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)

# Winter term 2019/20

## October 17, 2019

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

**Nikolay Martynchuk **(Friedrich-Alexander-Universität Erlangen-Nürnberg)** **

**Scattering monodromy in integrable Hamiltonian systems**

*Abstract:*The notion of Hamiltonian monodromy was introduced by Duistermaat, who defined this invariant as an obstruction to the existence of global action-angle coordinates in integrable Hamiltonian systems. Since then, non-trivial monodromy was observed in various specific examples of integrable systems, such as the spherical pendulum, the Lagrange top, and the hydrogen atom in crossed fields.

## October 24, 2019

*16:00 (Mathematical Colloquium Jena), *

** Ulf Hashagen **(Forschungsinstitut für Technik- und Wissenschaftsgeschichte, Deutsches Museum München)

**Rechnen, Denken und Erfinden im Zeitalter des Barock: Die Rechenmaschinen von Schickard, Pascal und Leibniz**

**Rechnen, Denken und Erfinden im Zeitalter des Barock: Die Rechenmaschinen von Schickard, Pascal und Leibniz**

## November 7, 2019

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

** Uri Grupel **(Universität Innsbruck)

**Intersections with random geodesics in high dimensions**

*Abstract:* Abstract: Given a large subset of the sphere *A* ⊆ *S*^{n}^{-}* ^{1}* does the ratio of lengths between a random geodesic Γ and the intersection Γ ∩

*A*represent the size of

*A*or does it tend to a zero-one law (as the dimension grows)? We will show that for any large set

*A*we have a distribution that is not concentrated around neither zero nor one.

In contrast to the case of the sphere, for any convex body in high dimensions, we can find a subset, of half the volume, such that the ratio of lengths between the intersection of the random geodesic with the convex body and the intersection of the subset with the random geodesic will be close to zero-one law.

The analysis of the two cases has different flavors. For the sphere we analyze the singular values of the Radon transform, in order to bound the variance of the length of the random intersection. For convex bodies, we use concentration of measure phenomena.

The results on the sphere can be generalized to the discrete torus or to intersection on the sphere with higher dimensional subspaces.

(Contact: T. Wannerer)

## November 14, 2019

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

**Jonas Knörr **(Goethe-Universität Frankfurt)** **

**Smooth valuations on convex functions**

*Abstract:* In recent years, valuations on functions arose as a natural generalization of valuations on convex bodies, and various types of valuations on different spaces of functions have been studied and classifed.

I will present some results from an ongoing project examining the space of* dually epi-translation* invariant valuations on convex functions.We will see how these functionals are related to translation invariant valuations on convex bodies and how one can exploit this relation to establish a notion of smoothness. It turns out that the dense subspace of smooth valuations can be described using integration of differential forms over the graph of the differential of a convex function (or more generally, the differential cycle) and I will present a sketch of proof for this result.

As an application, we will see that the subspace of smooth and rotation invariant valuations admits a very simple description.** **

(Contact: T. Wannerer)

*16:00 (Mathematical Colloquium Jena), *

**Prof. Nikola Sandrić **(University of Zagreb, z.Z. Humboldt-Stipendiat Jena)** **

**Stochastics stability of Markow processes **

*Abstract:* One of the classical directions in the analysis of Markov processes is studying their long-time behavior, the so-called stochastic stability. Stochastically stable Markov process naturally appear as mathematical models of many phenomena arising in nature and engineering, such as problems related to population dynamics, turbulent fuid flows, and homogenization of heterogeneous structures. The goal of this exposition is to motivate and gradually introduce the notion of stochastic stability, first by discussing the most simple probabilistic models (random walks and Lévy process), then classical diffusion processes, and finally diffusion processes with jumps.** **

## November 28, 2019

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

** Igor Khavkine** (

**Czech Academy of Sciences, Prague)**

**IDEAL Characterization of Cosmological and Black Hole Spacetimes**

*Abstract:* t.b.a.** **

(Contact: V. Matveev)

## December 5, 2019

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

**Siegfried Beckus ** (Universität Potsdam)** **

**TBA**

*Abstract:* t.b.a.** **

(Contact: M. Schmidt)

## January 16, 2020

*16:00 (Mathematical Colloquium Jena), *

**Daniel Rosen ** (Ruhr-Universität Bochum)** **

**TBA**

*Abstract:* t.b.a.** **

(Contact: T. Wannerer)