singularities is controlled by the knots arising as their links, and one may ask how the relevant knot theory is reflected in the themes 1) and 2) above. I will give an introduction to plane curves and discuss the relation to 1) and possibly 2), highlighting a recent result about "orbital integrals on p-adic groups (obtained by myself and Tsai) where the topology of the singularities informs the arithmetic. Little background knowledge will be required, apart from knowing what knots, finite fields, and the general linear group are.
Algebra and Discrete Mathematics Seminar

Toni Annala (Institute for Advanced Study)
Topologically protected tricolorings
Friday 16 December 2022,   14:00,   M237
Topological vortices are codimension-one topological defects that arise in various physical systems, such as liquid crystals, Bose--Einstein condensates, and vacuum structures of Yang--Mills theories. I will explain how, under certain homotopical assumptions that are satisfied in many realistic systems, topological vortex configurations admit faithful presentations in terms of colored link diagrams. The most well-known coloring scheme of links is given by tricolorings: each arc of the link diagram is colored by one of three possible colors (red, green, or blue) in such a way that, in each crossing, either all arcs have the same color, or all arcs have a different color. A tricolored link is topologically protected if it cannot be transformed into a disjoint union of unlinked simple loops by a sequence of color-respecting isotopies and color-respecting local cut-and-paste operations. The latter operations are referred to as allowed local surgeries. We use equivariant bordism groups of three-manifolds to construct invariants of colored links that are conserved in allowed local surgeries, and employ the invariant to classify all tricolored links up to local surgeries. The talk is based on joint work with Hermanni Rajamäki, Roberto Zamora Zamora, and Mikko Möttönen.
Algebra and Discrete Mathematics Seminar

Tuomas Tuukkanen (Princeton & Aalto)
Fermionic Fock Spaces in Conformal Field Theory (MSc thesis presentation)
Friday 16 December 2022,   11:00,   M3 (M234)
mathematical physics seminar (Kytölä / Peltola / Sahlsten)

Vivian Healey (Texas State University)
Loewner evolution, Dyson Brownian motion, and tree embeddings
Thursday 15 December 2022,   10:15,   M3 (M234)
The Loewner equation gives a correspondence between curves in the upper half-plane (or disk) and continuous real functions (called the driving function for the equation). When the driving function is Brownian motion, the result is Schramm-Loewner Evolution (SLE). In this talk, we will discuss links between multiple Loewner evolution and Dyson Brownian motion. First, we show that multiple radial SLE is generated by Dyson Brownian motion on the circle. Second, we show that in the chordal case, scaling the Brownian term to 0 in a branching Dyson Brownian motion generates tree embeddings in the halfplane. If time allows, we will also discuss the Dyson superprocess, which is the scaling limit of this driving measure when the branching structure is conditioned to converge to the continuum random tree. (Joint work with Gregory Lawler and Govind Menon)
mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Anne Schreuder (Cambridge University)
On Lévy-driven Loewner Evolutions
Thursday 08 December 2022,   10:15,   Y405
This talk is about the behaviour of Loewner evolutions driven by a Lévy process. Schramm's celebrated version (Schramm-Loewner evolution), driven by standard Brownian motion, has been a great success for describing critical interfaces in statistical physics. Loewner evolutions with other random drivers have been proposed, for instance, as candidates for finding extremal multifractal spectra, and some tree-like growth processes in statistical physics. Questions on how the Loewner trace behaves, e.g., whether it is generated by a (discontinuous) curve, whether it is locally connected, tree-like, or forest-like, have been partially answered in the symmetric alpha-stable case. We consider the case of general Levy drivers. Joint work with Eveliina Peltola (Aalto and Bonn).
mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Delara Behzad (Aalto University)
On Schubert derivation and applications
Thursday 01 December 2022,   10:15,   Y405
mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Okko Makkonen
Complexity of matrix multiplication
Wednesday 30 November 2022,   16:15,   M3 (M234)
The complexity of matrix multiplication represents the number of operations needed to compute a matrix product in the asymptotic limit. The first advance in asymptotic complexity was made in 1969 when Strassen introduced an algorithm that is capable of computing the product of two N × N matrices with O(N^{2.81}) operations, which is better than the naive algorithm that takes O(N^3) operations. The current record is an algorithm that is able to compute the product using just O(N^{2.372}) operations. We present the basic tools that are used to analyze this problem and present an algorithm that is even better than the Strassen algorithm. This includes studying the matrix multiplication tensor, its rank, and the so-called border rank.
ANTA Seminar

Lauri Särkiö
Parabolic Lipschitz truncation
Wednesday 30 November 2022,   12:15,   M3 (M234)
Seminar on analysis and geometry

Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Wednesday 30 November 2022,   09:30,   Riihi (Y225a)
Further information

