### Department of Mathematics and Systems Analysis

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- Studies
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* Dates within the next 7 days are marked by a star.

Konstantin Avrachenkov (INRIA Sophia Antipolis)**Hedonic coalitional game approach to network partitioning***** ** Monday 02 March 2020, 15:15, M205

The traditional methods for detecting community structure in a network are based on selecting dense subgraphs inside the network. Here we propose to use the methods of coalitional game theory that highlight not only the link density but also the mechanisms of cluster formation. Specifically, we propose an approach which is based on hedonic coalitional games. This approach allows to find clusters with various resolution. Furthermore, the modularity-based approach and its generalizations as well as ratio cut and normalized cut methods can be viewed as particular cases of the hedonic games. Finally, for methods based on potential hedonic games we suggest a very efficient computational scheme using Gibbs sampling.
Bio: Konstantin Avrachenkov received the masters degree in control theory from St. Petersburg State Polytechnic University in 1996, the Ph.D. degree in mathematics from the University of South Australia in 2000, and the Habilitation (Doctor of Science) degree from the University of Nice Sophia Antipolis in 2010. Currently, K. Avrachenkov is Director of Research at Inria Sophia Antipolis. His main research interests are Markov chains, Markov decision processes, stochastic games and singular perturbations. He applies these methodological tools to the modelling and control of telecommunication systems and to design data mining and machine learning algorithms. He has won 5 best paper awards. He is an Associate Editor
of the International Journal of Performance Evaluation, Probability in the Engineering and InformationalSciences, ACM TOMPECS and Stochastic Models.

Aalto Stochastics & Statistics Seminar

Chris Brzuska**Reading circle on lattices and lattice-based cryptography: on public key crypto and complexity***** ** Tuesday 03 March 2020, 10:15, M3 (M234)

The reading circle will gather around 10 times, check the ANTA seminar page for detailed times and talk titles.

ANTA

Laia Amoros and Taoufiq Damir**Reading circle on lattices and lattice-based cryptography: hardness of lattice problems***** ** Wednesday 04 March 2020, 10:15, M3 (M234)

The reading circle will gather around 10 times, check the ANTA seminar page for detailed times and talk titles.

ANTA

Carlos Mudarra**Bounded extension operators for jets of class C^{1,w} in Hilbert spaces***** ** Wednesday 04 March 2020, 12:15, M3 (M234)

Seminar on analysis and geometry

Lauri Hitruhin**TBA**

Wednesday 11 March 2020, 12:15, M3 (M234)

Seminar on analysis and geometry

Sari Rogovin**Poincaré inequalities and a general quasihyperbolic growth condition**

Wednesday 18 March 2020, 12:15, M3 (M234)

Seminar on analysis and geometry

Emanuel Carneiro**TBA**

Wednesday 25 March 2020, 12:15, M3 (M234)

Seminar on analysis and geometry

Lauri Viitasaari**Variability of functions and Hölder driven differential systems with BV-coefficients**

Wednesday 08 April 2020, 12:15, M3 (M234)

Partial differential equations and differential systems play fundamental role in many aspects of our daily life. However, in many applications, especially in the field of stochastic differential or partial differential equations, the underlying equation does not make sense in a classical way, and one has to consider integral equations instead. Moreover, even the concept of integral is subtle. For example, a typical situation is that one needs to consider $\int_0^t \varphi(X_s)\,dY_s$, where $\varphi$ is a given function and $X,Y$ are some continuous but non-differentiable objects. Several powerful theories have emerged to treat these situations, such as rough path theory or the theory of regularity structures. On the other hand, these methods are applied in situations where the function $\varphi$ is typically smooth, and most of the existing methods break down completely if one allows discontinuities in $\varphi$ (provided that $Y$ is not too "nice"). In particular, this is the case if $\varphi$ is a general BV-function.
In this talk we combine tools from fractional calculus and harmonic analysis to some fine properties of BV-functions and maximal functions, allowing us to give a meaningful definition for (multidimensional) integrals $\int_0^t \varphi(X_s)\,dY_s$, provided that the functions $X$ and $Y$ are regular enough in the Hölder sense. The key idea is that the function $X$ should not spend too much, in some sense, time on the bad regions of $\varphi$. We quantify this in terms of potential theory and Riesz energies. We discuss several consequences, and provide existence and uniqueness results for certain differential systems involving BV-coefficients. Extensions and further topics are discussed.
The talk is based on a joint work with Michael Hinz (Bielefeld University) and Jonas Tölle (University of Helsinki).

Seminar on analysis and geometry

Peter Lindqvist (NTNU)**The time derivative in some Evolutionary p-Laplace Equations: a problematic quantity**

Wednesday 26 February 2020, 12:15, M3 (M234)

Seminar on analysis and geometry

Laia Amoros**Reading circle on lattices and lattice-based cryptography: basics on lattices**

Wednesday 26 February 2020, 10:15, M3 (M234)

The reading circle will gather around 10 times, check the ANTA seminar page for detailed times and talk titles.

ANTA

Tuomas Hytönen (University of Helsinki)**Commutators and Jacobians**

Tuesday 25 February 2020, 15:15, U5

The commutator of two objects A and B is the expression AB-BA, a measure of the extent to which A and B fail to commute. Probably the most famous instance arises from the uncertainty principle in Quantum Mechanics, when A and B are the position and momentum operators, or (in a common representation of these operators) multiplication by x and differentiation in x, respectively. The commutators featuring in this talk are distant cousins of the Heisenberg commutator: again, one of the operators is multiplication by a function, while the other one is an (singular) integral operator. Among other things, such commutators have am interesting connection to a distinguished nonlinear partial differential equation, the prescribed Jacobian problem.

Department Colloquium

Kim Myyryläinen (Aalto University)**What is...Bounded Mean Oscillation (BMO)?**

Tuesday 25 February 2020, 14:15, M2 (M233)

The space of bounded mean oscillation (BMO) consists of functions whose mean oscillation over cubes is uniformly bounded. The mean oscillation tells that how much function differs in average from its integral average. One of the most important theorems concerning BMO (the John-Nirenberg inequality) states that the logarithmic blowup is the worst possible behaviour for a BMO function. It also implies that BMO is a substitute for the space of bounded functions in the sense that every BMO function is locally exponentially integrable. As one application of BMO, many interesting linear operators in harmonic analysis fail to map bounded functions to bounded functions but instead map bounded functions to BMO.

What is...? Seminar

Marti Prats**Minimizers for the thin one-phase free boundary problem (continues)**

Thursday 13 February 2020, 14:15, M235a (Tuuma)

We will give an overview of the literature on the non-negative minimizers for the one-phase free boundary problem of Alt and Caffarelli. This functional contains two competing terms, the standard Dirichlet energy and the measure of the set where the function is positive. Every minimizer is harmonic in its positive phase and vanishes elsewhere. Many questions arise regarding the regularity of the free boundary of such a minimizer, some of them still open.
We will also discuss how these ideas can be brought to the thin one-phase free boundary problem, where the first term is a weighted Dirichlet energy related to the Poisson extension used to compute the fractional Laplacian, and the second competing term is only evaluated in a hyperplane. Minimizers of such a functional will have vanishing fractional Laplacian in the hyperplane's positive phase. This intrinsic nonlocallity will make some arguments to vary substantially.

Seminar on analysis and geometry

Matias Vestberg**Regularity properties of weak solutions to doubly singular equations**

Wednesday 12 February 2020, 12:15, M3 (M234)

Seminar on analysis and geometry

Alexander Engström**Standard monomials of plane partitions**

Tuesday 11 February 2020, 16:15, M2 (M233)

A set of standard monomials of an ideal gives a vector space basis for its residue ring. If the ideal is from a finite variety, then the number of points of the variety and the number of standard monomials is equal and the natural combinatorial question is to find an explicit bijection. Together with Sanyal and Stump we did that for varieties from lattice path matroid, and first I will sketch that construction. Extending from one to several lattice paths and requiring that they don't intersect constitutes a classical combinatorial object in bijection with plane partitions. There are several famous open and proved conjectures on plane partitions thanks to their presence in random matrix theory and mathematical physics. In the final part of the talk I will define the tentative monomials. They are in bijection with the plane partitions and it's proven that they have several of the properties required by standard monomials. Based on further computational evidence, I conjecture that the tentative monomials are standard monomials of plane partitions.

Algebra and discrete mathematics seminar

Dr. Lina Reichenberg (Chalmers/ Aalto University)**The Cost of Future Low-carbon Electricity System without Nuclear power in Sweden**

Tuesday 11 February 2020, 13:30, M2 (M233)

We would like to invite you for the first talk associated with the project Advanced analytics for planning future energy systems funded by the Aalto Science Institute.
In this meeting, Dr. Lina Reichenberg (Chalmers/ Aalto University) will be giving a talk on The Cost of Future Low-carbon Electricity System without Nuclear power in Sweden. Her presentation will be followed by a discussion session and some coffee/ tea.

Advanced analytics for planning future energy systems

Prashanta Garain**Harnack's inequality for the fractional parabolic doubly nonlinear equation**

Wednesday 05 February 2020, 12:15, M3 (M234)

Seminar on analysis and geometry

Dario Gasbarra (University of Helsinki)**Algebraic Stein operators for Gaussian polynomial random variables**

Tuesday 04 February 2020, 16:15, M2 (M233)

For a standard Gaussian random variable N, integration by parts gives
the Stein equation
E(Nf(N)- Df(N))=0
The Stein equation characterizes the distribution and it is the key
in proving quantitative limit theorems towards the Gaussian.
Here we take the first steps in extending the methodology, and give
an algorithm producing Stein differential operators
with polynomial coefficients for target random variables
of the form X= p(N_1, ..., N_d), with Gaussian N and polynomial p.
This work is in collaboration with Ehsan Azmoodeh (Bochum)
and Robert Gaunt (Manchester).

