Matematiikan ja systeemianalyysin laitos

# Esitelmiä, seminaareja ja väitöksiä

* Seuraavan viikon tapahtumat merkitty tähdellä

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)

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

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

Tapani Matala-aho
TBA
Wednesday 19 October 2022,   16:15,   M3 (M234)
ANTA 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

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

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

Wontae Kim
TBA
Wednesday 02 November 2022,   12:15,   M3 (M234)
Seminar on analysis and geometry

Sheldy Ombrosi
TBA
Wednesday 23 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

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

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

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

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.

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

Matteo Allaix
Introduction to Quantum Error Correction (Part 2)
Wednesday 26 January 2022,   15:15,   M3 (M234) and Zoom
Further information
In this seminar, we will first show the Quantum Teleportation algorithm, one of the most important known quantum algorithms. After a short description of quantum channels and quantum noise, we will finally show an example of a 3-qubit quantum error correction algorithm.
ANTA Seminar

Wontae Kim
Some extensions on the higher integrability of the parabolic p-Laplace system
Wednesday 26 January 2022,   12:15,   M3 (M234)
Seminar on analysis and geometry

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

Dr. Tapani Matala-aho
Hermite-Thue equation: Padé approximations and Siegel's lemma, Part 2
Wednesday 19 January 2022,   16:15,   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

Timo Takala
An interesting example of a JNp function
Wednesday 19 January 2022,   12:15,   M3 (M234)
Seminar on analysis and geometry

Olle Hallqvist Elias (Alfréd Rényi Institute of Mathematics)
Interlacements and the GFF
Friday 14 January 2022,   14:00,   Zoom
Further information
mathematical physics, Kytölä & Peltola

Exterior powers, Polynomial rings, and Representation of Lie Algebras
Friday 14 January 2022,   11:00,   Zoom
Further information
I will report on some recent work of myself, A.Contiero and D. Martins about representing lie algebras of vector space endomorphisms on exterior algebras, seeing it as the finite type case of the celebrated DJKM bosonic vertex operator representation of gl_∞(Q).
mathematical physics, Kytölä & Peltola

Olga Chekeres (University of Connecticut)
Quantum Wilson surfaces and topological interactions
Tuesday 04 January 2022,   17:00,   Zoom
Further information
mathematical physics, Kytölä & Peltola

Julien Roussillon (KTH)
Confluence of correlation functions in Liouville theory
Monday 03 January 2022,   11:00,   Zoom
Further information
mathematical physics, Kytölä & Peltola

Okko Makkonen
New schemes for secure distributed matrix multiplication (MSc thesis presentation)
Friday 17 December 2021,   13:00,   M3 (M234) and Zoom
Further information
ANTA Seminar

Perttu Saarela
On coding theory and private information retrieval: A new robust scheme for Reed-Muller codes (MSc thesis presentation)
Friday 17 December 2021,   12:00,   M3 (M234) and Zoom
Further information
ANTA Seminar

MSc Joona Karjalainen (Aalto, candidate) & Prof. Remco van der Hofstad (TU Eindhoven, opponent)
Structure and estimation of network models with overlapping communities (DSc defence)
Friday 17 December 2021,   12:00,   M1 (M232)
Further information
Live video stream: https://aalto.zoom.us/j/65777606406 Abstract: Many types of data in different fields of science can be naturally represented as networks. Social relationships in groups of people, the structure of the internet, and traffic networks can all be understood as collections of nodes and connections between them. Real-world networks often show signs of community structure, i.e., some groups of nodes are more densely connected to each other than to the rest of the nodes. Since communities may emerge through many different mechanisms, it is natural to describe these networks with statistical models where the communities are allowed to overlap. Even in the absence of obvious communities, various other types of structure are commonly observed in data. For example, the degrees of adjacent nodes tend to be correlated, and node pairs have an increased probability of being adjacent if they have common neighbors. This dissertation is concerned with the structure of large and sparse statistical network models with overlapping communities. This structure is described using statistical quantities and distributions and their limits as the number of nodes tends to infinity. The focus is on the asymptotic behavior of subgraph frequencies, joint degree distributions of adjacent nodes, and various summary statistics. New results are proved on their convergence, and exact formulas are provided for their limits. These results lead to new estimators of the model parameters based on counting the frequencies of small subgraphs. The consistency of these estimators is proved under complete or partly incomplete data. The results show that the models have structural similarities with many real-world networks, such as non-trivial clustering, degree correlations, and power laws. This illustrates how some empirical observations on network data can be explained with an underlying overlapping community structure.

