Math Colloquium

### Speaker: Finnur Lárusson, Adelaide University

### Title: Chaotic holomorphic automorphisms of Stein manifolds with the

volume density property

Location: VR-II, V-158

Time: Tuesday July 9 at 11.00 am

### Abstract:

I will report on joint work with Leandro Arosio. Let $X$ be

a Stein manifold of dimension $n\geq 2$ satisfying the volume density

property with respect to an exact holomorphic volume form. For example,

$X$ could be $\C^n$, any connected linear algebraic group that is not

reductive, the Koras-Russell cubic, or a product $Y\times\C$, where $Y$

is any Stein manifold with the volume density property. We prove that

chaotic automorphisms are generic among volume-preserving holomorphic

automorphisms of $X$. In particular, $X$ has a chaotic holomorphic

automorphism. Forn\ae ss and Sibony proved (but did not explicitly

state) this for $X=\C^n$ in 1997. We follow their approach closely.

Peters, Vivas, and Wold showed that a generic volume-preserving

automorphism of $\C^n$, $n\geq 2$, has a hyperbolic fixed point whose

stable manifold is dense in $\C^n$. This property can be interpreted as

a kind of chaos. We generalise their theorem to a Stein manifold as above.

Math Colloquium

### Speaker: Guðmundur Magnússon, HI

### Title: Multi Dispatcher Systems and interacting policies

Location: VR-II, V-258

Time: Tuesday June 18 at 11.00 am

### Abstract:

This project explores the performance of parallel server system. The focus of the project is a system using multiple heuristic policies to route jobs to a server. To achieve this there is a simulator created that uses the Monte Carlo method to numerically simulate the performance of a system. It displays with figures the result of some simulations under different conditions and answers how different policies interact in this multi dispatcher system.

BSc thesis under the supervision of Esa Olavi Hyytiä.

Math Colloquium

### Speaker: Sylvain Arguillère, CNRS – Institut Camille Jordan – MMCS

### Title: Shape analysis through flows of diffeomorphisms

Location: VR-II, V-258

Time: Thursday June 13 at 11.00 am

### Abstract:

The goal of shape analysis is to compare shapes in a way that takes into account their geometric properties. The end goal is to give an adapted framework for the statistical analysis of medical data, in order to identify sick patients automatically for example. In this talk, I will describe a method introduced by Alain Trouvé, which allows to compare shapes through flows of diffeomorphisms with minimal energy, using tools from differential geometry and optimal control.

Math Colloquium

### Speaker: Wolfgang Woess, TU Graz

### Title: THE LANGUAGE OF SELF-AVOIDING WALKS

Location: VR-II, V-155

Time: Tuesday June 4 at 11.00 am

### Abstract:

Let X = (VX, EX) be an infinite, locally finite, connected graph without

loops or multiple edges. We consider the edges to be oriented, and EX is equipped with

an involution which inverts the orientation. Each oriented edge is labelled by an element

of a finite alphabet Σ. The labelling is assumed to be deterministic: edges with the same

initial (resp. terminal) vertex have distinct labels. Furthermore it is assumed that the

group of label-preserving automorphisms of X acts quasi-transitively. For any vertex o

of X, consider the language of all words over Σ which can be read along self-avoiding

walks starting at o. We characterize under which conditions on the graph structure this

language is regular or context-free. This is the case if and only if the graph has more

than one end, and the size of all ends is 1, or at most 2, respectively. (joint work with Christian Lindorfer).

Math Colloquium

### Speaker: Primoz Potocnik, University of Ljubljana

### Title: Symmetries of finite graphs – a personal overview

Location: VR-II, V-158

Time: Tuesday May 28 at 11.00 am

### Abstract:

Whether a graph is more or less symmetric is typically measured in terms of its automorphism group consisting of all permutation of its vertices which preserves the adjacency relation. The highest level of symmetry is achieved when the automorphism group has only one orbit on the vertices and/or edges of the graph. I will give a personal and gentle overview of the problems and the results about this class of graphs.

Math Colloquium

### Speaker: Giulio Cerbai, University of Florence

### Title: Sorting Permutations Using Pattern-Avoiding Stacks

Location: Tg-227

Time: Thursday May 9 at 11.40 am

### Abstract:

The problem of sorting a permutation using a stack was proposed by Knuth in the 1960s. As it is well known, sortable permutations can be characterized in terms of pattern avoidance and their enumeration is given by the Catalan numbers. Since then, lots of generalizations have been proposed, either by increasing the number of stacks or by using different sorting devices (queues, pop stacks…). Unfortunately, the same problem with 2 stack in series is too hard and both the characterization and the enumeration of the sortable permutations are still unknown.