Algebra and discrete mathematics seminar

Marti Prats**Minimizers for the thin one-phase free boundary problem**

Wednesday 29 January 2020, 12:15, M3 (M234)

We will give an overview of the literature on the non-negative minimizers for the one-phase free boundary problem of Alt and Caffarelli. This functional contains two competing terms, the standard Dirichlet energy and the measure of the set where the function is positive. Every minimizer is harmonic in its positive phase and vanishes elsewhere. Many questions arise regarding the regularity of the free boundary of such a minimizer, some of them still open.
We will also discuss how these ideas can be brought to the thin one-phase free boundary problem, where the first term is a weighted Dirichlet energy related to the Poisson extension used to compute the fractional Laplacian, and the second competing term is only evaluated in a hyperplane. Minimizers of such a functional will have vanishing fractional Laplacian in the hyperplane's positive phase. This intrinsic nonlocallity will make some arguments to vary substantially.

Seminar on analysis and geometry

Volker Mehrmann (TU Berlin)**Stability analysis of energy based dynamical system models**

Tuesday 28 January 2020, 15:15, U5

Dissipative port-Hamiltonian systems are an important class of models that arise in all areas of science and engineering, whenever one uses energy as the major modeling concept. Despite the fact that the model class looks very unstructured at first sight, it has remarkable algebraic and geometric properties. Systems can be coupled in a network fashion in a structure preserving way, Galerkin projection preserves the stucture. We will illustrate these and further system properties, showing for examples that stability and passivity are automatic. In the linear case Jordan structures for purely imaginary eigenvalues, eigenvalues at infinity, and even singular blocks in the Kronecker canonical form are very restricted and furthermore the structure leads to fast and efficient iterative solution methods for the associated linear systems.
Motivated from an industrial application of studying brake squeal, we study questions like the spectral properties or distance to instability/stability for this system class. We use this large scale industrial finite element model to illustrate our theoretical findings with numerical computation results.

Department Colloquium

MSc. Giovanni Barbarino**What is a port-Hamiltonian System?**

Tuesday 28 January 2020, 14:15, M2 (M233)

We introduce the standard dissipative port-Hamiltonian (pH) systems through examples and basic results, giving hints on the broad variety of application areas where pH systems play a role.
In the particular case of linear time-invariant systems, the spectral structure of the associated pencil can be studied through its Kronecker canonical form, that will be briefly reviewed.

What is...? Seminar

Prof. Prabhu Manyem (Nanchang Institute of Technology)**Combinatorial Optimisation: Spanning and Steiner trees, Bin Packing and Second Order Logic**

Monday 27 January 2020, 15:15, Y225a (Riihi)

Prof. Froilán M. Dopico **Sets of matrix polynomials with bounded rank and degree and their generic eigenstructures**

Thursday 23 January 2020, 12:40, M3 (M234)

Low rank perturbations of matrices, matrix pencils, and matrix polynomials appear naturally in many applications where just a few degrees of freedom of a complicated system are modified. As a consequence many papers have been published in the last 15 years on this type of problems for matrices and pencils, but just a few for matrix polynomials. A possible reason of this lack of references on low rank perturbations of matrix polynomials is that the set of matrix polynomials with bounded (low) rank and degree is not easy to describe explicitly when the rank is larger than one. The purpose of this talk is to describe such sets both in terms of its generic eigenstructures and in terms of products of two factors. We will consider unstructured matrix polynomials, as well as symmetric and skew-symmetric matrix polynomials.

Annachiara Korchmaros**Colored best match graphs**

Tuesday 21 January 2020, 16:15, M2 (M233)

In this talk we deal with a family of directed graphs, called colored best match graphs, arising from applications to evolutionary theory. We give an outline of the basic properties of such graphs and present some results in the case where their vertices are colored with two colors.

Algebra and discrete mathematics seminar

Taoufiq Damir**A Brief Introduction to the Theory of Lattices**

Tuesday 14 January 2020, 16:15, M2 (M233)

Lattices are central to number theory and discrete geometry. In addition to their arithmetic and geometric appeal, lattices are also extensively used in applied areas, such as coding theory, cryptography and other areas of digital communications.
The aim of the talk is to give a gentle introduction to theory of lattices, we will start by reviewing the necessary background including relevant definitions, problems and theorems. We will then highlight some links between the theory and applications.

Algebra and discrete mathematics seminar

Quan Wang**Master thesis talk**

Monday 30 December 2019, 14:00, M305

Joni Virta (University of Turku)**Fast tensorial independent component analysis**

Wednesday 18 December 2019, 16:15, M1 (M232)

Stochastic Sauna 2019

Tom Claeys (Université Catholique de Louvain)**Random growth, interacting particles, and Riemann-Hilbert problems: from KPZ to KdV**

Wednesday 18 December 2019, 15:15, M1 (M232)

Stochastic Sauna 2019

Vesa Julin (University of Jyväskylä)**The Gaussian isoperimetric problem for symmetric sets**

Wednesday 18 December 2019, 14:00, M1 (M232)

Stochastic Sauna 2019

Jaron Sanders (TU Eindhoven)**Markov chains for error accumulation in quantum circuits**

Wednesday 18 December 2019, 13:00, M1 (M232)

Stochastic Sauna 2019

Kaie Kubjas (Aalto)**Exact solutions in log-concave maximum likelihood estimation**

Wednesday 18 December 2019, 11:00, M1 (M232)

Stochastic Sauna 2019

Teemu Pennanen (King's College London)**Convex duality in nonlinear optimal transport**

Wednesday 18 December 2019, 10:00, M1 (M232)

Stochastic Sauna 2019

Dr. Riikka Kangaslampi (Tampere University)**Introduction to hypergraphs**

Tuesday 17 December 2019, 16:15, M3 (M234)

In network science problems complex systems or datasets are often modelled as weighted graphs. These models are simple and powerful, but in some cases insufficient to capture the network structure information, if there are higher-order interactions among more than a pair of nodes. Hypergraphs are a generalisation that can be used to tackle this difficulty.
In this talk I will introduce hypergraphs and some of their basic properties and provide a few examples of networks where hypergraphs would be a natural way to describe the interactions. If time permits, I will also discuss current results and research problems related to Ricci curvatures of hypergraphs.

ANTA Seminar

Prof. Norbert Peyerimhoff (Durham University)**Expander graphs and curvature**

Tuesday 17 December 2019, 15:15, M3 (M234)

Expander graphs are increasing families of graphs which are at the same time sparse and very well connected. They are not only of
practical relevance for the construction of robust networks but their theoretical research uncovered many suprising connections with various mathematical disciplines: representation theory (Kazdhan property (T)), geometric group theory (Cayley graphs), combinatorics (zigzag products), number theory (Ramanujan graphs), spectral theory (Cheeger inequalities) and probability theory (random walks and random covers). Another challenging question about graphs are to introduce proper notions of curvature. In this talk, I will briefly present an analytical approach, due to Bakry-Emery, which allows to define curvature on graphs. Once these concepts are introduced, I will discuss relations between expander graphs and Bakry-Emery curvature.

ANTA Seminar

Camilla Hollanti and Ellie Dillon**Mentoring breakfast **

Tuesday 10 December 2019, 09:30, M-wing common room

Information about departments mentoring program. Please join if you are interested in being a mentor or getting one, or just hearing a bit more about mentoring in general.

Sami Helander (Aalto)**On Adaptive functional data depths**

Monday 09 December 2019, 14:15, Y313

Typically, in the functional context, data depth approaches heavily emphasize the location of the functions in the distribution, therefore often missing important shape or roughness features. Commonly, these depth approaches either integrate pointwise depth values to achieve a global value, or measure the expected distance from a function to the distribution. In this talk, we introduce a new class of functional depths, based on the distribution of depth values along the domain, and discuss their properties. We study the asymptotic properties of these $J$th order $k$th moment integrated depths, and illustrate their usefulness in supervised functional classification. In particular,
we demonstrate the importance of receptivity to shape variations, and show that, similarly to existing depth notions, the new class of depth functions takes into account the variation in location, while remaining receptive to variations in shape and roughness.

Aalto Stochastics and Statistics seminar

Tommi Summanen**Karkeiden stokastisten osittaisdifferentiaaliyhtälöiden diskretoinnista (kandiesitelmä)**

Wednesday 04 December 2019, 15:15, Tuuma (M235a)

Elias Jäämeri**MSc thesis presentation: On code-based cryptography**

Wednesday 04 December 2019, 15:15, M3 (M234)

ANTA Seminar

Emma-Karoliina Kurki**Extension results for Muckenhoupt weights**

Wednesday 04 December 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Toni Annala (University of British Columbia)**Deriving intersection theory and algebraic cobordism**

Tuesday 03 December 2019, 16:15, M2 (M233)

I will quickly introduce intersection theory and algebraic cobordism and recall some
foundational difficulties in the subject. I will then outline how derived algebraic geometry, introduced
by Toën-Vezzosi and Lurie, can be used to overcome many of these difficulties. Finally, I will outline
the current state of the art understanding of these new ``derived'' cohomology theories. The talk is
partly based on joint work with Shoji Yokura.

Algebra and Discrete Mathematics Seminar

Muhammad Ardiyansyah (Aalto)**Introduction to Phylogenetic Algebraic Geometry**

Tuesday 03 December 2019, 15:15, M2 (M233)

Phylogenetics is the study of how various organisms are related, and is very closely related to taxonomy, the classification of organisms. This relationships are usually decribed using evolutionary trees, which will be our basic objects. We will view this topics from algebraic viewpoint. We will introduce some basic models on phylogenetics.
By phylogenetic algebraic geometry we mean the study of algebraic varieties which represent models of evolution. In fact, under many standard models of molecular evolution (for example, DNA sequences), for a fixed tree topology, the joint distribution of bases at the leaves are described by polynomial equations in the parameters of the model. This fact lead us to search for polynomials, called phylogenetic invariants, which vanish on any joint distribution arising from the tree and model, regardless of parameter values.