Dissertation
DI, VTM Emma-Karoliina Kurki
Weight theory on bounded domains and metric measure spaces
Friday 25 November 2022,   12:00,   M1 (M232)

ForAlli
Ad hoc formalization (ForAlli monthly special)
Thursday 24 November 2022,   16:15,   M2 (M233)
ForAlli

Delara Behzad (Aalto University)
On Schubert derivation and applications
Thursday 24 November 2022,   10:15,   Y405
mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Sheldy Ombrosi
Theory of weights in regular trees
Wednesday 23 November 2022,   12:15,   M3 (M234)
Seminar on analysis and geometry

Olli Huopio
Master Thesis Talk : A sensor fusion algorithm for land vehicle positioning
Monday 21 November 2022,   14:00,   Riihi (Y225a)

Alex Karrila (Åbo Akademi)
The phases of random Lipschitz functions on the honeycomb lattice
Monday 21 November 2022,   11:00,   Y229a
stochastics and mathematical physics seminar (Kytölä, Leskelä, Peltola)

Teemu Lundström
Yamada Polynomials from Transfer-Matrix Methods
Friday 18 November 2022,   14:15,   M237
Spatial graphs are graphs that are embedded in three-dimensional space. They are in some sense a generalization of knots and the theory of spatial graphs is closely related to knot theory. In knot theory, one can distinguish between two inequivalent knots by computing some algebraic invartiant of them, for example, the Jones polynomial. Similar invariants have been invented for spatial graphs and one important such invariant is the Yamada Polynomial, first introduced by Shuji Yamada in 1989. In this talk I will introduce spatial graphs and the Yamada polynomial defined for them. I will focus on computing the polynomial for certain classes of graphs that have a layer-like structure. Computing the Yamada polynomial for a spatial graph can be computationally demanding, but by focusing on such graphs we are able to apply the so called transfer-matrix method with which we are able to find a closed form formula for two infinite families of spatial graphs.
Algebra and Discrete Mathematics Seminar

Johan Lindell (first speaker), Salla Tanskanen (second speaker), Matias Koponen (third speaker, topic presentation)
Bachelor's thesis presentations
Wednesday 16 November 2022,   15:15,   M2 (M233)
Further information

Kim Myyryläinen
A weighted fractional Poincare inequality, Part 2
Wednesday 16 November 2022,   12:15,   M3 (M234)
Seminar on analysis and geometry

Pengmin Hua (PhD midterm review talk)
Optimal control of indoor thermal comfort based on district heating with thermal energy storage
Monday 14 November 2022,   11:00,   Y229c
PhD midterm review talks

Kirthivaasan Puniamurthy (PhD midterm review talk)
On proving adaptive security for Yao's garbling scheme
Monday 14 November 2022,   10:00,   Y229c
PhD midterm review talks

Niklas Miller (PhD midterm review talk)
Lattice point enumeration and wiretap decoding probability estimates
Monday 14 November 2022,   09:00,   Y229c
PhD midterm review talks

Paul Van Dooren
Social Balance, Gossiping and Riccati Equations
Friday 11 November 2022,   13:30,   M203
Social networks with positive and negative links often split into two antagonistic factions. Examples of such a split abound: revolutionaries versus an old regime, Republicans versus Democrats, Axis versus Allies during the second world war, or the Western versus the Eastern bloc during the Cold War. Although this structure, known as social balance, is well understood, it is not clear how such factions emerge. An earlier model could explain the formation of such factions if reputations were assumed to be symmetric. We show this is not the case for non-symmetric reputations, and propose an alternative model which (almost) always leads to social balance, thereby explaining the tendency of social networks to split into two factions. In addition, the alternative model may lead to cooperation when faced with defectors, contrary to the earlier model. The difference between the two models may be understood in terms of the underlying gossiping mechanism: whereas the earlier model assumed that an individual adjusts his opinion about somebody by gossiping about that person with everybody in the network, we assume instead that the individual gossips with that person about everybody. It turns out that the alternative model is able to lead to cooperative behavior, unlike the previous model.

Osama Abuzaid (PhD midterm review talk)
On self avoiding random walks and Schramm Loewner evolutions
Thursday 10 November 2022,   13:00,   M2 (M233)
PhD midterm review talks

Serge Kas Hanna
Introduction to federated learning
Wednesday 09 November 2022,   16:15,   M3 (M234)
Distributed learning (DL) is a machine learning (ML) setting where several parties (e.g., mobile devices or computer clusters) collaboratively train an ML model under the orchestration of a central entity. DL can be applied in the case where the data is centralized, i.e., owned by a single entity, and also when the data is decentralized, i.e., owned by several parties. In the centralized data setting, DL is attractive when the data is too large for one entity to process by itself. Here, a central entity can make the learning process tractable by distributing the data across several helper nodes and outsourcing part of the computations. The DL setting can also present itself naturally when the training data is owned by several decentralized parties. Federated learning (FL) is a branch of DL where the data is decentralized and owned by several independent parties who agree to collaboratively train an ML model but want to maintain the privacy of their local data. In addition to privacy, communication efficiency is also a first-order concern in FL, especially when the data is owned by several mobile devices operating over a network. In this talk, I will introduce distributed learning and federated learning and discuss some of the challenges associated with such distributed systems. I will also explain how basic optimization algorithms, such as gradient descent, can be applied to distributed learning and adapted to the setting of federated learning.
ANTA Seminar