In this work we start the analysis of a new sorting device, consisting in two restricted stacks in series, where each stack cannot contain a given pattern. We will use a right-greedy procedure, thus generalizing the case of the 2-West sortable permutations. Our goal is to provide the first results in this new framework, hoping to gain a better understanding of the general 2-stacksort problem.

Math Colloquium

### Speaker: Arkadiusz Lewandowski, Jagiellonian University

### Title: Properties of solution trajectories for a metrically regular generalized equation

Location: Tg-227

Time: Thursday May 2 at 11.40 am

### Abstract:

It is known that given a smooth strictly pseudoconvex domain, all of its boundary points admit a peak function and an exposing map. We shall discuss the recent question of Deng, Guan, and Zhang (TAMS, 2016), concerning the existence of smooth families of peak functions and exposing maps at the boundary points of strictly pseudoconvex domains forming the family varying in a smooth way.

Math Colloquium

### Speaker: Iman Mehrabi Nezhad, HÍ

### Title: Properties of solution trajectories for a metrically regular generalized equation

Location: VR-II 258

Time: Thursday April 11 at 10.00 am

### Abstract:

The presentation starts from a tangible example, analysis of electrical circuits. Using the circuit theory laws, and considering *set-valued maps* to model the i-v characteristics of semiconductors like diode, and transistor, a *generalized equation* is obtained. The main concern of the talk is to investigate how perturbing the input signal will affect the output variables. The problem is studied in two cases: the static case, where the input signal is a DC source; and the dynamic case, where there exists an AC source in the circuit. We will review the electronic part very briefly as we are more interested in the mathematical model.In the static case, the problem can be reduced to the existence or absence of *local stability* properties of the solution map, or *metric regularity* for the inverse map. In the dynamic case, using methods of variational analysis and strong metric regularity property of an auxiliary map, we are able to prove the regularity properties of the solution trajectories inherited by the input signal. Furthermore, we establish the existence of continuous solution trajectories for the perturbed problem.

Math Colloquium

### Speaker: Ahmed Zeriahi, Université Toulouse III, Paul Sabatier

### Title: Pluripotential Kähler-Ricci flows

Location: VR-II 258

Time: Thursday March 28 at 11.40 am

### Abstract:

We will first give an introduction to the Kähler-Ricci flow

on Kähler compact manifolds.

Next, we will review a recent joint work with Chinh H. Lu and Vincent

Guedj on a weak version of this theory

motivated by the study of the Kähler-Ricci flow on complex projective

varieties with mild singularities.

This study requires the development of a Parabolic Pluripotential Theory

on compact Kähler manifolds.

It bowls down to define and study weak solutions for some parabolic

complex Monge-Ampère equations,

extending the celebrated Bedford-Taylor theory in the degenerate

elliptic case.

arXiv:1810.02121 https://arxiv.org/abs/1810.02121

Math Colloquium

### Speaker: Nick Poovuttikul, University of Iceland

### Title: Is hydrodynamics a theory of series expansion?

Location: VR-II 258

Time: Thursday March 21 at 11.40 am

### Abstract:

Hydrodynamics is one of the most successful theories in physics which describe dynamics across various length scales: from a few micrometers to the scale of galaxies. (some) Physicists tried to come up with an explanation why such a simple set of equations works so well. One of the most accepted explanations is based on the theorem by Nother which related the existence of divergence free quantities to the continuous global symmetries of the system. According to this, hydrodynamics is the gradient expansion of these quantities.

There are, however, many problems with this ‘explanation’, loosely speaking due to the lack of proper definitions of this gradient expansion scheme. I will go through a few scenarios where sometimes the procedure gives a non-sensible prediction such as the water is unstable, sometimes the gradient expansions is non-analytical (which can be observed experimentally), sometimes it gives a signal that travel faster than the speed of light or doesn’t even give the same collective excitations that were observed in the real systems, even in the regime where the hydrodynamic should be applicable.

Unfortunately, I have no mathematically satisfying answer to this question. So this overview talk will be a list of personal questions and puzzles I found while trying to understand what hydrodynamics really means.