Algebra and Discrete Mathematics Seminar

Paavo Raittinen (Aalto)** On early detection of high-risk prostate cancer: applied discovery and validation models using genotype information**

Monday 02 December 2019, 14:15, Y313

Prostate cancer incidence rate is extremely high and on the rise, counting over 1.2 million new cases annually and causing 350 000
deaths in 2018. While the prognosis is typically good, approximately 20% of the new cases classifies as high-risk prostate cancer with
dire consequences. Moreover, the initial prostate cancer diagnosis always reflects as worry and quality of life impairment. The initial
prostate cancer determination is based on prostate specific antigen (PSA) measure, which cannot distinguish between low-risk and high-risk
cases. After the PSA determination, the tumor state is characterized with various invasive methods such as Gleason score and T-stage
classification. However, both methods display inaccuracy and puts patient under infection risk. Our take on this challenge is to use
inflammation-related gene single nucleotide polymorphisms (SNP) as predictors of high-risk prostate cancer. SNP is a low-cost,
non-invasive, and stable biomarker. We have explored inflammation SNP association with high-risk prostate cancer in a genotyped part of Finnish Randomized
Screening for Prostate Cancer cohort (n = 2715) and found several statistically significant associations.
Furthermore, our validation model using unknown prostate cancer cohort collected during hospital visits (n = 888) is in concordance with our
discovery model. Remarkably, few SNPs increase early high-risk prostate cancer detection over PSA alone.

Aalto Stochastics and Statistics seminar

Stavros Evdoridis**Boundary behaviour of harmonic mappings**

Wednesday 27 November 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Prof. Kaisa Nyberg (Aalto University)**Cryptographic nonlinearity criteria**

Tuesday 26 November 2019, 15:15, U6

Block ciphers are arguably the most important cryptographic primitives, since they can be used as building blocks of cryptographic protocols that provide various kind of information security services, such as confidentiality, integrity and authentication.
To be secure a block cipher must be resistant against statistical attacks that exploit probabilistic properties that allow distinguishing the cipher from a random permutation. Since the publication of the first statistical cryptanalysis methods in early 1990s which exploited differential propagation and linear relations, a number of new more complex properties, e.g. boomerangs and differential-linear relations have been discovered that can be exploited efficiently to distinguish the cipher from random and also to recover part of the secret key.
It is quite well understood how to construct differential and linear distinguishers of iterated block ciphers based on the differential and linear properties of the round function captured by DDT tables and LAT tables. These tools have been also used to construct boomerang and differential-linear distinguishers. Recently, Cid et al. (2018) discovered a more efficient method by identifying the boomerang property of the round function. This involves a tool called Boolean Connectivity Table (BCT). Subsequently, Bar-On et al. (2019) found a similar improvement for differential-linear relations using a tool named Differential-Linear Connectivity Table (DLCT).
In this talk a brief survey of these tools and relationships between them will be given. Also examples of commonly used building blocks of round functions and properties of their DDT, LAT, BCT and DLCT tables will be discussed.

Department Colloquium

Estuardo Alpirez Bock**What is...Cryptanalysis via DDTs and LATs?**

Tuesday 26 November 2019, 14:15, M2 (M233)

We first take a closer look at block ciphers as integral building blocks of encryption schemes. We thereby review the security properties we wish to obtain from block ciphers. Then, we focus on S-boxes, which correspond to the only non-linear part of block ciphers. Finally we introduce linear approximation tables (LAT) and differential distribution tables (DDT) as methods for assessing the security of the S-boxes.

What is...? seminar

Joona Karjalainen (Aalto)**Modeling overlapping communities with random intersection graphs**

Monday 25 November 2019, 14:15, Y313

Many real-life networks can be naturally modeled by assuming an underlying community structure on the nodes. When each node can belong to more than one community, we say that the communities overlap. This talk discusses the modeling of such networks with random intersection graphs. We review some of their asymptotic properties, such as subgraph counts, and discuss consistent moment-based parameter estimation in a sparse setting.

Aalto Stochastics and Statistics seminar

Bas Lemmens (University of Kent)**Horofunctions, fixed points, and illuminating the unit ball**

Thursday 21 November 2019, 15:15, M2 (M233)

A central problem in metric fixed point theory is to understand when a nonexpansive (i.e. Lipschitz with constant 1) self-map of a metric space has a fixed point. Even in the case where the metric space is a finite dimensional normed space, this is a subtle problem, as the map need not be a Lipschitz contraction and the space is not bounded, so neither the contraction mapping theorem nor the Brouwer fixed point theorem applies. In this talk I will give necessary and sufficient conditions for a nonexpansive map on a finite dimension normed space to have a bounded non-empty fixed point set. Moreover, we will provide a procedure that can detect fixed points of such maps using sets that illuminate the unit ball of the normed space. We will see how horofunctions play a role in this problem. Time permitting I will also discuss some applications to stochastic games.

Kytölä

Stanislav Nagy (Charles University)**Geometry of multivariate quantiles**

Thursday 21 November 2019, 10:15, Y313

The halfspace depth is a tool of non-parametric statistics, whose main aim is a reasonable generalisation of quantiles to multivariate data. It was first proposed in 1975; its rigorous investigation starts in the 1990s, and still an abundance of open problems stimulates the research in the area. We present interesting links of the halfspace depth, and some well-studied concepts from geometry. Using these relations we resolve several open problems concerning the depth, and outline perspectives for future research not only in non-parametric statistics, but also in certain areas of convex geometry.
The talk is intended to be largely self-contained; no particular knowledge of probability and statistics is necessary.

Aalto Stochastics and Statistics seminar

Jan Härkönen (Aalto University)**Quantum Monte Carlo simulation of positron annihilation radiation in solids (MSc project presentation)**

Wednesday 20 November 2019, 14:15, M3 (M234)

This project concentrates on simulating the momentum density of annihilating electron-positron pairs. We use the CASINO simulation program in order to optimize the wave function of a system to simulate the the momentum density using Quantum Monte Carlo methods. The simulations involve diamond, silicon and germanium FCC-lattices.

Aalto Stochastics & Statistics Seminar / Ilmonen-Kytölä-Leskelä

Julian Weigt**L^p-boundedness of the gradient of the local fractional maximal**

Wednesday 20 November 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Jukka Kohonen (Aalto)**Combinatorics of maniplexes**

Tuesday 19 November 2019, 17:15, M2 (M233)

This is a short introduction to maniplexes. A maniplex is an edge-colored regular graph of a certain kind. Maniplexes were proposed in 2010 by Steve Wilson to generalize and connect the ideas of a map and an abstract polytope. For example, the flag graph of an
abstract polytope is a maniplex. I will present some algorithmics and preliminary results of our efforts to exhaustively list all small maniplexes. Joint work with Gabe Cunningham (UMass Boston) and Katja Berčič (FAU Erlangen-Nürnberg).

Algebra and Discrete Mathematics Seminar

Laura Jakobsson (Aalto)**Introduction to Representation Stability**

Tuesday 19 November 2019, 16:15, M2 (M233)

In this talk we give a short introduction to category theoretic representation stability. We cover the main definitions and theorems of representation stability for categories of combinatorial nature and look at some of the examples including FI-modules.

Algebra and Discrete Mathematics Seminar

Anton Vavilov**Geometry of Julia and Fatou sets for hyperbolic rational maps **

Tuesday 19 November 2019, 13:15, M3 (M234)

Marko Voutilainen (Aalto)**Modeling and estimation of multivariate strictly stationary processes**

Monday 18 November 2019, 14:15, Y313

We discuss how discrete and continuous time multivariate stationary processes can be characterized by an AR(1) type of equation and Langevin equation, respectively. Under the assumption of finite second moments, this leads to quadratic matrix equations for the model parameter matrix that are known as continuous time Riccati equations (CAREs). Based on the equations, we define an estimator for the parameter that inherits consistency and the rate of convergence from autocovariance estimators of the (observed) stationary process. Furthermore, the limiting distribution is given by a linear function of the limit random variable of the autocovariance estimators.

Aalto Stochastics and Statistics seminar

Cintia Pacchiano**Parabolic minimizers to the Total Variation Flow.**

Wednesday 13 November 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Olga Kuznetsova (Aalto)**Introduction to non-parametric algebraic statistics**

Tuesday 12 November 2019, 15:15, M2 (M233)

The goal of statistics is to estimate the probability distribution of a random variable from data. Traditionally, statisticians assumed that the distribution belongs to a certain family with finitely many parameters. In non-parametric statistics, one departs from this assumption to allow for more accurate reflections of real-life probability distributions. We will discuss the connection non-parametric statistics and geometric combinatorics.

Algebra and Discrete Mathematics Seminar

Kari Väisänen**Functionals of linear growth on metric measure spaces (diplomityöesitelmä)**

Tuesday 12 November 2019, 15:15, M3 (M234)

Daniel Heinlein**A short introduction to subspace coding**

Monday 11 November 2019, 14:15, M140 Majakka

Subspace codes are sets of subspaces in a finite vector space augmented with a suitable metric. This talk presents an application in network coding, introduces basic notation, commonly used tools, symmetry, and relations to related structures. Rank metric codes and a connection to subspace codes are depicted. A family of constructions commonly referred to as "linkage constructions" is presented.

