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 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 2018

## 17. May 2018

*14:30 (A&G), seminar room 3517***Gil Solanes **(Universitat Autònoma de Barcelona)

**Integral geometry of isotropic spaces**

**Abstract: **The kinematic formula of Blaschke and Santaló measures the set of euclidean motions that bring a convex body to intersect another one. Similar formulas exist for other kinds of objects (e.g. smooth submanifolds), and more general ambients, including rank one symmetric spaces. The explicit determination of the kinematic formulas in these spaces is an ongoing program, which has seen important progress based on fundamental results by S. Alesker in the theory of valuations. After reviewing the classical case of real space forms, we will see how the kinematic formulas have been obtained in complex space forms, and other isotropic spaces.

(Contact person: T. Wannerer)

## 24. May 2018

*14:30 (A&G), seminar room 3517***Nguyen-Bac Dang** (École Polytechnique)

**A positive cone in the space of continuous translation invariant valuations**

**Abstract:** I will discuss a joint work with Jian Xiao. In this talk, I will exploit some ideas coming from complex geometry to define a cone in the space of continuous translation invariant valuations. This cone allows us to define a subspace of valuations V' and a norm on it. I will then explain how the convolution of valuations on smooth valuations in V' extends continuously with respect to the topology induced by this norm so that V' has a structure of graded Banach algebra. Finally, I will give two applications of our construction.

(Contact person: T. Wannerer)

## 31. May 2018

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

**Felipe Ramos-Garcia**(Universidad Autónoma de San Luis Potosí)

**Title: Weak forms of equicontinuity **

**Abstract: **We will show how to use different forms of equicontinuity to classify dynamical systems with discrete spectrum (or Kronecker).

(Contact person: T. Jäger)

## 7. June 2018

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

**Asymptotically autonomous random dynamical systems**

**Abstract:** Random dynamical systems (RDS), i.e. dynamical systems on metric spaces driven by some noise, have been broadly studied in the past. They emerge naturally in many situations, such as solutions of SDE's or a model iterated function systems. Due to the influence of the noise, those systems are per se non-autonomous, but using a dynamical model for the noise, one can write them as autonomous skew product flows defined on the product of a probability space and the metric phase space.

We study random dynamical systems, where even the deterministic part is non-autonomous already. By this we mean noise driven systems whose skew product flow has an explicit dependence on time. Especially we are interested in systems that are asymptotically autonomous, which means that the skew product flow converges as time tends to infinity.

In this talk I will present a general framework for autonomous and non-autonomous RDS. Then I will focus on stochastic approximations, a particular class of asymptotically autonomous RDS, including examples and a bifuraction result. At the end I will address some open questions concerning generalizations of rsults for autonomous RDS to the non-autonomous setting.

(Contact person: T. Jäger)

## 21. June 2018

*14:30 (A&G), seminar room 3517***Florian Besau** (Goethe-Universität Frankfurt)

**TBA**

(Contact person: T. Wannerer)