Singular modules for affine Lie algebras and applications to irregular WZNW conformal blocks
Thursday 16 December 2021,   15:15,   M2 (M233)
Eveliina Peltola

Marc Härkönen (Georgia Institute of Technology)
Solving PDE with nonlinear algebra
Thursday 16 December 2021,   11:00,   M3 (M234) and https://aalto.zoom.us/j/66578928227
In an undergraduate differential equations course we learn to solve a linear ordinary differential equation by factoring the characteristic polynomial. This works also for in more generality for linear PDE with constant coefficients, where primary decomposition of ideals and modules plays the role of factorization. The celebrated Fundamental Theorem by Ehrenpreis and Palamodov equates the primary components to families of solutions for the corresponding PDE. This yields an alternative characterization of an ideal or module as a set of solutions to a PDE, which can be exploited in computations. In this talk I will present some historical notes along with some recent algorithmic advances in this direction.
Kubjas

Ifrah Sheikh
Kierretyn nauhan mallinnuspalkkina Kirchhoffin yhtälön avulla
Wednesday 15 December 2021,   14:15,   Zoom
Further information
Kandidaatintyö
Harri.Hakula@aalto.fi

Niklas Miller
On tame lattices
Wednesday 15 December 2021,   09:30,   Zoom
Further information
Tame lattices were introduced in 2020 by Mantilla-Soler and Damir, to capture the key properties of lattices arising from tame abelian number fields of either prime degree or conductor, via the Minkowski embedding. Families of well-rounded sublattices of tame lattices were constructed to generalize the observations of Costa et al., that certain submodules of the ring of integers of tame number fields of odd prime degree produce well-rounded lattices. Later the packing density of well-rounded tame sublattices was characterized and it was also noted that they are either generic well-rounded or similar to the root lattice A_n. Tame well-rounded sublattices closely resemble nearly orthogonal lattices, which have a basis of almost orthogonal vectors. In a 2020 paper by Fukshansky et al., nearly orthogonal well-rounded lattices were studied in more detail, and it was shown that they are, among other things, not local maxima to the sphere packing density function.
ANTA Seminar

Marianne Honkasaari
On Optimization of the Logistics Related to Recycling of Nutrients in Wastewater Sludges (Master's thesis presentation)
Tuesday 14 December 2021,   15:00,   Zoom
Further information

Roosa Ilvonen
Using simulated TMS-EEG data in source localization analysis
Tuesday 14 December 2021,   14:15,   Zoom
Further information
Kandidaatintyö: https://aalto.zoom.us/j/67770051751
Harri.Hakula@aalto.fi

Mikko Seesto
Machine learning with qubits: Experimental realisation of a quantum kernel method
Tuesday 14 December 2021,   10:00,   M3 (M234)

Prof. Joachim Schöberl
NGSolve - A finite element package for teaching and research
Thursday 09 December 2021,   13:15,   Zoom
Further information

Matteo Allaix
Introduction to Quantum Error Correction
Wednesday 08 December 2021,   14:15,   M3 (M234)
In this seminar, we will introduce some definitions of quantum information theory in order to describe some quantum error correction algorithms. We will first define density operators and mixed state to introduce the Von Neumann entropy and some distance measures for quantum systems. After a brief review of classical error correction, we will show an example in the quantum setting.
ANTA Seminar

Lauri Särkiö (masters thesis talk)
Local higher integrability of the parabolic p-Laplace equation
Wednesday 08 December 2021,   12:15,   M3 (M234)
Seminar on analysis and geometry

Algebraic fingerprinting and the shortest even cycle problem
Thursday 02 December 2021,   10:00,   Zoom
Further information
This talk gives an introduction to the algebraic fingerprinting technique in algorithm design and looks at a recent application of the technique to the shortest even cycle problem in directed graphs. (Joint work with Andreas Björklund and Thore Husfeldt --- https://arxiv.org/abs/2111.02992 .)
StAGe

Systeemitieteiden kandidaattiseminaari / Bachelor seminar in systems analysis
Thursday 02 December 2021,   09:30,   Zoom
Further information

Emma-Karoliina Kurki
Characterizations of weak reverse Hölder inequalities on metric spaces
Wednesday 01 December 2021,   12:15,   M3 (M234)
Seminar on analysis and geometry