ANTA Seminar

Hoa Ngo (Aalto)**First passage percolation on mixed sparse random graphs with two types of nodes**

Monday 11 November 2019, 14:15, Y313

A mixed graph is a graph consisting of both undirected edges and directed edges.This talk discusses first passage percolation on a connected mixed random graph with a given degree sequence, where an undirected edge is formed between type-1 nodes and a directed edge between type-1 and type-2 nodes. Weights on edges are assumed to be independent and exponentially distributed. We analyze a flooding time, which is the minimum time that a uniformly chosen node reaches all other nodes. We derive an asymptotic formula for the flooding time as the number of nodes tend to infinity. As an application, we discuss continuous time information spreading on a random regular graph, where we also take into account the impact of passive nodes. Type-1 nodes can be interpreted as active message spreaders and type-2 nodes can be interpreted as passive receivers which may only receive the message. In this setting we derive an asymptotic formula for the flooding time which is also called the broadcast time in the literature

Aalto Stochastics and Statistics seminar

Nadir Sahllal (Universite Mohammed V de Rabat)**Steganography and error correction codes**

Wednesday 06 November 2019, 15:15, M3 (M234)

The goal of steganography is to communicate in secrecy by hiding the very presence of the message within a host object called the cover. The actual embedding involves making small modifications to
the cover. Error correction codes gave steganography the perfect environment to develop over the past few decades. In this talk we will explore the relations between steganography and error correcting codes, and describe some of the most prominent steganographic algorithms.

ANTA Seminar

Karl Brustad**Sublinear operators and the comparison principle in elliptic equations**

Wednesday 06 November 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Luca Sodomaco (Università degli Studi di Firenze)**On the ED polynomial of a real algebraic variety**

Tuesday 05 November 2019, 15:15, M2 (M233)

Let X be a real algebraic variety in a Euclidean space (V,q). The distance function from X is the smallest positive real root of an algebraic function. In particular, we introduce a polynomial, called ED polynomial of X (where ED stands for ``Euclidean Distance''), which, for any data point u in V, has among its roots the distance t from u to X. The t^2-degree of the ED polynomial is the known Euclidean Distance degree of X.
We show a duality property when X is a projective variety. When X is transversal to the isotropic quadric Q=V(q), we show that the ED polynomial of X is monic and we describe completely its lowest term.
In the second part, we show how the above general theory fits in the spectral theory of tensors. More precisely, we study ED polynomials of Segre-Veronese varieties, namely the varieties of partially symmetric rank-one tensors.
Its roots are related to the singular values of a tensor and to the best rank-one approximation problem. Focusing on symmetric tensors, singular values are replaced by E-eigenvalues.
We provide a closed formula for the product of the singular values of a partially-symmetric tensor. In the symmetric case, the formula generalizes the fact that the determinant of a symmetric matrix is equal to the product of its eigenvalues.

Algebra and Discrete Mathematics Seminar

Timo Takala**Time mollifications in a space-time cylinder (diplomityöesitelmä)**

Tuesday 05 November 2019, 15:15, M3 (M234)

Professor Emeritus Raimo P. Hämäläinen (Aalto)**Frank P. Ramsey Medal 2019 Acceptance Talk**

Monday 04 November 2019, 15:15, M1 (M232)

Further information

Professor Emeritus Raimo P. Hämäläinen has been awarded The Frank P. Ramsey Medal, which is the highest award of the Decision Analysis Society (DAS) of the Institute of Operations Research and the Management Sciences (INFORMS). He received the award on 21 October at the INFORMS Annual Conference in Seattle.
Raimo will give his Medal Acceptance talk on Monday, 4 November at 15.15 in Lecture Hall M1 (Otakaari 1, please note the new room). After the talk a bubbling toast and sweets are offered.

Niko Lietzén (Aalto)**Complex-valued latent variable models**

Monday 04 November 2019, 14:15, Y405

In several fields of science, a generic problem consists of separating useful signals from uninteresting noise and interference. The problem can be approached by implementing latent variable models. In our approach, we aim to find latent processes, when only linear mixtures of them are observable. In this context, we provide an estimation procedure for complex-valued stochastic processes. Furthermore, we study the asymptotic behavior of the so-called unmixing estimators. We provide novel asymptotic theory for scenarios, when the estimators are not root-n consistent and the limiting distributions are not Gaussian.

Aalto Stochastics and Statistics seminar

Dr. Dmitrii Pasechnik (University of Oxford)**Optimisation, dimension reduction, representation theory, reproducibility**

Friday 01 November 2019, 13:00, AS1 (TUAS/Maarintie 8)

Prof. Edith Elkind (University of Oxford)**Representation, stability and diversity in group decision-making**

Thursday 31 October 2019, 10:00, TU1 (TUAS/Maarintie 8)

Vito Buffa**Remarks on time-smoothing for parabolic variational problems in metric measure spaces**

Wednesday 30 October 2019, 12:15, M3 (M234)

One important component in the treatment of parabolic variational problems is represented by time-smoothing, which consists in the time-mollification of the parabolic Sobolev functions related to the problem, and in finding the appropriate estimates for the mollified function and its gradient. In the metric setting the process is quite delicate because of the lack of linearity in the notion of the "gradient"; this issue was circumvented by M. Masson and J. Siljander in 2012 by using J. Cheeger's differential theory, but the approach shows some limitations. We shall see how a module-theoretic characterization of the differential structure of metric measure spaces, developed by N. Gigli, allows to simplify the result by Masson and Siljander and to extend its validity to more general situations.

Seminar on analysis and geometry

Elina Robeva (University of British Columbia)**Maximum Likelihood Estimation of Totally Positive Densities **

Tuesday 29 October 2019, 15:15, U6

Nonparametric density estimation is a challenging problem in theoretical statistics -- in general a maximum likelihood estimate (MLE) does not even exist! Introducing shape constraints allows a path forward. In this talk I will discuss non-parametric density estimation under total positivity (i.e. log-supermodularity) and log-concavity. I will first show that though they possess very special structure, totally positive random variables are quite common in real world data and possess appealing mathematical properties. Given i.i.d. samples from a totally positive distribution, we prove that the maximum likelihood estimator exists with probability one assuming there are at least 3 samples. We characterize the domain of the MLE and show that it is in general larger than the convex hull of the observations. If the observations are 2-dimensional or binary, we show that the logarithm of the MLE is a tent function (i.e. a piecewise linear function) with "poles" at the observations, and we show that a certain convex program can find it. Instead of using a maximum likelihood estimator, we discuss the possibility of using kernel density estimation. This new estimator raises an abundance of theoretical questions.

Department Colloquium

Olga Kuznetsova (Aalto University)**What is...Maximum Likelihood Estimation?**

Tuesday 29 October 2019, 14:15, M2 (M233)

Maximum Likelihood Estimation (MLE) is a method of estimating a probability distribution by maximising the likelihood function such that the observed data is the most probable. We will discuss the basics of MLE in traditional (parametric) statistics and how this approach has been generalised for non-parametric statistics.

What is...? seminar

Jaakko Lehtomaa (University of Helsinki)**On asymptotic independence and support detection techniques for heavy-tailed multivariate data**

Monday 28 October 2019, 14:15, Y405

One of the central objectives of modern risk management is to find a set of risks where the probability of multiple simultaneous catastrophic events is negligible. That is, risks are taken only when their joint behavior seems sufficiently independent. Our objective is to provide additional tools for describing dependence structures of multiple risks when the individual risks can obtain very large values.
The study is performed in the setting of multivariate regular variation. We show how asymptotic independence is connected to properties of the support of the angular measure and present an asymptotically consistent estimator of the support. The estimator generalizes to any dimension greater than or equal to two and requires no prior knowledge of the support. The validity of the support estimate can be rigorously tested under mild assumptions by an asymptotically normal test statistic.

Aalto Stochastics and Statistics seminar

Jie Li**An introduction to secure distributed matrix multiplication**

Thursday 24 October 2019, 15:15, M3 (M234)

Matrix multiplication is one of the key operations in various engineering applications. A user who has limited computation capability may wish to compute the product of two matrices with the assistance of several distributed servers. However, security becomes an issue when these servers are untrustworthy. In this talk, we focus on information-theoretically secure distributed matrix multiplication with the goal of minimizing the communication overhead.

ANTA Seminar

Neea Palojärvi (Åbo Akademi)**On $\tau$-Li coefficients and explicit zero-free regions**

Wednesday 23 October 2019, 15:15, M3 (M234)

In this talk I will give an introduction to $\tau$-Li coefficients and my results considering the coefficients and explicit zero-free regions. The $\tau$-Li coefficients are members of an infinite sequence of real numbers which can be used to determine whether certain functions satisfy the Generalized Riemann Hypothesis or not. In the talk, I describe how finitely many $\tau$-Li coefficients can be used to determine whether certain functions have certain zero-free regions inside the critical strip or not.

ANTA Seminar

Milo Orlich (Aalto)**Early history of homological algebra and category theory **

Wednesday 23 October 2019, 14:15, M2 (M233)

In various fields of maths one meets the concept of a sequence of objects (which can be groups, modules, algebras,...) together with maps d_i going from object A_i to object A_{i-1}. The maps can be group homomorphisms, module homomorphisms, and so on, according to the nature of the objects under consideration. The very simple property these maps are required to satisfy is that, at any position in the sequence, the composition of map d_i with map d_{i-1} is equal to the zero map. An example of such a sequence of objects and maps (called in general a "complex") is the de Rham complex. Homological algebra is the study of such complexes and it was born around 70 years ago mainly thanks to new ideas in category theory and algebraic topology. In this talk we will consider a few of the key events and characters that lead to the birth and the early development of homological algebra.