Muhammad Ardiyansyah (Aalto University)
Dimensions of the factor analysis model and its higher order generalizations
Wednesday 09 November 2022,   15:00,   M2 (M233)
The factor analysis model is a statistical model where a certain number of hidden random variables, called factors, affect linearly the behaviour of another set of observed random variables, with additional random noise. The main assumption of the model is that the factors and the noise are Gaussian random variables. In this talk, we do not assume that the factors and the noise are Gaussian, hence the higher order moment and cumulant tensors of the observed variables are generally nonzero. This motivates the generalized notion of kth-order factor analysis model, that is the family of all random vectors in a factor analysis model where the factors and the noise have finite and possibly nonzero moment and cumulant tensors up to order k. This subset may be described as the image of a polynomial map onto a Cartesian product of symmetric tensor spaces. We provide its dimension and conditions under which the image has positive codimension. This talk is based on joint work with Luca Sodomaco.
Algebra and Discrete Mathematics Seminar

Kim Myyryläinen
A weighted fractional Poincare inequality, Part 1
Wednesday 09 November 2022,   12:15,   M3 (M234)
Seminar on analysis and geometry

talk canceled / rescheduled to a later time
talk canceled / rescheduled to a later time
Thursday 03 November 2022,   10:15,
mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Wontae Kim
Existence theory for the parabolic double phase problem
Wednesday 02 November 2022,   12:15,   M3 (M234)
The classical approach in existence theory does not give the existence and uniqueness of the weak solution to this problem since the function space for the gradient of weak solutions involves the time variable. We discuss the recent approach to the existence theories and how the regularity results are able to be applied to the existence theory.
Seminar on analysis and geometry

ForAlli
Views on formalization of mathematics
Thursday 27 October 2022,   16:15,   M2 (M233)
We will watch the recordings from Microsoft Research Summit session "Empowering mathematicians with technology" (provided they are available).
ForAlli

Ellen Powell (Durham University)
Characterising the Gaussian free field
Thursday 27 October 2022,   10:15,   Y405
I will discuss recent approaches to characterising the Gaussian free field in the plane, and in higher dimensions. The talk will be based on joint work with Juhan Aru, Nathanael Berestycki, and Gourab Ray.
mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Thursday 27 October 2022,   09:30,   Riihi (Y225a)
Further information

Tapani Matala-aho
A criterion for irrationality
Wednesday 26 October 2022,   16:15,   M3 (M234)
Take your favorite real or p-adic number, say Phi. Let us assume there exist nice rational approximations for your number. Then these approximations will be written as numerical linear forms. We will give a criterion for the irrationality of your number by using a sequence of these numerical linear forms. Moreover, a lower bound is given for the quantity N*Phi-M, where N, M are integers and N is nonzero. However, it is a challenge to find an appropriate sequence of numerical linear forms for an arbitrary number. In this lecture we will not consider this problem. But we note, if your number is a value of a Taylor series or a (generalized) continued fraction, then we may build a candidate sequence from the truncated series or Padé approximations or use the convergents of the continued fraction.
ANTA Seminar

Asadollah Aghajani
Liouville type results for quasilininear elliptic equations with gradient dependence
Wednesday 26 October 2022,   12:15,   M3 (M234)
Seminar on analysis and geometry

Lisa Nicklasson (Università di Genova)
Ideals arising from Bayesian networks
Thursday 20 October 2022,   11:15,   Zoom
Further information
A Bayesian network is a statistical model which can be presented graphically by a directed acyclic graph. The nodes in the graph are discrete random variables, and the edges encode dependencies between the variables. Bayesian nets can also be described algebraically as varieties of homogeneous prime ideals. In this talk we will discuss connections between algebraic properties of such ideals and combinatorial properties of the graphs. In particular, we would like to understand when the variety is toric and when the ideal is quadratic.
Algebra and Discrete Mathematics Seminar

