### Matematiikan ja systeemianalyysin laitos

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* Seuraavan viikon tapahtumat merkitty tähdellä

Cintia Pacchiano**Parabolic minimizers to the Total Variation Flow.***** Today * ** Wednesday 13 November 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Marko Voutilainen (Aalto)**Modeling and estimation of multivariate strictly stationary processes***** ** Monday 18 November 2019, 14:15, Y405

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

Anton Vavilov**Geometry of Julia and Fatou sets for hyperbolic rational maps ***** ** Tuesday 19 November 2019, 13:15, M3 (M234)

Laura Jakobsson (Aalto)**Introduction to Representation Stability***** ** Tuesday 19 November 2019, 16:15, M2 (M233)

Algebra and Discrete Mathematics Seminar

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

Julian Weigt**Derivative-level L^p bounds for the local fractional maximal function**

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

Seminar on analysis and geometry

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

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

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

Joona Karjalainen (Aalto)**TBA**

Monday 25 November 2019, 14:15, Y405

Aalto Stochastics and Statistics seminar

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

Stavros Evdoridis**Boundary behaviour of harmonic mappings**

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

Seminar on analysis and geometry

Paavo Raittinen (Aalto)**TBA**

Monday 02 December 2019, 14:15, Y405

Aalto Stochastics and Statistics seminar

Muhammad Ardiyansyah (Aalto)**TBA**

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

Algebra and Discrete Mathematics Seminar

Toni Annala (University of British Columbia)**TBA**

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

Algebra and Discrete Mathematics Seminar

Emma-Karoliina Kurki**TBA**

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

Seminar on analysis and geometry

Sami Helander (Aalto)**TBA**

Monday 09 December 2019, 14:15, Y405

Aalto Stochastics and Statistics seminar

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