## Category: Málstofa í stærðfræði

Carlos Argaez Garcia, september 24, 2019

Math colloquium

#### Titill: Pattern avoidance in various domains

Staðsetning: HB5 (Háskólabíó)
Tími: Föstudag 25.oktúber kl. 11:40

#### Ágrip:

When one searches the web for „pattern avoidance“ most of the results are about pattern avoiding permutations and their variants, such as colored, partial, multi-, affine, signed, and poset permutations. However there are definitions and results about similar concepts in other objects, such as graphs and topological spaces. We will survey these examples of pattern avoidance as well as highlighting more recent variants, such as polyominoes, integer partitions and alternating sign matrices.

This talk will be accessible to any student who has walked past a room where discrete mathematics was being taught.

## Björn Birnir

Carlos Argaez Garcia, ágúst 23, 2019

Math colloquium

#### Titill: When can we expect the Greenland glacier to melt?

Staðsetning: VR-II,V-258
Tími: Þriðjudag 27.ágúst kl. 11:00

#### Ágrip:

It was suggested by Rose (2005) that because of the migratory and responsive nature of the capelin, a small pelagic fish that is key to the ecology and fisheries of the North Atlantic, it can be viewed as the „canary in the coalmine“ to detect signals of environmental changes in the Arctic Ocean. In this talk we will combine analysis of data and extensive simulations of the migrations of the capelin and its physiology to analyze the changes in the ocean environment taking place over the last half-century. The environmental data for the last thirty year is obtained from a database called Copernicus, constructed by the European Union. Our goals will be to understand and predict the migrations of the capelin and its interactions with the ocean environment. We will explain how these have changed over time and how they are likely to change in the future. Then we will explain how our simulations can be compared with data, with the aim of finding out the rate of the temperature changes in the Arctic Ocean and when thresholds for major disruptions in Arctic environments are likely to be reached. The recent changes in the spawning routes of the capelin lead to a startling prediction.

Carlos Argaez Garcia, ágúst 20, 2019

Math Phys seminar

#### Titill: Continuous Quantum Walks

Staðsetning: VR-II, V-158
Tími: Fimmtudag 22.ágúst kl. 11:00

#### Ágrip:

Continuous quantum walks arise naturally as quantum analogues of continuous random walks, but in contrast to their classical counterparts, they exhibit some curious and counter-intuitive properties. I will give an introductory talk on continuous quantum walks and present some of these exciting properties.
The motivation for studying quantum walks largely comes from quantum physics and quantum computing, however, the emphasis of this talk will be on the mathematics. In particular, no prior knowledge of anything quantum is assumed.

## Finnur Lárusson

Valentina Giangreco, júní 7, 2019

Málstofa í stærðfræði

### Titill: Chaotic holomorphic automorphisms of Stein manifolds with the volume density property

Staðsetning: VR-II, V-158
Tími: þriðjudagur 9. júlí kl. 11.00

### Ágrip:

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.

## Guðmundur Magnússon

Valentina Giangreco, júní 7, 2019

Málstofa í stærðfræði

### Titill: Multi Dispatcher Systems and interacting policies

Staðsetning: VR-II, V-258
Tími: þriðjudagur 18. júní kl. 11.00

### Ágrip:

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.

## Sylvain Arguillère

Valentina Giangreco, júní 7, 2019

Málstofa í stærðfræði

### Titill: Shape analysis through flows of diffeomorphisms

Staðsetning: VR-II, V-258
Tími: fimmtudagur 13. júní kl. 11.00

### Ágrip:

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.

## Wolfgang Woess

Valentina Giangreco, maí 31, 2019

Málstofa í stærðfræði

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

Staðsetning: VR-II, V-155
Tími: þriðjudagur 4. júní kl. 11.00

### Ágrip:

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).

## Primoz Potocnik

Valentina Giangreco, maí 20, 2019

Málstofa í stærðfræði

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

Staðsetning: VR-II, V-158
Tími: þriðjudagur 28. maí kl. 11.00

### Ágrip:

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.

## Giulio Cerbai

Valentina Giangreco, maí 1, 2019

Málstofa í stærðfræði

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

Staðsetning: Tg-227
Tími: Fimmtudagur 9. maí kl. 11.40

### Ágrip:

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.

Valentina Giangreco, apríl 28, 2019

Málstofa í stærðfræði

### Fyrirlesari: Arkadiusz Lewandowski, Jagiellonian University

Staðsetning: Tg-227
Tími: Fimmtudagur 2. maí kl. 11.40

### Ágrip:

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.