Caroline Wormell (Sorbonne, Paris)
Decay of correlations for conditional measures and some applications
Thursday 20 October 2022,   10:15,   Y228b
The forward evolution of chaotic systems notoriously washes out inexact information about their state. When advected by a chaotic system, physically relevant measures therefore often converge to some reference measure, usually the SRB measures. This property implies various important statistical behaviours of chaotic systems. In this talk we discuss the behaviour of slices of these physical measures along smooth submanifolds that are reasonably generic (e.g. not stable or unstable manifolds). We give evidence that such conditional measures also have exponential convergence back to the full SRB measures, even though they lack the regularity usually required for this to occur (for example, they may be Cantor measures). Using Fourier dimension results, we will prove that CDoC holds in a class of generalised baker's maps, and we will give rigorous numerical evidence in its favour for some non-Markovian piecewise hyperbolic maps. CDoC naturally encodes the idea of long-term forecasting of systems using perfect partial observations, and appears key to a rigorous understanding of the emergence of linear response in high-dimensional systems.
Mathematical physics seminar

Emanuel Carneiro (ICTP Trieste)
On sign Fourier uncertainty
Wednesday 19 October 2022,   12:15,   M3 (M234)
The quest to find the sharp forms of functional inequalities has always been a beautiful and challenging theme in analysis. In this talk we will discuss a few sharp inequalities related to Fourier uncertainty principles. We address the problem of prescribing the sign of a function and its Fourier transform at infinity, and doing this in an optimal way (in an appropriate sense). This phenomenon was introduced by Bourgain, Kahane and Clozel in 2010 under the name of "sign Fourier uncertainty", and brings interesting connections to the sphere packing problem.
Seminar on analysis and geometry

Gregory Arone (Stockholm University)
The S_n-equivariant topology of partition complexes
Thursday 13 October 2022,   11:15,   M2 (M233)
Let n be a positive integer. Consider the poset of partitions of the set {1, ... , n}, ordered by refinement. Its geometric realization is a topological space that encodes information about the combinatorial properties of the partition poset. We obtain a sequence of spaces T_1, T_2, ..., T_n, ...,. In fact it is a symmetric sequence of spaces, by which we mean that the n-th space T_n has a natural action of the symmetric group S_n. These spaces have many interesting properties, and they arise in a number of places in mathematics, from the study of Lie algebras to algebraic topology to mathematical biology. We will survey some of the properties and applications of the spaces T_1, ..., T_n,..., focusing on the properties of the action of the symmetric groups. In particular, we will give a "branching rule" that describes the restriction of T_n to a Young subgroup of S_n (this is joint work with Lukas Brantner). The proof uses discrete Morse theory, and it generalizes many previous results. I will show some applications and some open questions.
Algebra and Discrete Mathematics Seminar

Augustin Lafay (Aalto)
Geometrical lattice models, algebraic spiders and applications to random geometry
Thursday 13 October 2022,   11:00,   Y228b
mathematical physics seminar (Kytölä / Peltola / Sahlsten)

Milo Orlich (Aalto)
Asymptotic results on Betti numbers of edge ideals of graphs via critical graphs
Thursday 06 October 2022,   11:15,   M2 (M233)
To any graph G one can associate its edge ideal. One of the most famous results in combinatorial commutative algebra, Hochster's formula, describes the Betti numbers of the edge ideal in terms of combinatorial information on the graph G. More explicitly, each specific Betti number is given in terms of the presence of certain induced subgraphs in G. The machinery of critical graphs, relatively recently introduced by Balogh and Butterfield, deals with characterizing asymptotically the structure of graphs based on their induced subgraphs. In a joint work with Alexander Engström, we apply these techniques to Betti numbers and regularity of edge ideals. We introduce parabolic Betti numbers, which constitute a non-trivial portion of the Betti table. Usually, the vanishing of a Betti number has little impact on the rest of the Betti table. I this talk I will describe our main results, which show that on the other hand the vanishing of a parabolic Betti number determines asymptotically the structure and regularity of the graphs with that Betti number equal to zero.
Algebra and Discrete Mathematics Seminar

Mikhail Basok (University of Helsinki)
Dimer model on Riemann surfaces and compactified free field
Thursday 06 October 2022,   11:00,   Y228b
We consider a random height function associated with the dimer model on a graph embedded into a Riemann surface. Given a sequence of such graphs approximating the surface in a certain sense we prove that the corresponding sequence of height functions converges to the compactified free field on the surface. To establish this result we follow approach developed by Dubédat: we introduce a family of observables of the model which can be expressed as determinants of discrete perturbed Cauchy-Riemann operators, we analyze the latter using Quillen curvature formula.
mathematical physics seminar (Kytölä / Peltola / Sahlsten)

Ragnar Freij-Hollanti
Combinatorial derived matroids
Wednesday 05 October 2022,   16:15,   M3 (M234)
Let M be an arbitrary matroid. In the 70's, Gian-Carlo Rota and Henry Crapo asked for a natural definition of a matroid dM that has as its ground set the collection of (co)circuits of M. We will first survey two earlier such constructions, namely the Exley-Wang derived matroid, and (co)-adjoint lattices. These constructions have several nice properties, but are only defined for certain special classes of matroids, and are not necessarily unique. We will then introduce a recent construction by the speaker, called combinatorial derived matroids. These are uniquely defined for any matroid M, but computing them has proven an elusive task. We will give all the definitions, compute some illuminating examples, and offer a few conjectures. This is joint work with Relinde Jurrius and Olga Kuznetsova.
ANTA Seminar

Mohamed Serry (University of Waterloo)
Physics of phonation offset: towards understanding relative fundamental frequency observations
Thursday 29 September 2022,   13:15,   M2 (M233)
Relative fundamental frequency (RFF) is a promising assessment technique for vocal pathologies. Herein, we explore the underlying laryngeal factors dictating RFF behaviors during phonation offset. To gain physical insights, we investigate a simple analytical impact oscillator model and follow that with a numerical study using the well-established bodycover model of the vocal folds (VFs). Study of the impact oscillator suggests that the observed decrease in fundamental frequency during offset is due, at least in part, to the decrease in collision forces during abduction. Moreover, the impact oscillator elucidates a correlation between sharper drops in RFF and increased stiffness of the VFs, supporting experimental RFF studies. The body-cover model study further emphasizes the correlation between the drops in RFF and collision forces and displays the potential role of the cricothyroid muscle to mitigate the RFF reduction.
Applied Mathematics / David Radnell

Tobias Boege (Aalto University)
Ingleton's inequality for entropies
Wednesday 28 September 2022,   14:00,   Y307
The Ingleton inequality is a necessary condition for a matroid to be linearly representable and it comes in the form of a linear inequality in its rank function. In a probability-theoretic reinterpretation of the inequality, linear subspaces are replaced by discrete random variables and ranks by Shannon entropies. In this setting, the Ingleton inequality no longer holds universally for representable rank functions but only if additional linear constraints are assumed. In this talk, I give an overview of these so-called conditional Ingleton inequalities, their historical roots and my own contribution to finishing their classification for four discrete random variables.
Algebra and discrete mathematics seminar

Heini Kanerva
Master thesis talk : Detection of spruces damaged by the European spruce bark beetle from unmanned aerial vehicle imagery using deep learning
Friday 23 September 2022,   13:00,   M134
Detection of spruces damaged by the European spruce bark beetle from unmanned aerial vehicle imagery using deep learning

Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Friday 23 September 2022,   09:30,   Riihi (Y225a)
Further information

Matematiikan kandidaattiseminaari / Bachelor seminar in mathematics
Friday 23 September 2022,   09:15,   Y308
Further information

Joe Thomas (Durham)
Quantum Unique Ergodicity for random bases on Cayley Graphs
Monday 19 September 2022,   14:15,   M3 (M234)
The quantum unique ergodicity conjecture is a long-standing open problem concerning the extent to which eigenfunctions of the Laplacian on a manifold are delocalised in the presence of ergodic classical dynamics. Similar enquires have also taken place in the discrete setting which can be seen as a toy model for the continuous case. In this talk, I will review notions of quantum (unique) ergodicity in the setting of regular graphs. I will then discuss some recent joint work with Michael Magee (Durham) and Yufei Zhao (MIT) where we show the existence of an abundance of bases of eigenfunctions that satisfy a quantum unique ergodicity result in the setting of Cayley graphs.
Seminar / Tuomas Sahlsten

Elif Sacikara
q-Analogues of Matroids
Wednesday 14 September 2022,   16:15,   M3 (M234)
In combinatorics, a q-​analog of a discrete structure is defined by replacing finite sets with finite dimensional vector spaces. On the other hand, matroids are defined as a combinatorial abstraction of several objects such as linearly independent vectors or graphs. In this talk, we first define a matroid with certain equivalent axiomatic definitions by supporting them with examples. Then we discuss their q-​analogs by comparing differences and similarities with the classical case. Finally, as a construction and an application of a q-​matroid, we mention their relation with a q-​analog of other combinatorial objects called designs, and state some open questions. This work is a part of the research project supported by Women in Numbers - Europe.
ANTA Seminar

Pavlo Yatsyna
How many variables will it take?
Wednesday 07 September 2022,   16:15,   M3 (M234)
This talk will be about the representation of integers by quadratic forms. We will survey what is known about the quadratic forms that represent all eligible integers of totally real number fields. It will include the recent results, from the joint work with Vitezslav Kala, Dayoon Park, and Blazej Zmija, on the density of real quadratic number fields that have a universal quadratic form with a fixed number of variables.
ANTA Seminar

Matematiikan kandidaattiseminaari / Bachelor seminar in mathematics
Friday 02 September 2022,   09:15,   M1 (M232)
Further information

Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Friday 26 August 2022,   09:30,   Riihi (Y225a)
Further information