Augustin Lafay (ENS)
Web models as generalizations of statistical loop models
Friday 26 November 2021,   10:15,   Zoom
Further information
Two dimensional gases of non intersecting loops have been a subject of study in mathematical physics for more than thirty years because of their numerous connections to integrability, two dimensional conformal field theory, random geometry and combinatorics. In this talk, I will present a natural generalization of loop models to gases of graphs possessing branchings. These graphs are called webs and first appeared in the mathematical community as diagrammatic presentations of categories of representations of quantum groups. The web models posses properties similar to the loop models. For instance, it will be shown that they describe, for some tuning of the parameters, interfaces of spin clusters in Zn spin models. Focusing on the numerically more accesible case of Uq(sl3) webs (or Kuperberg webs), it is possible to identify critical phases that are analogous to the dense and dilute phases of the loop models. These phases are then described by a Coulomb Gas with a two component bosonic field.
Kytölä & Peltola

Tuomas Kelomäki
A Geometric Proof of the Borsuk-Ulam Theorem
Thursday 25 November 2021,   10:00,   M3 (M234)
We will introduce a classical result in topology called the Borsuk-Ulam theorem and provide a somewhat elementary proof to it. The machinery used in the proof will not use any algebraic topology. Instead we will make use of a carefully constructed simplicial approximation. If the time allows, we will also show some applications of the theorem. Since I am a new PhD student this talk will be based on my master thesis and will not contain any new results.
StAGe Seminar

Cintia Pacchiano
Higher integrability and stability for (p,q)-quasiminimizers
Wednesday 24 November 2021,   12:15,   M3 (M234)
Seminar on analysis and geometry

Sonja Oksanen (Aalto)
Predicting residential property prices with decision tree models (MSc thesis presentation)
Monday 22 November 2021,   14:15,   M203
The price of a residential property is determined by diverse attributes, such as the size, condition, or location of a property. A number of studies have predicted property prices utilising these attributes and researched the most significant determinants in property price formation. Typically, property prices have been estimated with so called hedonic price models. Recently, however, the popularity of machine learning methods in property price estimation has increased. In this thesis, a machine learning framework for predicting residential property prices is developed. Random forests, gradient boosting machine, and XGBoost algorithms are implemented. Property prices are predicted utilising real-life data of apartment transactions with information of location-specific attributes and specific housing features. The results indicate that the machine learning models predict residential property prices accurately. XGBoost and gradient boosting machine outperform random forests in prediction accuracy, and XGBoost produces the best computational performance. Finally, the derived machine learning framework is tested on a research area in a city district of Espoo where the future average price level of the district is predicted. The developed machine learning framework can improve understanding of the formation of residential property value and thus be used as a tool for decision making by different operators, such as real estate investors, urban planners, home buyers, or politicians.
Lasse Leskelä

Oskar Henriksson
Geometric perspectives on the steady states of chemical reaction networks
Thursday 18 November 2021,   10:00,   M3 (M234)
This talk gives an introduction to the algebraic study of biochemical reaction networks, and some of the ways in which tools from computational algebraic geometry can help us understand their dynamics. In particular, we will discuss some recent results about generic dimension and monomial parametrizability of the set of steady states, based on a joint work in progress with Elisenda Feliu and Beatriz Pascual Escudero. No background in chemistry or algebraic geometry will be assumed.

Matteo Allaix
Introduction to Quantum Information Theory
Wednesday 17 November 2021,   15:15,   M3 (M234)
In this seminar, we will introduce the basic notations and definitions of Quantum Information Theory. We will first describe the three postulates of quantum mechanics and then we will introduce the notions of qubit, quantum state, quantum gate, entanglement and possibly distance measures.
ANTA Seminar

Julian Weigt
Covering techniques for the maximal operator
Wednesday 17 November 2021,   12:15,   M3 (M234)
Seminar on analysis and geometry

Yizheng Yuan
Refined regularity of SLE
Monday 15 November 2021,   14:15,   Y229a
SLE (Schramm-Loewner evolution) is a family of random planar curves that have some natural conformal invariance properties. They appear in a variety of planar models that exhibit conformal invariance in the scaling limit. Regarding their regularity, the optimal Hoelder and p-variation exponents are known from previous works. In this talk, I will present refinements of the regularity statements to the logarithmic scale. I will present a new argument for obtaining these results and discuss some applications.
Eveliina Peltola