Algebra and Discrete Mathematics Seminar

Vesa Vuojamo**Euclidean time-frequency transforms**

Wednesday 23 October 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Shinji Koshida (Chuo University)**Coupling of multiple Schramm-Loewner evolution and Gaussian free field**

Monday 21 October 2019, 14:15, Y405

It is known that Schramm Loewner evolution (SLE) is coupled with Gaussian free field (GFF) to give a solution to the flow line problem for an imaginary surface. I will overview our recent work where we extended this coupling to the case of multiple SLE. There, we found that the SLE partition function that defines a multiple SLE and the boundary perturbation for GFF are determined essentially uniquely so that the associated multiple SLE and GFF are coupled with each other.

Aalto Stochastics and Statistics seminar

Dissertation

Matthias Grezet**On Matroid Theory and Distributed Data Storage**

Thursday 17 October 2019, 15:00, M1 (M232)

Defense of doctoral dissertation in mathematics. Opponent Prof. Thomas Britz, Custos Prof. Camilla Hollanti.

Doctoral defense (ANTA)

Prof. Fabricio Oliveira (Aalto University)**Optimisation under uncertainty for real-world production systems: theoretical aspects and practical challenges**

Tuesday 15 October 2019, 15:15, M1 (M232)

In this talk, we introduce the framework of optimisation under uncertainty, which consists of collection of disciplines such as stochastic programming, robust optimisation, scenario generation, decomposition methods, and others related. When properly combined, these allow the development of mathematical programming-based decision support tools that can meaningfully consider the inherent uncertainty associated with input data. We illustrate the capabilities of such framework by means of examples derived from real-world problems in which the combination of two or more of these disciplines allowed the development of enhanced models which, ultimately, led to more efficient decision support tools. We will also discuss some of the technical details behind the development of these applications and present future perspectives in terms of research development.

Department Colloquium

David Adame-Carrillo (Universitat Politècnica de Catalunya)**Towards extended Minimal Models in Conformal Field Theory**

Tuesday 15 October 2019, 10:15, M2 (M233)

We present a physics approach to conformal field theory in two dimensions: the bootstrap approach. In this approach, one directly imposes conditions on correlation functions inspired by conformal symmetries. Within this framework, we give emphasis to the fusion rules of degenerate representations. Using fusion rules, we build a well-known set of simple models called Minimal Models. Finally, we propose an extension of them at central charge c=0.

Aalto Stochastics and Statistics Seminar (Ilmonen, Kytölä, Leskelä)

Barbarino Giovanni (Aalto University)**Symbols for matrix-sequences: Application-Driven Structure**

Thursday 10 October 2019, 13:00, Y225a

Applied Math Group Meeting

Marti Prats**Measuring Triebel-Lizorkin fractional smoothness on domains in terms of first-order differences**

Wednesday 09 October 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Lauri Viitasaari (Aalto)**Stochastic heat equation revisited - quantitative approximation results**

Tuesday 08 October 2019, 11:15, Y405

Partial differential equations, PDEs, describe many real life phenomena, and they are a subject of active research. Recently a growing attention have been paid to stochastic versions of PDEs - stochastic partial differential equations, or SPDEs for short. Such equations arise naturally as a random shock may represent some external random force affecting the system, or possibly some measurement errors. However, in the study of SPDEs many classical approaches breaks down completely. Indeed, even the concept of differential is subtle - the solution being typically only Hölder continuous. Moreover, as there is a random force affecting the system, the solution is also a random object. Typically, analysing this randomness is very complicated.
In this talk, we discuss d-dimensional stochastic heat equations driven by a Gaussian noise which is white in time and has a spatial covariance given by the Riesz kernel. Basic theory and properties of the solutions are discussed. As a main result, we present a quantitative central limit theorem stating that the spatial average of the solution over an Euclidean ball is close to a Gaussian distribution, when the radius of the ball tends to infinity. Our central limit theorem is described in the total variation distance, using Malliavin calculus and Stein's method. We also provide a functional central limit theorem and analogous results in the case of space-time white noise. Extensions and further open questions are discussed.

Aalto Stochastics and Statistics seminar

Henrik Leino**Probabilistic interpretation of one-dimensional Gaussian quadrature rules (kandiesitelmä)**

Thursday 03 October 2019, 11:15, M3 (M234)

Miina Virtanen**Removal of false positives in brain tractograms with affine transformation matrices (kandiesitelmä)**

Thursday 03 October 2019, 10:15, M3 (M234)

Emilia Ruha**Pointwise estimate for oscillation of a locally integrable function (kandiesitelmä)**

Thursday 03 October 2019, 09:15, M3 (M234)

Louna Seppälä**Diophantine perspectives to the exponential function and Euler's factorial series**

Wednesday 02 October 2019, 15:15, M203

This is a brief excursion to the methods and results of my doctoral thesis. The focus is on two functions: the exponential function and Euler's factorial series. By constructing explicit Padé approximations, we are able to improve lower bounds for linear forms in the values of these functions. The first part of the talk contains some historical background and auxiliary techniques. In the second part, some selected results are presented.

ANTA Seminar

Prashanta Garain**Existence results to some singular p-Laplace equations**

Wednesday 02 October 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Florian Kohl (Aalto)**A Gentle Introduction to Ehrhart Theory**

Tuesday 01 October 2019, 15:15, M2 (M233)

In this talk, I will give a gentle introduction to lattice polytopes and Ehrhart theory. We will start in dimension 2 with Pick's theorem. Pick's Theorem provides a simple formula for calculating the area of a lattice polygon in terms of the number of lattice points in the interior and the number of lattice points on the boundary. We will see how the generalization of Pick's theorem to higher dimensions naturally leads to Ehrhart theory. No background knowledge about lattice polytopes and Ehrhart theory required.

Algebra and Discrete Mathematics Seminar

Sylvester Eriksson-Bique (UCLA)**Loewner carpets and quasi symmetric maps**

Wednesday 25 September 2019, 12:15, M3 (M234)

Can we classify subsets of the plane that are 2-Ahlfors regular and 2-Loewner? In general, can we describe planar Loewner metric spaces. In this talk I will discuss my and my co-authors results on constructing examples, giving sufficient conditions and finding uniformizing maps for these spaces. Connections to Sobolev extension domains and geometric group theory will be described.

Seminar on analysis and geometry

Lucas Dias Condeixa (Aalto University)**What is...optimisation under uncertainty?**

Tuesday 24 September 2019, 14:15, M2 (M233)

TBA

What is...? seminar

Dario Gasbarra (University of Helsinki)**Stein operators for Gaussian polynomial random variables: an algebraic approach**

Monday 23 September 2019, 15:15, Y405

For a standard Gaussian random variable N, integration by parts gives the Stein equation E(Nf(N)- Df(N))=0
The Stein equation characterizes the distribution and it is the key in proving quantitative limit theorems towards the Gaussian.
Here we take the first steps in extending the methodology, and give an algorithm producing all the Stein differential operators
with polynomial coefficients for target random variables
of the form X= p(N_1, ..., N_d), with Gaussian N and polynomial p.
This is a joint work with Ehsan Azmoodeh (Bochum)
and Robert Gaunt (Manchester)

Aalto Stochastics and Statistics seminar

Fredrik Hoeg (NTNU)**Concave power solutions of the Dominative p-Laplace equation**

Wednesday 18 September 2019, 14:15, M3 (M234)

Seminar on analysis and geometry

Daniel Faraco (UA Madrid)**Non-linear Beltrami equation**

Wednesday 18 September 2019, 13:15, M3 (M234)

Seminar on analysis and geometry

Jens Habermann (Erlangen)**Finite propagation speed for parabolic quasiminimizers**

Wednesday 18 September 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Jukka Kohonen (Aalto)**Clustering, combinatorics and computation -- and some connections**

Monday 16 September 2019, 14:15, Y405

Aalto Stochastics and Statistics seminar

Antonella Nastasi (Palermo)**Weak solution for Neumann (p, q)-Laplacian problem on Riemannian manifold**

Wednesday 11 September 2019, 14:15, M3 (M234)

Seminar on analysis and geometry

Michael Collins (Erlangen)**Existence of variational solutions to a Cauchy-Dirichlet problem with time-dependent boundary data on metric measure spaces**

Wednesday 11 September 2019, 13:15, M3 (M234)

Seminar on analysis and geometry

Andreas Heran (Erlangen)**Harnack inequality for porous medium type equations**

Wednesday 11 September 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Alexandros Grosdos (Osnabrück University)**The 0-1-2 of local Dirac mixture moments**

Monday 09 September 2019, 17:00, M237

Moments in statistics are quantities that reveal the shape of a distribution and have recently gained attention from an algebraic point of view. When they are polynomials in the
parameters, one can define the moment ideal that is interesting both for statistical inference
and for its algebraic properties. In this talk we focus on the local Dirac case. Local order 0
has been well studied in algebraic geometry as well as signal processing. For 1st order Diracs
we obtain minimal generating sets of the ideals in question. Symbolic algebra is used to efficiently solve the problem of parameter identifiability for a mixture with few terms. For larger
mixtures we turn to Prony and numerical algebra methods. Our results are showcased with
examples in signal processing and statistics. We finally hint to conjectures and open problems
for higher local orders.
This talk is based on joint work with Markus Wageringel.

Applied Algebra Afternoon

Georgy Scholten (North Carolina State University)**Semi-Inverted Linear Spaces**

Monday 09 September 2019, 16:30, M237

The image of a linear space under inversion of some coordinates is an affine
variety whose structure is governed by an underlying hyperplane arrangement.
We generalize work by Proudfoot and Speyer and show that some circuit polynomials form a universal Grobner basis for the ideal of polynomials vanishing
on this variety. The proof relies on degenerations to the Stanley-Reisner ideal
of a simplicial complex determined by the underlying matroid. Moreover, if the
linear space is real, then the semi-inverted linear space is also an example of a
hyperbolic variety, meaning that all of its intersection points with a large family
of linear spaces are real.