Guilherme Sales Santa Cruz
On Assessing Valuation Robots (Master's thesis presentation)
Monday 15 August 2022,   15:15,   Zoom
Further information

Dr Vinay Kumar BR (INRIA Sophia Antipolis)
A probabilistic broadcast mechanism on random geometric graphs
Friday 12 August 2022,   11:00,   M3 (M234)
We consider the problem of energy-efficient broadcasting on homogeneous random geometric graphs (RGGs) within a large finite box around the origin. A source node at the origin encodes $k$ data packets of information into $n\ (>k)$ coded packets and transmits them to all its one-hop neighbors. The encoding is such that, any node that receives at least $k$ out of the $n$ coded packets can retrieve the original $k$ data packets. Every other node in the network follows a probabilistic forwarding protocol; upon reception of a previously unreceived packet, the node forwards it with probability $p$ and does nothing with probability $1-p$. We are interested in the minimum forwarding probability which ensures that a large fraction of nodes can decode the information from the source. We deem this a \emph{near-broadcast}. The performance metric of interest is the expected total number of transmissions at this minimum forwarding probability, where the expectation is over both the forwarding protocol as well as the realization of the RGG. In comparison to probabilistic forwarding with no coding, our treatment of the problem indicates that, with a judicious choice of $n$, it is possible to reduce the expected total number of transmissions while ensuring a near-broadcast. Techniques from continuum percolation and ergodic theory are used to characterize the probabilistic broadcast algorithm. Joint work with Navin Kashyap and D. Yogeshwaran
Aalto Stochastic & Statistics Seminar / Lasse Leskelä

Dr. Matteo Mucciconi (University of Warwick)
Some recent results in Integrable Probability
Tuesday 02 August 2022,   14:00,   M3 (M234)
In the last 25 years the study of solvable growth models related to the Kardar-Parisi-Zhang (KPZ) stochastic partial differential equation uncovered connections with a number of seemingly unrelated fields including representation theory, combinatorics, Integrable Systems and so on. This program, commonly referred to as Integrable Probability, delivered a host of remarkable successes, including the characterization of new universal processes or the explicit solution of the KPZ equation under certain initial data. In this talk I will review some of these progresses, highlighting some recent ones.
Mathematical physics seminar / Shinji Koshida

Vili Nieminen
Local Poisson's Equation Approximation by Probabilistic Algorithm (Master Thesis talk)
Thursday 21 July 2022,   14:00,   M203

Konsta Holopainen
On predicting performance in heart failure patients (Master's thesis presentation)
Monday 27 June 2022,   14:15,   M3 (M234)

Tuomo Valtonen (BSc presentation)
List-decoding of Reed-Solomon codes
Friday 17 June 2022,   11:00,   M1 (M232)
ANTA Seminar

Olli Pasanen (Patria)
On Bayesian methods for program authorship attribution
Friday 17 June 2022,   10:15,   M3 (M234)

Matematiikan kandiseminaari / Bachelor seminar (mathematics)
Friday 17 June 2022,   09:15,   M1 (M232)
Further information

Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Wednesday 15 June 2022,   09:30,   Riihi (Y225a)
Further information
The link to the zoom-meeting is available from Juho Roponen

Matematiikan kandiseminaari / Bachelor seminar (mathematics)
Friday 10 June 2022,   09:15,   M240
Further information
Kandityöesitelmät: (n. 9.15) Henri Lahdelma: Lämpöyhtälön ratkaisujen sileys ja derivaattojen estimaatit. (n. 9.45) Kasper Lahtonen: Investing with hidden Markov models. (n. 10.15) Leo Laitinen: Homeogeenisen kappaleen MRI-signaali yleisteyillä gradienttikentillä. Aihe-esittelyt (kandityöesitelmien jälkeen): Joona Lindell, Teemu Korhonen, Tommi Huhtinen.

Joanna Bisch (University of Lille)
Functions of symmetric Toeplitz matrices
Tuesday 07 June 2022,   14:15,   M3 (M234)

Elmer Bergman (Aalto University)
Connectivity of passive random intersection graphs and their intersection with ErdősRényi graphs
Monday 30 May 2022,   14:15,   M3 (M234)
This thesis studies the connectivity of passive random intersection graphs. In addition to this, it studies the connectivity of an intersection between a passive random intersection graph and an ErdősRényi graph. Random intersection graphs can be used to model many real-life phenomena. For example, social networks and communication in sensor networks can be modelled by random intersection graphs. A random intersection graph is a random graph, where nodes are assigned attributes according to some random process. Two nodes are connected by an edge if they have at least one attribute in common. For a passive random intersection graph, each attribute is given a number according to some probability distribution. Each attribute then chooses that number of nodes, uniformly at random from the whole set of nodes. The chosen nodes are given the respective attribute. Two nodes are thus connected, if at least one attribute chooses them both. This thesis presents zero-one laws on passive random intersection graphs being connected and not having isolated nodes. This thesis also presents zero-one laws on the intersection between a passive random intersection graph and an ErdősRényi graph, being connected and not having isolated nodes.
MSc thesis presentation / Lasse Leskelä