Miikka Tiainen
Computational Entropy from Distributional hardness (master's thesis presentation)
Monday 15 November 2021,   10:00,   Zoom
Further information
A central problem in cryptography is the construction of basic primitives, or lowlevel algorithms, from computational complexity-based assumptions. One way of viewing the hardness of a problem from the view of a computationally bounded adversary is via the notion of entropy. Much like the toss of a normal coin is considered random due to limitations of human observers, the real entropy, or uncertainty, of a system can be much higher or lower than the entropy that is observable by an efficient adversary. In this thesis we establish results obtaining this type of computational entropy from distributionally hard primitives. This notion of distributional hardness captures that it is hard for an adversary to output a uniform pre-image of a randomly sampled image value. We use this computational entropy from distributional hardness to expand on existing results constructing pseudorandom generators from next-block pseudoentropy, and statistically hiding commitment schemes from accessible entropy. Although the existence of such constructions were implicit in existing literature, we establish much more efficient constructions with tighter bounds on the computational entropy than has previously been considered. Furthermore, the current known optimal construction of pseudorandom generators in terms of input (or seed) length appears to hold with equivalent parameters for the much more general notion of distributional hardness, establishing that the much more general notion of distributional hardness may in itself yield conceptually interesting constructions. We improve on existing results using known known information theoretic inequalities. Most centrally we use an inequality due to Bretagnolle and Huber relating the statistical distance and relative entropy of distributions in a much tighter way in the context of highly disjoint distributions than the famous Pinsker bound. Join Zoom Meeting https://aalto.zoom.us/j/68643838319

Dissertation
Valentina Candiani, opponent: Prof. Erkki Somersalo (Case Western Reserve University, Cleveland)
Computational approaches in electrical impedance tomography with applications to head imaging
Friday 12 November 2021,   13:15,   M1 (M232)

Prof. Daniela Calvetti (Case Western Reserve University, Cleveland)
Bayes meets Data Science to identify changes in brain activity during meditation from MEG measurements
Thursday 11 November 2021,   13:15,   M1 (M232)

Distinguishing Phylogenetic Networks Using Phylogenetic Invariants
Thursday 11 November 2021,   10:00,   M3 (M234)
Phylogenetics is a field in biology that studies the evolutionary relationship between organisms. Phylogenetic networks can represent evolutionary events that cannot be described by phylogenetic trees. In this talk, we introduce how to define a phylogenetic model on a particular class of phylogenetic networks to obtain a probability distribution on tuples of DNA bases observed from the extant species. Moreover, we will introduce the notion of distinguishability of phylogenetic networks. Using an algebraic approach, namely using discrete Fourier transformation, we will present some results on the distinguishability of some level-2 networks using phylogenetic invariants, which are polynomials associated with a phylogenetic network model.

Kristian Moring
Hölder regularity for obstacle problem to the porous medium equation
Wednesday 10 November 2021,   12:15,   M3 (M234)
Seminar on analysis and geometry

Ettore Teixeira Turatti (University of Florence)
Tensors determined by their eigenscheme
Thursday 04 November 2021,   10:00,   M3 (M234)
We will introduce the notion of eigentensor and eigenschemes for multisymmetric tensors. We then study the question: given a general tensor t, there exist other tensors that have the same eigentensors of t? We will show that if there is at least a component of degree odd, then just t has these eigentensors, otherwise there is a 1-dimensional space of tensors with the same eigentensors as t.

Niklas Miller
The Twisted Ring-LWE Problem
Wednesday 03 November 2021,   15:15,   M3 (M234)
In an interesting paper by Ortiz, Araujo, Aranha, Costa and Dahab, the authors consider a generalisation of the Ring-LWE problem. The usual RLWE uses the canonical embedding to map an underlying ring to a lattice in R^n. The twisted RLWE (RLWE^t) generalises this by considering a twisted embedding. The authors provide a security reduction from RLWE to RLWE^t, and show that the twisted embedding allows for more algebraic lattices to be used in lattice-based cryptosystems.
ANTA Seminar

Kim Myyryläinen
Wednesday 03 November 2021,   12:15,   M3 (M234)
Seminar on analysis and geometry

Lassi Ruoppa
Maximal number of subsets occurring as substrings / Osamerkkijonoina esiintyvien osajoukkojen maksimaalinen lukumäärä (Kandiseminaari)
Tuesday 02 November 2021,   10:15,   Zoom
https://aalto.zoom.us/j/68278283503