Applied Algebra Afternoon

Alex Heaton (MPI Leipzig)**An SOS counterexample to an inequality of symmetric functions**

Monday 09 September 2019, 15:30, M237

It is known that differences of symmetric functions corresponding to various bases are nonnegative on the nonnegative orthant exactly when the partitions defining them are comparable in dominance order. The only exception is the case of homogeneous symmetric functions where it is only known that dominance of the partitions implies nonnegativity of the corresponding difference of symmetric functions. It was conjectured by Cuttler, Greene, and Skandera in 2011 that the converse also holds, as in the cases of the monomial, elementary, power-sum, and Schur bases. In this talk, we describe a counterexample, showing that homogeneous symmetric functions break the pattern. We use a semidefinite program to find a positive semidefinite matrix whose factorization provides an explicit sums of squares decomposition of the polynomial H44 − H521 as a sum of 41 squares. This certificate of nonnegativity disproves the conjecture, since a polynomial which is a sum of squares of other polynomials cannot be negative, and since the partitions 44 and 521 are incomparable in dominance order. This is joint work with Isabelle Shankar of UC-Berkeley.

Applied Algebra Afternoon

Miruna-Stefana Sorea (MPI Leipzig)**The shapes of level curves of real polynomials near strict local minima**

Monday 09 September 2019, 15:00, M237

We consider a real bivariate polynomial function vanishing at the origin and exhibiting a strict local minimum at this point. We work in a neighbourhood of the origin in which the non-zero level curves of this function are smooth Jordan curves. Whenever the origin is a Morse critical point, the sufficiently small levels become boundaries of convex disks. Otherwise, these level curves may fail to be convex.
The aim of this talk is two-fold. Firstly, to study a combinatorial object measuring this non-convexity; it is a planar rooted tree. And secondly, we want to characterise all possible topological types of these objects. To this end, we construct a family of polynomial functions with non-Morse strict local minima realising a large class of such trees.

Applied Algebra Afternoon

Francesco Spadaro**Constructing 2D Ising fermions with a geometrical-probabilistic approach**

Thursday 29 August 2019, 14:15, M3 (M234)

We will discuss a construction of correlations of discrete fermions for the two-dimensional critical FK-Ising and Ising models as expectations over geometrical configurations. The observable plays the role of a precursor for the free fermion in the Ising CFT, and it inspires the construction of CFT fields in the continuum case in terms of SLE/CLE measures.

Aalto Stochastics and Statistics Seminar (Ilmonen, Kytölä, Leskelä)

Kalle Kytölä**SLE random curves and conformal field theory**

Thursday 22 August 2019, 15:30, M3 (M234)

mathematical physics day (Kytölä)

Taha Ameen**Diagonalization of the 2D Ising model transfer matrix**

Thursday 22 August 2019, 15:00, M3 (M234)

mathematical physics day (Kytölä)

David Radnell**An introduction to the geometric structures underlying conformal field theory**

Thursday 22 August 2019, 14:00, M3 (M234)

mathematical physics day (Kytölä)

Christian Webb**On logarithmically correlated random fields**

Thursday 22 August 2019, 13:30, M3 (M234)

mathematical physics day (Kytölä)

Armando Gutiérrez**Elements of metric functional analysis**

Thursday 22 August 2019, 11:30, M3 (M234)

mathematical physics day (Kytölä)

Alex Karrila**On multiple SLE type scaling limits**

Thursday 22 August 2019, 11:00, M3 (M234)

mathematical physics day (Kytölä)

Jonna Mikkonen** Jäälauttakentän laskennallinen mallinnus (kandiesitelmä)**

Wednesday 21 August 2019, 15:15, M3 (M234)

Emma Järvinen**Neumannin ongelma eristävälle kiekkoinkluusiolle yksikkökiekossa (kandiesitelmä)**

Wednesday 21 August 2019, 14:15, M3 (M234)

Martti Ranta**Kiintopistelauseita ja niiden sovelluksia (kandiesitelmä)**

Wednesday 21 August 2019, 13:15, M3 (M234)

Lauri Särkiö**Polkujoukkojen mittaaminen kahdella eri modulilla (kandiesitelmä)**

Wednesday 21 August 2019, 11:15, M3 (M234)

Verna Heikkinen** Bayesian Reduced Rank Regression (BRRR): Application to Neuromagnetic Data (kandiesitelmä)**

Wednesday 21 August 2019, 10:15, M3 (M234)

Tuomas Tuukkanen** Rajoittamattomat operaattorit Hilbert-avaruuksissa (kandiesitelmä)**

Wednesday 21 August 2019, 09:15, M3 (M234)

Jyri Maanpää (Finnish Geospatial Research Institute)**End-to-end deep learning for autonomous steering of self-driving cars**

Tuesday 13 August 2019, 10:15, M3 (M234)

Master's thesis presentation

Dissertation

Alex Karrila (Aalto)**Conformally invariant scaling limits of random curves and correlations**

Friday 26 July 2019, 12:00, M1 (M232)

Further information

This dissertation studies mathematically the highly symmetric emergent structures in continuum limits of critical statistical-physics models. The results are formulated in terms of random curves and correlations.

Vincent Beffara (Université Grenoble Alpes)**Percolation for smooth 2D random fields**

Thursday 25 July 2019, 14:15, M3 (M234)

Aalto Stochastics and Statistics Seminar (Ilmonen, Kytölä, Leskelä)

Prof. Ahmad Yousefian Darani (University of Mohaghegh Ardabili)**Cyclic DNA Codes over ${F}_2+u{F}_2+u^2{F}_2$**

Thursday 27 June 2019, 14:15, M3 (M234)

In this talk we study the structure of cyclic DNA codes of even length over the ring
${F}_2+u{F}_2+u^2{F}_2$ where $u^3=0$.
We investigate two presentations of cyclic codes of even length over
${F}_2+u{F}_2+u^2{F}_2$ satisfying the reverse
constraint and the reverse-complement constraint.

ANTA Seminar

Mihaela Mihaylova (Aalto U)**Correlations studies of LDL-aggregation, LDL-lipidome and clinical data of bariatric surgery patients**

Tuesday 25 June 2019, 11:15, M2 (M233)

Atherosclerotic cardiovascular disease (ASCVD), also known as coronary artery disease (CAD), is one of the leading causes of death in the world.[1] A consensus has been reached that the main cause of ASCVD are low-density lipoproteins (LDL). [2] ASCVD develops in the innermost layer of the coronary artery wall (intima). Once LDL particles enter the wall, they are retained, modified, and accumulate there. [3]
There are several well-known risk factors of ASCVD, among which obesity, smoking, hypertension and LDL-cholesterol concentration in the plasma.[3] A novel approach to assessing the risk of ASCVD however suggests that, not only the concentration, but also the quality of LDL might be associated with ASCVD. [3] It shows that the susceptibility of LDL particles to aggregate (in the presence of the enzyme hrSMase) varies between humans and depends on the composition of the LDL particles. [3] The presence of aggregation-prone LDL in the plasma was found to be associated with future coronary artery disease (CAD) deaths. [3] This makes investigating LDL-aggregation further particularly important.
This masters thesis studies LDL aggregation of patients who underwent bariatric surgery - a procedure performed on people with obesity, for the purpose of weight loss.
It focuses on four main points:
● Creating a nonlinear mixed-effects model of LDL-aggregation and obtaining a single quantitative measure of LDL-aggregation.
● Investigating whether there is a significant difference in LDL-aggregation in patients before and after bariatric surgery
● Studying correlations between LDL-aggregation and lipids from the LDL-lipidome, as well as correlations with clinical data of bariatric surgery patients.
● Investigating whether there is a significant difference in the LDL-lipidome lipids and clinical parameters in the patients before and after the operation
The presentation will discuss the progress made on the project. It will cover the following points.
● Problem Overview: Theory and Data
● Solution Plan
● Step 1: Modelling of LDL-aggregation
- Nonlinear Mixed-Effect Models
- Modelling using the Bayesian approach
- Modelling Problems
- Possible Solutions
References:
[1] George, S. and Johnson, J. (2010). Atherosclerosis: Molecular and Cellular Mechanisms. Weinheim: Wiley-VCH-Verl.
[2] Ference, B. et al (2017). Low-density lipoproteins cause atherosclerotic cardiovascular disease. 1. Evidence from genetic, epidemiologic, and clinical studies. A consensus statement from the European Atherosclerosis Society Consensus Panel. European Heart Journal, 38(32), pp.2459-2472.
[3] Ruuth, M. et al (2018). Susceptibility of low-density lipoprotein particles to aggregate depends on particle lipidome, is modifiable, and associates with future cardiovascular deaths. European Heart Journal, 39(27),pp.2562-2573.

Aalto Stochastics & Statistics Seminar

Miikka Runolinna** Transitiivisuus hyperbolisissa satunnaisverkoissa (kandiesitelmä)**

Monday 24 June 2019, 13:15, M3 (M234)

Tommi Gröhn**Klikkien esiintymistiheydet satunnaisessa leikkausverkossa (kandiesitelmä)**

Monday 24 June 2019, 11:15, M3 (M234)

Lauri Ahlberg**The maths behind Bitcoin (kandiesitelmä)**

Monday 24 June 2019, 10:15, M3 (M234)

Tatu Hyytiäinen**Changepoint detection in network activity measurement data (diploma thesis talk).**

Tuesday 18 June 2019, 14:15, M2 (M233)

Prof. Jeffrey Ovall, (Portland State)**A Trefftz Finite Element Method on Exotic Meshes **

Monday 17 June 2019, 13:15, M3 (M234)

Over the past decade, there has been growing interest in the
development of finite element methods on meshes whose cells are
more general than the traditional triangles and quadrilaterals in 2D or tetrahedra and hexahedra in 3D, and this work has focused (almost) exclusively on
polytopal meshes. We consider finite element methods employing meshes consisting of quite general curvilinear polygons. These methods are in the
spirit of Trefftz methods for second order linear elliptic equations,
in that the local finite element spaces are defined implicitly in
terms of local Poisson problems involving polynomial data.
Immediately one must decide what should be meant by ``polynomial
on a curve'', and perhaps the two most natural choices are:
polynomials with respect to arclength or other natural parameter
related to the curve, or restrictions of polynomials in 2D to the
curve. We discuss why the latter space is preferred, and indicate how
to work with it in practice. Having made this choice, we introduce a
natural interpolation operator, and establish convergence results with
respect to mesh size. Several numerical examples illustrate these
convergence results in practice. We also argue, and demonstrate, that it is possible to exploit the approximation power of singular functions that may exist
in our local space (if the cell has non-convex corners) in order to achieve optimal order convergence without the typical adaptive refinement techniques.

