The research seminars Analysis & Geometry (A&G) and Dynamical Systems & Mathematical Physics (DS&MP) are organised by the research groups of Prof. David Hasler, Prof. Daniel Lenz, Prof. Vladimir Matveev, Prof. Tobias Jäger, Prof. Anke Pohl and Prof. Thomas Wannerer.

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**When**: Thursdays @ 14:30-16:00 (A&G) and 16:00-17:30 (DS&MP)

**Where**: Ernst-Abbe-Platz 2, seminar room 3517 (OpenStreetMap)

# Winter term 2017

## 19. October 2017

*16:00 (DS&MP), seminar room 3517***Alexander Adam **(Institut Mathématique de Jussieu, UMPC, Paris)

**Expansion of horocycle ergodic average**

(Contact person: A. Pohl)

## 26. October 2017

**Dies Academicus**

*14:30 (A&G), seminar room 3517***Jun Jason Luo **(Chongqing University/Friedrich Schiller University Jena)

**Topological properties of self-similar fractal squares **

I will present some basic topological properties of a class of self-similar sets arising from a unit square. First we give a complete classification of their topology. Secondly we discuss their Lipschitz equivalence. The main approach used is to construct a Gromov hyperbolic graph on the symbolic space of the self-similar set and study its hyperbolic boundary properties. Further works on more general self-similar sets and even self-affine sets will be discussed as well.

(Contact person: M. Zähle)

## 2. November 2017

*16:00 (DS&MP), seminar room 3517*

**Christian Weiß **(Hochschule Ruhr West)

**Ergodic Quasi-Monte Carlo Methods **

(Contact person: A. Pohl)

## 9. November 2017

*14:30 (A&G), seminar room 3517***Louis Soares **(Jena)

**Resonances for Large Covers of Hyperbolic Surfaces**

(Contact person: L. Soares, A. Pohl)

*16:30 Mathematical Colloquium Jena, CZ3, SR 114*

**Vlada Limic**(Université Paris Sud 11)

**Near-critical random graphs and multiplicative coalescents**

## 16. November 2017

*16:00 (DS&MP), seminar room 3517***Maxim Kirsebom **(Aarhus University)

**The statistics of shrinking target problems in homogeneous dynamics**

*Abstract:* It is a common question in dynamics to ask how orbits of the system hit a target, i.e. a certain subset of the system. In the last couple of decades a new variation of this question emerged known as shrinking target problems. In this case we ask how orbits hit a sequence of sets of decreasing measure. Typical results in this direction are known as quantitative Poincaré recurrence, logarithm laws, dynamical Borel-Cantelli lemmas, hitting/return time statistics and extreme value distributions.

In this talk I will give an overview of these type of results, what information each result provides and how they are connected. I will also survey recent results in this direction. Finally, I will present own results on extreme value distributions for one-parameter subgroups acting on homogeneous spaces. For the purpose of the talk I will consider the concrete case of extremes for shortest vectors in lattices in SL(d,R)/SL(d,Z).

(Contact person: A. Pohl)

## 23. November 2017

*16:30 Mathematical Colloquium Jena, CZ3, SR 308*

**Andres Koropecki**(Universidade Federal Fluminense/Friedrich Schiller Universität Jena)

**Boundary dynamics for surface homeomorphisms**

Abstract: I will discuss recent results about the dynamics on the boundary of invariant domains for a surface homeomorphism, and its relationship with the induced dynamics in the prime ends compactifications.

## 30. November 2017

*14:30 (A&G), seminar room 3517***Eugenia Saorín Gómez** (FSU Jena)

**The difference body is a prototype of a valuation under volume constraints**

The abstract can be found here.

(Contact person: V. Matveev)

## 7. Dezember 2017

*14:30 (A&G), seminar room 3517***Claudio Gorotski **(Universidade Sao Paulo)

**Geometry of orbit spaces**

The abstract can be found here.

(Contact person: V. Matveev)

## 14. Dezember 2017

*14:30 (A&G), seminar room 3517***Alexander Lytchak** (Universität Köln)

** Minimal discs in metric spaces**

*Abstract: * The question of existence of minimal area fillings of prescribed contours goes back to Lagrange and is known under the name Plateau problem.

The investigation of the problem was the source for the creation of many flourishing theories, for instance the geometric measure theory. In the talk I will discuss the problem

and its solution in the framework of singular metric spaces and explain some applications. The talk will be based on a series of papers with Stefan Wenger.

(Contact person: V. Matveev)

## 11. January 2018

*14:30 (A&G), seminar room 3517***Sabrina Kombrink **(Universität zu Lübeck)

**TBA**

(Contact person: A. Pohl)

## 18. January 2018

*14:30 (A&G), seminar room 3517***Christian Seifert** (TU Hamburg)

**TBA**

(Contact person: M. Tautenhahn)