Lassi Ruoppa
Maximal number of subsets occurring as substrings (B.Sc. thesis presentation)
Tuesday 02 November 2021,   10:15,   Zoom
Further information
Let s be a string of length n over the alphabet [m]:={1,2,...,m}. We say that a set S occurs as a substring in s, if some substring of s contains precisely the elements of S, some possibly repeated. We write C(m,n) for the maximum number of subsets occurring as substrings across all strings of length n over [m]. We will present both an efficient algorithm for computing C(m,n) and exact analytic expressions for entries on the diagonal C(m,m) and first superdiagonal C(m,m+1).
ANTA Seminar

Alexander Engström (Aalto)
Betti polytopes
Thursday 28 October 2021,   10:00,   M3 (M234)
Milo Orlich and I recently proved that if certain Betti numbers of some ideals vanish, then almost all those ideals have the same CastelnuovoMumford regularity. The almost is crucial, otherwise it is false. Instead of Betti numbers vanishing, one might consider inequalities for them to get Betti polytopes, and the similar question if almost all of ideals on a facet have the same CastelnuovoMumford regularity. I will discuss some rather preliminary work in progress with Milo.
StAGe

AGENT Forum 2021
Wednesday 27 October 2021,   11:00,   AS2
Further information

Kalle Kytölä
Formal proofs for (and by) amateurs, informally
Tuesday 26 October 2021,   15:15,   M2 (M233)
An informal discussion of formal proofs (in Lean).

Bachelor Seminar in Systems Analysis
Friday 22 October 2021,   09:30,   Zoom
For Zoom link contact Juho Roponen

Milo Orlich(Aalto)
Parabolic Betti numbers and regularity of edge ideals of graphs
Thursday 21 October 2021,   10:00,   M3 (M234)
To a finite undirected graph G with no multiple edges and no loops, one associates its so-called edge ideal I(G), in a polynomial ring with coefficients in a field. The Betti numbers are numerical invariants defined in a purely algebraic way for any homogeneous ideal in such a polynomial ring, in particular for edge ideals I(G). The Betti numbers of an edge ideal I(G) have well-known combinatorial interpretations in terms of the graph G. However, a satisfactory explicit description of these numbers in terms of "easy" invariants of G (such as the number of edges of G, the number of triangles, etc.) is still out of reach in general. Another numerical invariant, much coarser than the Betti numbers, is the regularity of I(G). In spite of the great deal of research the regularity of I(G) has been the subject of, there are still no general "easy" formulas for it, either. In a recent joint work with Alexander Engström we introduce the concept of "parabolic Betti number" and employ methods from extremal graph theory to determine the exact value of the regularity of I(G), for almost all graphs G with a given parabolic Betti number equal to zero. Large part of the talk will be devoted to defining all the notions involved, in order to make it as accessible as possible. Next week's talk by Alex Engström is going to be closely related, and this talk can be seen as an introduction to that.
StAGe

Aleksi Avela
On Handling Imbalanced Data in Text Classification (Master's thesis presentation)
Wednesday 20 October 2021,   16:00,   Zoom
Further information

Florian Kohl (Aalto)
Unconditional Reflexive Polytopes
Thursday 14 October 2021,   10:00,   M3 (M234)
A convex body is unconditional if it is symmetric with respect to reflections in all coordinate hyperplanes. In this talk, we investigate unconditional lattice polytopes with respect to geometric, combinatorial, and algebraic properties. In particular, we characterize unconditional reflexive polytopes in terms of perfect graphs. As a prime example, we study a type-B analogue of the Birkhoff polytope. No background knowledge of polytopes or graphs is needed. In particular, I will explain every word in the title. This talk is based on joint work with McCabe Olsen and Raman Sanyal.
StAGe --- Seminar on Statistics, Algebra, and Geometry

Dr. Tapani Matala-aho
Hermite-Thue Equation: Padé approximations and Siegels Lemma, Part 1
Wednesday 13 October 2021,   15:15,   Zoom
Further information
Padé approximations and Siegels lemma are widely used tools in Diophantine approximation theory. The appropriate homogeneous matrix equation representing both methods has an M x (L+1) coefficient matrix, where M≤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. We will present some key ingredients on how to find such a big common factor in the case of the exponential function. 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. Joint work with Louna Seppälä.
ANTA Seminar

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