Prof. Andreas Rupp (LUT University)
Partial differential equations on hypergraphs and networks of surfaces: Derivation and hybrid discretizations
Wednesday 18 May 2022,   14:15,   M2 (M233)

Prof. Paul Van Dooren
A voting system with a fixed point  or how to judge the judges
Tuesday 17 May 2022,   14:45,   M1 (M232)
A voting system is presented that is based on an iterative procedure converging to a unique fixed point. The votes expressed by p raters regarding the reputation of n items, go into a p × n voting matrix X, which is possibly sparse when each rater does not evaluate all items. From this matrix X, a unique rating of the considered items is finally obtained via an iterative procedure which updates as well the reputations of the n items and that of the p raters. The proposed method converges linearly to the unique vector of reputations and this for any rating matrix. We also show how it can be used to detect fraudulous voters. We give some possible applications of this voting system.

Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Wednesday 11 May 2022,   09:30,   Riihi (Y225a)
Further information

Joonatan Honkamaa (kandiesitelmä)
Johdatus homomorfisen salauksen menetelmiin ja nykytilaan
Friday 22 April 2022,   09:15,   M1 (M232)
ANTA Seminar

Matematiikan kandiseminaari / Bachelor seminar (mathematics)
Friday 22 April 2022,   09:15,   M1 (M232)
Program: hhttps://mycourses.aalto.fi/course/view.php?id=34597§ion=3

Wontae Kim
Higher integrability of the parabolic double phase system
Wednesday 20 April 2022,   12:15,   M3 (M234)
Seminar on analysis and geometry

Tarmo Kivioja
Master thesis talk: Estimating the covariance of scan registration based on the distribution-to-distribution normal distributions transform
Thursday 14 April 2022,   13:00,   M2 (M233)

Prof. Ivan Blanco-Chacon
Modular repersentations II: potentially diagonalisable modular lifts of large weights
Wednesday 13 April 2022,   15:15,   M3 (M234) and Zoom
Further information
This talk is an exposition of [1], where we produce modular representations of arbitrary weight lifting a given representation of fixed weight satisfying certain local properties at a given prime. This work has its motivation in the Langlands functoriality for GL(2), a topic which we will also comment about. It is highly advisable to have attended the first introductory talk. [1]: Blanco-Chacon, I., Dieulefait, L.: "Potentially diagonalisable modular lifts of large weights". Journal of Number Theory, 228, 188-207 (2021).
ANTA Seminar

Niko Sairo
Paperin laadun ennustamisesta (Master's thesis presentation)
Thursday 07 April 2022,   19:00,   M3 (M234)

Prof. Ivan Blanco-Chacon
On the R/P-LWE equivalence for cyclotomic subextensions and cryptoanalytic implications
Monday 04 April 2022,   12:00,   M3 and Zoom
Further information
NB: different zoom address! In this talk we address the equivalence between the RLWE and the PLWE problems for the maximal totally real subextension of the cyclotomic field of conductor 2^rpq, with p, q primes, joint work with López-Hernanz. These fields have been recently used to cryptoanalyse several cyclotomic instances. Likewise, we will show that these fields are immune under one of the attacks presented by Lauter et al in 2016 against PLWE. If time permits, we will comment our ongoing work towards the generalisation of this equivalence to abelian Q-extensions.
ANTA Seminar

Kristian Moring
Stability for the porous medium system
Wednesday 30 March 2022,   12:15,   M3 (M234)
Seminar on analysis and geometry

Niklas Miller
Lattice-based cryptography: learning with errors over cyclic algebras (part 2)
Wednesday 23 March 2022,   15:15,   M3 (M234) and Zoom
Further information
Since the introduction of the learning with errors (LWE) problem in 2005, various variants of this problem have emerged. Notably, RLWE is a variant which adds a ring structure to LWE samples, to reduce key size, for a potential loss in security. In this talk, I will present an article by Grover, Mendelsohn, Ling and Vehkalahti, where they introduce yet another variant, CLWE, where the samples come from orders of cyclic algebras. CLWE can be seen as a structured variant of module learning with errors (MLWE). CLWE is claimed to provide computational efficiency and security.
ANTA Seminar

Carlos Perez
On the two weight problem for two maximal functions: the case of cubes and the case of rectangles
Wednesday 23 March 2022,   12:15,   M3 (M234)
Seminar on analysis and geometry

Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Thursday 17 March 2022,   09:30,   Kappa (M222)
Further information

Julian Weigt
A Vitali/Besicovitch covering theorem for the boundary
Wednesday 16 March 2022,   12:15,   M3 (M234)
Seminar on analysis and geometry