Harri Hakula

Dr. Ramsès Fernàndez (Eurecat)**Problems and attacks for isogeny-based hash functions**

Wednesday 12 June 2019, 14:15, M3 (M234)

In this talk I will survey the main problems on isogenies of elliptic cuves believed to be hard in a quantum setting and how these problems relate to the security and the cryptanalysis of isogeny-based hash functions.

ANTA Seminar

Maximilien Dreveton (Inria Sophia Antipolis)**Almost exact recovery in label spreading**

Friday 07 June 2019, 12:15, M2 (M233)

In semi-supervised graph clustering setting, an expert provides cluster membership of few nodes. This little amount of information allows one to achieve high accuracy clustering using efficient computational procedures. Our main goal is to provide a theoretical justification why the graph-based semi-supervised learning works very well. Specifically, for the Stochastic Block Model in the moderately sparse regime, we prove that popular semi-supervised clustering methods like Label Spreading achieve asymptotically almost exact recovery as long as the fraction of labeled points does not go to zero and the average degree goes to infinity.

Aalto Stochastics & Statistics Seminar

Seppo Sorvari**Enemmistöäänestys ja iteratiiviset algoritmit binaarisissa joukkoistamistehtävissa (kandiesitelmä)**

Tuesday 04 June 2019, 16:15, M3 (M234)

Nuutti Vienola**From generalized linear models to logistic regression: a theoretical overview (kandiesitelmÃ¤)**

Tuesday 04 June 2019, 15:15, M3 (M234)

Diplomityöesitelmä Ville Romanov**The Bishop-Gromov volume inequality in Riemannian manifolds with a lower Ricci curvature bound**

Thursday 23 May 2019, 14:15, M2 (M233)

MSc Hoa Ngo (Aalto U)**First passage percolation on mixed sparse random graphs with two types of nodes**

Monday 20 May 2019, 15:15, M3 (M234)

A mixed graph is a graph consisting of both undirected edges and directed edges. This talk discusses first passage percolation on a connected mixed random graph with a given degree sequence, where an undirected edge is formed between type-1 nodes and a directed edge between type-1 and type-2 nodes. Weights on edges are assumed to be independent and exponentially distributed. We analyze a flooding time, which is the minimum time that a uniformly chosen node reaches all other nodes. We derive an asymptotic formula for the flooding time as the number of nodes tend to infinity. As an application, we discuss continuous time information spreading on a random regular graph, where we also take into account the impact of passive nodes. Type-1 nodes can be interpreted as active message spreaders and type-2 nodes can be interpreted as passive receivers which may only receive the message. In this setting we derive an asymptotic formula for the flooding time which is also called the broadcast time in the literature.

Aalto Stochastics & Statistics Seminar

Prof. Joerg Kliewer (New Jersey Institute of Technology)**Private and Distributed Function Computation**

Thursday 16 May 2019, 15:15, M3 (M234)

We consider the problem of private computation in a distributed storage system. In private computation, a user wishes to compute a function of f messages stored in noncolluding databases while revealing no information about the computation result to the databases. We first employ computation of a linear function of the messages, where linear codes are used to encode the information on the databases. We show that this private linear computation capacity, which is the ratio of the desired linear function size and the total amount of downloaded information, matches the maximum distance separable (MDS) coded capacity of private information retrieval for a large class of linear codes that includes MDS codes. Our converse result is valid for any number of messages and linear combinations, and the capacity expression depends on the rank of the coefficient matrix obtained from all linear combinations. We also present how our linear computation approach can be extended to computing arbitrary multivariate polynomials of the messages. Here, the presented schemes yield improved rates compared to the best known schemes from the literature for a small number of messages, while in the asymptotic case the rates match.

ANTA Seminar

Professor Aldo Conca (University of Genova, Italy)**Introduction to GrÃ¶bner bases**

Wednesday 15 May 2019, 15:15, M1 (M232)

GrÃ¶bner bases and related algorithms can be seen as generalizations of Gaussian elimination for linear systems and Euclid's algorithm for computing polynomial greatest common divisors of univariate polynomials. They can be used to solve algorithmically questions related to polynomials as, for example, the following:
1) deciding whether a system of polynomial equations has solutions,
2) deciding whether a polynomial can be written as linear combinations with polynomials coefficients of given polynomials,
3) deciding whether a polynomial can be written as polynomial function of given polynomials,
4) find the implicit equations of a locus given by a polynomial parametrization.
Questions of this type and their variations have several applications in mathematics, science and engineering.
The goal of the talk is to present a gentle introduction to GrÃ¶bner bases and related algorithms and their use to answer the questions above.

Department Colloquium

Giovanni Comi (UHH UniversitÃ¤t Hamburg)**A distributional approach to fractional Sobolev spaces and fractional variation**

Wednesday 15 May 2019, 12:15, M3 (M234)

Unlike their integer versions, the fractional Sobolev spaces $W^{\alpha, p}(\mathbb{R}^{n})$ do not seem to have a clear distributional nature. By exploiting suitable notions of fractional gradient and fractional divergence already existing in the literature, we introduce the new space $BV^{\alpha}(\mathbb{R}^{n})$ of functions with bounded fractional variation in $\mathbb{R}^n$ of order $\alpha \in (0, 1)$ via a new distributional approach. Thanks to the continuous inclusion $W^{\alpha, 1}(\mathbb{R}^{n}) \subset BV^{\alpha}(\mathbb{R}^{n})$, our theory provides a natural extension of the known fractional framework. In analogy with the classical $BV$ theory, we define sets with (locally) finite fractional Caccioppoli $\alpha$-perimeter and we partially extend De Giorgi's Blow-up Theorem to such sets, proving existence of blow-ups on points of the naturally defined fractional reduced boundary. In addition, we investigate the asymptotic behaviour of these fractional differential operators and we prove that the fractional $\alpha$-variation weakly and Gamma-converges as $\alpha \to 1^{-}$ to the standard De Giorgi's variation.

Seminar on analysis and geometry

Dr. Michał Lasoń (Jagiellonian University)**On some structures on matroids and related algebraic problems**

Tuesday 14 May 2019, 15:15, M3 (M234)

When an ideal is defined only by combinatorial means, one expects to have a combinatorial description of its algebraic invariants. An attempt to achieve this description often leads to surprisingly deep combinatorial questions. White's conjecture is an example. It asserts that the toric ideal associated to a matroid is generated by quadratic binomials. Another example is a question of Herzog and Hibi about existence of a quadratic Gröbner basis of the toric ideal of a matroid. Both problems reduce to questions about arrangements of bases in a matroid. We will review recent progress and state some intriguing open problems.

ANTA Seminar

Nicolas Dietrich (University of Salzburg)**Compactness results for parabolic problems**

Thursday 09 May 2019, 14:15, M2 (M233)

Seminar on analysis and geometry

Dr. Ragnar Freij-Hollanti**Introduction to secure multiparty computation**

Thursday 09 May 2019, 12:15, M3 (M234)

Guest lecture on the Applications of Coding Theory to Security course.

ANTA Seminar

Prof. Mateusz Michałek (Aalto/Max Planck)**From topology to algebraic geometry and back again**

Wednesday 08 May 2019, 15:15, M2 (M233)

I will present applications of secant varieties in topology through k-regular embeddings. An embedding of a variety in an affine space is called k-regular if any k points are mapped to linearly independent points. Numeric conditions for the existence of such maps are an object of intensive studies of algebraic topologists dating back to the problem posed by Borsuk in the fifties. Current world record results were obtained by Pavle Blagojevic, Wolfgang Lueck and Guenter Ziegler. Our results relate k-regular maps to punctual versions of secant varieties. This allows us to prove existence of such maps in special cases. The main new ingredient is providing relations to the geometry of the punctual Hilbert scheme and its Gorenstein locus. The talk is based on two joint works: with Jarosław Buczynski, Tadeusz Januszkiewicz and Joachim Jelisiejew and with Christopher Miller: arXiv:1511.05707 and arXiv:1512.00609.

ANTA Seminar

Ida Keskimäki**Tason symmetriat (kandiesitelmä)**

Tuesday 07 May 2019, 16:15, M3 (M234)

Dr Augusto Gerolin (VU Amsterdam)**An optimal transportation approach for the Schrödinger bridge problem and convergence of the Sinkhorn algorithm**

Monday 06 May 2019, 15:15, M3 (M234)

Aalto Stochastics & Statistics Seminar

Dissertation

MA Taneli Luotoniemi**Hyperspatial Interlace. Grasping Four-dimensional Geometry Through Crafted Models**

Friday 03 May 2019, 12:00, A1 hall, Otakaari 1X

Further information

Opponents: KuT, dos. Jyrki Siukonen, University of the Arts Helsinki and PhD, Prof. Thomas Banchoff, Brown University, USA
Custos: Prof. Helena Sederholm

Prof Thomas Banchoff (Brown University)**Meeting Salvador Dali in the Fourth Dimension**

Thursday 02 May 2019, 15:15, Aalto hall

Abstract: How did Salvador Dali choose an unfolded four-dimensional
cross as the central figure in one of his most famous religious
paintings? This talk will describe a ten-year series of meetings with
the artist starting in 1975 and a survey of forty years of
developments in computer graphics approaches to phenomena in four and
higher dimensions.

