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)

# Summer term 2017

## 6. April 2017

*14:30 (A&G), seminar room 3517***Boris Doubrov **(Belarussian State University, Minsk)

**Real hypersurfaces in C**^{3} with large symmetry

^{3}with large symmetry

*16:00 (DS&MP), seminar room 3517***Tobias Weich **(Universität Paderborn)

**Ruelle Resonanzen**

In a first part of the talk we introduce the notion of Ruelle resonances for dynamical systems and their implications for the decay of correlations. We will in particular focus on the modern spectral theoretical approach and explain how Ruelle resonances are related to poles of meromorphically continued resolvents. In the rest of the talk we will present two recent results on the support of the resonant states and the Ruelle spectrum on locally symmetric spcaes.

## 26. April 2017

*15:00 (A&G), seminar room 3319***Alexey Bolsinov** (Loughborough University)

**Projectively equivalent metrics in small dimensions**

## 27. April 2017

*16:00 Mathematical Colloquium Jena, CZ3, SR 308 - FÄLLT wegen Krankheit AUS!***Andreas Hamel** (Free University of Bozen)

**An abstract convexity approach to set relations and set optimization**

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## 11. May 2017

*14:30 (A&G), seminar room 3517***Siegfried Beckus **(Israel Institute of Technology)

**The space of Delone dynamical systems and related objects**

Recent developments show that the space of dynamical systems equipped with the Chabauty-Fell topology plays an important role in the spectral theory of Schrödinger operators as it greatly encodes topological and dynamical properties. Specifically, it is shown that the spectra of these operators behave continuous in the Hausdorff metric if and only if the underlying dynamical systems vary continuously in the Chabauty-Fell topology. This raises further questions whether other related quantities behave well in this topology. During the talk, we focus on the space of Delone dynamical systems in a locally compact, second countable Hausdorff group G acting by translation. Under the additional assumption of unique ergodicity of the limit point, the weak-* convergence of corresponding invariant probability measures on these Delone dynamical systems is proven.

Delone sets model solids in mathematical physics while associated Schrödinger operators describe the long time behavior of an particle in such a solid. Using the previously developed theory, we show that also other spectral quantities of these operators behave well in the Chabauty-Fell topology.

*16:00 (DS&MP), seminar room 3517***Martin Tautenhahn **(TU Chemnitz)

**Quantitative unique continuation and application to control theory for the heat equation**

## 18. May 2017

*14:30 (A&G), seminar room 3517***Zhiyuan Zhang** (Université Paris Diderot)

**Density of mode-locking for a class of skew-products**

**Density of mode-locking for a class of skew-products**

*16:30 Mathematical Colloquium Jena, CZ3, SR 317***Matthias Kreck** (Universität Bonn)

**Ein übersehenes Problem: Bettizahlen geschlossener Mannigfaltigkeiten**

## 01. June 2017

*16:00 (DS&MP), seminar room 3517***Felix Krahmer **(Technische Universität München)

**On the connection between analog and digital conversion and the roots of Chebyshev polynomials**

## 8. June 2017

*16:00 Mathematical Colloquium Jena, CZ3, SR 308***Erich Wittmann** (TU Dortmund)

**Was läuft im Mathmatikunterricht und in der Lehrerbildung falsch? Wie könnte umgesteuert werden?**

## 15. June 2017

*16:00 (DS&MP), SR 131 CZ*

**Pablo Ramacher**(Marburg)

**Equivariant convex and subconvex bounds for eigenfunctions and Hecke-Maas forms**

## 22. June 2017

*14:30 (A&G), seminar room 3517***Moussa Ndour **(TU Dresden)

**Qualitative changes in flow patterns**

We discuss a global approach for detecting early-warning signals for qualitative changes in flow patterns. As examples, we consider the double gyre and 4-mode quasi-geostrophic circulation models.

*16:00 (DS&MP), seminar room 3517***Maximilian Engel **(Imperial College London)

**Quasi-stationary dynamics and bifurcations of random dynamical systems**

We look at Markov processes that induce a random dynamical system evolving in a domain with forbidden states constituting a trap. The process is said to be killed when it hits the trap and it is assumed that this happens almost surely. We investigate the behavior of the process before being killed, asking what happens when one conditions the process to survive for a long time.

The topic goes back to the pioneering work by Yaglom in 1947 but in recent years new ideas have been developed. We discuss concepts like quasi-stationary and quasi-ergodic distributions, calling the associated random dynamics quasi-stationary or quasi-ergodic if such distributions exist. Given their existence, we can define average Lyapunov exponents and the Dichotomy spectrum of the random dynamical system with killing and describe the bifurcation behavior of typical examples of stochastic bifurcation theory within this environment. The underlying philosophy is to exhibit the local character of random bifurcations for stochastic differential equations which are usually hidden in the global analysis. We further relate these concepts to dynamical systems with holes.

## 29. June 2017

*16:00 Mathematical Colloquium Jena, CZ3, SR 309*

**Arno Berger**(University of Alberta)

**Digits and dynamics - A tour of Benford's Law**

Benford's Law (BL), a notorious gem of mathematics folklore, asserts that leading digits of numerical data are usually not equidistributed, as might be expected, but rather follow one particular logarithmic distribution. Since first recorded by Newcomb in 1881, this apparently counter-intuitive phenomenon has attracted much interest from scientists and mathematicians. This talk will introduce and discuss some of the intriguing aspects of BL, and relate them to problems in probability and number theory and, above all, dynamics.

In view of their pivotal role as models of many real-world processes, it is natural to ask whether dynamical systems can actually comply with BL in some sense or other and, if so, whether in turn something about dynamics can be learned from this. The talk will answer both questions in the affirmative. Moreover, all real data sets, such as e.g. data recorded from a dynamical system, necessarily are finite, and determining exactly what (and what not) BL means for such data will emerge as a formidable challenge in itself.

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## 06. July 2017

*14:30 (A&G), seminar room 3517***Pablo Roudriguez-Sanchez **(University of Wageningen)

### Invasive species: a mathematician among biologists

*16:00 (DS&MP), seminar room 3517***Sara Munday **(University of Bologna)

**A Birkhoff ergodic theorem for infinite measure systems**