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**

(Contact person: T. Jäger)

## 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.

(Contact person: T. Jäger)

## 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 Gorodski **(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***Christian Lange** (Universität Köln)

**Orbifolds all of whose geodesics are closed**

*Abstract: * In his thesis Zoll, a student of Hilbert, constructed surfaces all of whose geodesics are closed. We give more elementary proofs for the known facts that on such a Zoll surface all closed geodesics have the same length, and that the metric has to be round in case of the projective plane. For 2-orbifolds all of whose geodesics are closed the length spectrum may be more complicated. We explain why it is still rigid under changes of the metric. Depending on the time we discuss generalizations to periodic Hamiltonian flows and recent results on higher dimensional orbifolds all of whose geodesics are closed.

(Contact person: V. Matveev)

## 21. Dezember 2017

*14:30 (A&G), seminar room 3517***Fabio Tal **(Universidade Sao Paulo/FSU Jena)

**Rotation sets for a standard family of hamiltonian torus diffeomorphisms**

*Abstract: * We study the rotation sets for a natural parameter family of torus diffeomorphisms lifted that can be viewed as an analouge to the standard family of twist diffeomorphisms of the annulus. Our main goal is to identify the region O on the parameter space where the rotation set has nonempty interior, a property that is know to have several important dynamical consequences like the existence of periodic points of arbitrarily large prime period and positive topological entropy. Numerical evidence shows that the region O has very interesting geometry, and suggests several interesting question. We will present rigorous proofs that confirm some of the more identifiable aspects of O, as well as asymptotic bounds on its boundary both for large and small parameters. We also show a general result of continuity of the rotation set for families of hamiltonian homeomorphisms. This is joint work w. T. Jäger and A. Koropecki.

(Contact person: T. Jäger)

*16:30 (Mathematical Colloquium), Lecture Hall 3, CZ3***Harald Helfgott** (Universität Göttingen)

**Voronoi and Eratosthenes: sieves and the divisor problems**

*Abstract: * We show how to carry out a sieve of Erastosthenes up to N in space O(N^{3})$ and essentially linear time. This improves over the usual versions, which take space about O(N) and essentially linear time. The algorithm -- which, like the one in (Galway, 2000), is ultimately related to diophantine approximation -- can also be used to factorize integers n, and thus to give the values of arithmetical functions such as the Möbius function and the Liouville function for all integers up to N.

(Contact person: A. Pohl)

## 11. January 2018

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

**Steiner formula for fractal sets**

(Contact person: A. Pohl)

## 18. January 2018

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

**On traces of Dirichlet forms**

(Contact person: M. Tautenhahn)

*16:00 (DS&MP), seminar room 3517***Konstantin Hoffmann **(FSU Jena)

**Entropy and statistics of DNA sequences**

*Abstract:* The statistical structure of DNA sequences shows long-range dependencies that are reflected in a decrease of the entropy of associated Markov approximations. We describe some statistical tools that can be used to quantify this phenomena.

(Contact person: T. Jäger)

## 8. Februar 2018

*16:30 (Mathematical Colloquium), SR 309, CZ3***Bernd Sturmfels** (MPI-MIN Leipzig)

**Tensors and their Eigenvectors**

*Abstract: *