Mathematics and Arts Colloquium

Dissertation

Matias HeikkilÃ¤**On Multivariate Extremes**

Monday 29 April 2019, 13:00, M1 (M232)

Further information

Filosofian maisteri Matias HeikkilÃ¤ vÃ¤ittelee maanantaina 29.4.2019 klo 13 Aalto-yliopiston perustieteiden korkeakoulussa salissa M1, Otakaari 1, Espoo. VÃ¤itÃ¶skirjassa âOn Multivariate Extremesâ tutkittiin harvinaisten ilmiÃ¶iden ennustamista.
VÃ¤itÃ¶stilaisuuden vastavÃ¤ittÃ¤jÃ¤nÃ¤ toimii Assist. Prof. Anna Kiriliouk, University of Namur. Kustoksena toimii professori Pauliina Ilmonen matematiikan ja systeemianalyysin laitokselta.
VÃ¤itÃ¶stiedote Perustieteiden korkeakoulun verkkosivuilla: https://www.aalto.fi/fi/tapahtumat/vaitos-matematiikan-alalta-fm-matias-heikkila

Vesa Kaarnioja**Higher order QMC rules for uncertainty quantification using periodic random variables**

Friday 26 April 2019, 13:00, M3 (M234)

A popular model for the parametrization of random fields in
uncertainty quantification is given by the so-called affine model,
where the input random field is assumed to depend on uniformly
distributed random variables in a linear manner. In this talk, we
consider a different -- yet equally valid -- model for the input
random field, where the random variables enter the input field as
periodic functions instead. The field can be constructed to have the
same mean and covariance function as the affine random field. This
setting allows us to construct simple lattice QMC rules that obtain
higher order convergence rates, which we apply to elliptic PDEs
equipped with random coefficients.
This is a joint work with Frances Kuo and Ian Sloan.

Professor Ago-Erik Riet (University of Tartu)**Permutation Codes**

Thursday 25 April 2019, 11:15, M140 (Majakka)

Codes over permutations can potentially be applied for error correction in flash memories. Information in a flash memory is stored as electric charge in memory cells. Permutation codes are useful to combat errors of charge leakage over time and overshoot while writing. In this approach, within a block of numbered cells all charges are assumed to be different and their relative ranking defines a permutation.
Various distance metrics can be defined in the symmetric group of all permutations over the set $\{1,2,\ldots,n\}$, used to define codes, with varying degrees of usefulness to flash memories.
In this talk I review some of my work with coauthors on permutation codes for error correction. I also review a potential source coding into permutations framework proposed by us. I also introduce multipermutation codes which is a possible relaxation of permutation codes to the case when some charges within the block can be equal. I briefly discuss the difficulties of encoding information into and decoding from permutations.

ANTA Seminar

Professor Vitaly Skachek (University of Tartu)**Constructing Asynchronous Batch Codes using Hypergraphs**

Tuesday 23 April 2019, 15:15, M1 (M232)

Batch codes were first proposed by Ishai et al. as a means for balancing load in distributed storage systems. They are also of potential use in private information retrieval. In this talk, we present a new variant of batch codes termed "asynchronous batch codes", which are designed for parallel recovery of information symbols from the coded database, where different requests take different service time (i.e. the requests are served in an asynchronous manner).
It turns out that the graph-based batch codes studied by Rawat et al. are asynchronous. By building on the ideas therein, we show that hypergraphs of Berge girth at least 4 yield graph-based asynchronous batch codes. We prove the hypergraph-theoretic proposition that the maximum number of hyperedges in a hypergraph of a fixed Berge girth equals the quantity in a certain generalization of the hypergraph-theoretic (6,3)-problem. We then apply the constructions and bounds by Erdos, Frankl and Rodl to obtain batch code constructions and bounds on the optimal redundancy of the graph-based asynchronous batch codes.
We show that the optimal redundancy $\rho(k)$ of graph-based asynchronous batch codes of dimension $k$ with the query size $t=3$ is $2\sqrt{k}$. Moreover, for a general fixed value of $t \ge 4$, $\rho(k) = O\left({k}^{1/(2-\epsilon)}\right)$ for any small $\epsilon > 0$. For a general value of $t \ge 4$, $\lim_{k \rightarrow \infty} \rho(k)/\sqrt{k} = \infty$.
(Joint work with Ago-Erik Riet and Eldho K. Thomas)

Department Colloquium

Saara Vestola**Pintojen luokittelu Conwayn vetoketjulla (kandiesitelmä)**

Tuesday 16 April 2019, 16:15, M3 (M234)

Karl Brustad (NTNU, Trondheim)**Segre's Theorem. An analytic proof of a result in differential geometry.**

Wednesday 10 April 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Dr. Jie Li**High-Rate MDS Code Constructions for Distributed Storage Systems**

Tuesday 02 April 2019, 15:15, M3 (M234)

NOTE: TUESDAY!
Distributed storage systems with high reliability have wide applications in large data centers, peer-to-peer storage systems, and storage in wireless networks. To ensure reliability, the redundancy is crucial for these systems. A popular option to introduce redundancy is to employ erasure codes such as MDS (Maximum Distance Separable) codes, which can efficiently store data and protect against node failures. In this talk, we will introduce several novel high-rate MDS code constructions which have optimal repair bandwidth and some other key properties. In addition, two generic transformations for MDS codes will also be given, one is to enable optimal repair in MDS code and the other is to reduce the sub-packetization level of existing MDS codes, which address two major concerns in high-rate MDS codes for DSSs.

ANTA seminar

Kristian Moring**Global higher integrability of weak solutions for systems of porous medium type**

Wednesday 27 March 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Professor Paavo Pylkkänen (University of Helsinki)**Explaining consciousness in terms of information**

Tuesday 26 March 2019, 16:15, M1 (M232)

Conscious experience has become the focus of intensive interdisciplinary study over the past few decades. By now there are a number of candidate theories of consciousness, many of which make use of notions of information in their attempted explanations of consciousness. This talk provides first a brief overview of consciousness studies and then considers how consciousness can be understood in the light of two approaches that make an appeal to information: David Bohms active information approach, and Giulio Tononis mathematical integrated information theory of consciousness.

Department Colloquium

Dr Elena Magnanini (U Modena)**On the scaled cumulant generating function of the triangle observable in the dense Erdӧs-Rényi model**

Thursday 21 March 2019, 10:15, M3 (M234)

Further information

The computation of the probability of rare events is the main purpose of large deviations theory. For instance, in a simple case, one can consider the rare event in which a sum of i.i.d. Bernoulli variables attains a value which is larger than its average. A completely different and much more difficult problem, is the computation of large deviations probability of nonlinear functionals of the Bernoulli variables, e.g. cubic polynomials. A case in which such nonlinear problems arise is, for instance, the study of complex networks. In this talk I will present the behavior of the so-called scaled cumulant generating function of the number of triangles of an Erdӧs-Rényi random graph (dense case). The scaled cumulant generating function is strictly connected with the theory of large deviations since, when it is possible to apply the Gärtner-Ellis theorem, it turns out to be the Legendre transform of the rate function. More precisely, the aim of this talk is twofold. On one hand, to describe a modified version of a known Monte Carlo method, called Cloning algorithm, tailored for approximating the scaled cumulant generating function of an additive observable in the framework of random graphs. One the other hand, keeping the focus on the triangle observable, to present the numerical investigation performed in the region where the analytical expression of such function is not known (replica breaking regime).

Istvan Prause**Schwarz lemma, quasiconformal mappings and interpolation**

Wednesday 20 March 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Prof. Christine Kelley (University of Nebraska-Lincoln)**Communicating over channels with partial erasures**

Wednesday 13 March 2019, 15:15, M3 (M234)

Channels with partial erasures were recently introduced to characterize erasure events in applications where some partial information about an erased symbol or packet is known. After some background on partial erasure channels, we will introduce a multilevel coding scheme for designing codes over these channels. We also characterize cases of channel parameters when capacity can be achieved using such a scheme. Time permitting, we will look at fountain codes over partial erasure channels as well as simple relay channels where at least one link is a partial erasure channel.

ANTA seminar

Olli Saari (University of Bonn)**On endpoint regularity of maximal functions**

Wednesday 13 March 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Dissertation

Razane Tajeddine**Doctoral thesis defense: Private Information Retrieval from Coded Storage**

Thursday 07 March 2019, 14:00, M1 (M232)

Opponent: Prof. Simon Blackburn, Custos: Prof. Camilla Hollanti.

ANTA

Prof. Simon Blackburn (Royal Holloway)**The Walnut Digital Signature Algorithm**

Thursday 07 March 2019, 10:15, M3 (M234)

NOTE different day and time!
Walnut is a digital signature algorithm that was first proposed in 2017 by Anshel, Atkins, Goldfeld and Gunnells. The algorithm is based on techniques from braid group theory, and is one of the submissions for the high-profile NIST Post Quantum Cryptography standardisation process. The talk will describe Walnut, and some of the attacks that have been mounted on it. No knowledge of cryptography or the braid group will be assumed. Based on joint work with Ward Beullens (KU Leuven).

ANTA seminar

Cintia Pacchiano**The total variation flow**

Wednesday 06 March 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Leah Schätzler (University of Erlangen)**Existence of variational solutions for doubly nonlinear equations of porous medium type**

Wednesday 27 February 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

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