# Münchner Mathematisches Kolloquium

Am Freitag, 30. Juni 2006, um 16 Uhr c.t. spricht

im Hörsaal E 27 über das Thema

## How to play mathematical billiards?

*Zusammenfassung:*
In the 1870's, when laying down the foundations of statistical physics, Ludwig Boltzmann formulated his celebrated 'ergodic hypothesis'. According to this assumption, in large mechanical systems in equilibrium the time averages of observables can be replaced by their equilibrium averages. The mathematical interpretation and understanding of this hypothesis led in the 1930's to the birth of the ergodic theory. Several geometric (e. g. geodesic flows on negatively curved manifolds), number-theoretic and probabilistic models have been proven to be ergodic before Yakov Sinai, in 1963, conjectured that the 'simplest' mechanical model, namely the system of hard balls on a torus is ergodic as well. