Rudolf Hilfer (Universität Stuttgart, Institute for Computational Physics)

Ergodicity breaking, stationarity and local equilibrium

Abstract: The presentation reveals a fundamental dichotomy in ergodic theory between subsets of vanishing and
non-vanishing measure with respect to their induced automorphisms. The observation seems to be related
to fundamental open problems of statistical physics such as local equilibrium in time and emerges from
a scaling limit.

(Contact: M. Zähle)

 

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24. January 2019

14:30 (DS&MP), seminar room 3517

Bernardo Melo de Carvalho (Universidade de Minas Gerais/FSU Jena)

Beyond Topological Hyperbolicity

Abstract:  In this talk we will discuss the dynamics of systems admitting some sort of hyperbolicity on non-trivial continua. They are called Continuum-wise Hyperbolic. We plan to introduce interesting examples of these systems and to characterize the possible dynamic phenomena which can occur.

(Contact: T. Jäger)

 

16:00 (A&G), seminar room 3517

Martin Henk (Technische Universität Berlin)

The dual Minkowski problem

Abstract: The (classical) Minkowski problem asked for sufficient and necessary conditions such that a finite Borel measure on the sphere is the surface area measure of a convex body.  Its solution, based on works by  Minkowski, Aleksandrov and Fenchel&Jessen, is one of the centerpieces of the classical Brunn-Minkowski theory.

There are two far-reaching extensions of the classical Brunn-Minkowski theory, the L_p-Brunn-Minkowski theory and  the dual Brunn-Minkowski
theory. In the talk we will discuss the analog of the (classical) Minkowski problem within the dual Brunn-Minkowski theory, i.e., the characterization problem of the dual curvature measures. These measures were recently introduced by Huang, Lutwak, Yang and Zhang and are  the counterparts to the surface area measures within the dual theory.

(Contact: T. Wannerer)

 

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7. February 2019

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

Christoph Thäle (Ruhr-Universität Bochum)

Monotonicity for random polytopes

Abstract: Random polytopes are classical objects studied at the crossroad of convex geometry and probability. In this talk we discuss several monotonicity questions for random polytopes. As a special case we consider the expected f-vector of random projections of regular polytopes.

(Contact: T. Wannerer)

 

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28. March 2019

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

Antonio Lerario (SISSA, Trieste)

Probabilistic Enumerative Geometry

Abstract: Enumerative geometry deals with the problem of counting ("enumerating") geometric objects satisfying some constraint on their arrangement. For example: "how many lines in three-space intersect at the same time four given lines?" The answer is two if we are allowed to look for complex lines, but it depends on the four given lines if we search for real lines. In the complex framework this question (and similar) can be answered using a beautiful, sophisticated technique called Schubert calculus: it is the study of the way cycles intersect in complex Grassmannians. Unfortunately, over the reals this technique loses its power: this is the old problem of finding real solutions to real equations, for which the number of complex solutions only gives upper bounds. In this talk I will present a probabilistic approach to this problem, trying to address questions like: "how many lines in three-space intersect four given random lines?"
The answer to this question comes through the study of integral geometry in real Grassmannians and has surprising connections to convex geometry and representation theory...

(Contact: T. Wannerer)

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