Rahinatou Njah
Doctoral studies mid-term review talk: Algebraic number theory and applications to security
Friday 11 March 2022,   11:00,   Zoom
Further information
ANTA

Dr. Tapani Matala-aho
Hermite-Thue equation: Padé approximations and Siegel's lemma, Part 4
Wednesday 09 March 2022,   15:15,   M3 and Zoom
Further information
Padé approximations and Siegel's lemma are widely used tools in Diophantine approximation theory. The homogeneous matrix equation representing both methods has an M x (L+1) coefficient matrix, where M is at most L. Due to the Bombieri-Vaaler version of Siegel's lemma, the upper bound of the minimal non-zero solution of the matrix equation can be improved by finding a big common factor of all the M x M minors of the coefficient matrix. Further, in the case M = L, the existence of this common factor is a step towards understanding the nature of the 'twin-type' Hermite-Padé approximations to the exponential function. In this second lecture we reproduce the classical type II Hermite-Padé approximations of the exponential series by computing the homogeneous vector of the L x L minors (Cramer's rule). These minors are Vandermonde-type block determinants which are challenging to unwrap. For that we introduce appropriate determinant calculus tools which have interest of their own sake. Joint work with Louna Seppälä.
ANTA Seminar

Cintia Pacchiano
Stability for quasiminimizers of a (p,q)-Dirichlet integral
Wednesday 09 March 2022,   12:15,   M3 (M234)
Seminar on analysis and geometry

Matematiikan kandiseminaari / Bachelor seminar (mathematics)
Friday 04 March 2022,   09:15,   M237
Program: https://mycourses.aalto.fi/course/view.php?id=34597§ion=3

Emma-Karoliina Kurki
Characterizing A1 and RH-infinity on metric measure spaces
Wednesday 02 March 2022,   12:15,   M3 (M234)
Seminar on analysis and geometry

Uula Ollila
Master Thesis Talk : Accelerating Convolutional Neural Network Inference on Digital Signal Processor
Friday 25 February 2022,   10:00,   Zoom
Further information
https://aalto.zoom.us/j/7736264770

Dr. Tapani Matala-aho
Hermite-Thue equation: Padé approximations and Siegel's lemma, Part 3
Wednesday 23 February 2022,   15:15,   M3 and Zoom
Further information
Padé approximations and Siegel's lemma are widely used tools in Diophantine approximation theory. The homogeneous matrix equation representing both methods has an M x (L+1) coefficient matrix, where M is at most L. Due to the Bombieri-Vaaler version of Siegel's lemma, the upper bound of the minimal non-zero solution of the matrix equation can be improved by finding a big common factor of all the M x M minors of the coefficient matrix. Further, in the case M = L, the existence of this common factor is a step towards understanding the nature of the 'twin-type' Hermite-Padé approximations to the exponential function. In this second lecture we reproduce the classical type II Hermite-Padé approximations of the exponential series by computing the homogeneous vector of the L x L minors (Cramer's rule). These minors are Vandermonde-type block determinants which are challenging to unwrap. For that we introduce appropriate determinant calculus tools which have interest of their own sake. Joint work with Louna Seppälä.
ANTA Seminar

Carlos Perez
Generalized Poincaré Inequalities and Harmonic Analysis
Wednesday 23 February 2022,   12:15,   M3 (M234)
Seminar on analysis and geometry

Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Monday 21 February 2022,   09:30,   Zoom
Further information
The link to the zoom-meeting is available from Juho Roponen

Niklas Miller
Lattice-based cryptography: learning with errors over cyclic algebras (part 1)
Wednesday 09 February 2022,   15:15,   M3 (M234) and Zoom
Further information
Since the introduction of the learning with errors (LWE) problem in 2005, various variants of this problem have emerged. Notably, RLWE is a variant which adds a ring structure to LWE samples, to reduce key size, for a potential loss in security. In this talk, I will present an article by Grover, Mendelsohn, Ling and Vehkalahti, where they introduce yet another variant, CLWE, where the samples come from orders of cyclic algebras. CLWE can be seen as a structured variant of module learning with errors (MLWE). CLWE is claimed to provide computational efficiency and security.
ANTA Seminar

Kim Myyryläinen
A weak Gurov-Reshetnyak class. Part 2
Wednesday 09 February 2022,   12:15,   M3 (M234)
Seminar on analysis and geometry

Dr. Tapani Matala-aho, Niklas Miller, and Rahinatou Njah
Mini Math Days (talks from the Finnish math days)
Wednesday 02 February 2022,   16:15,   M3 (M234) and Zoom
Further information
ANTA Seminar

Kim Myyryläinen
A weak Gurov-Reshetnyak class. Part 1
Wednesday 02 February 2022,   12:15,   M3 (M234)
Seminar on analysis and geometry

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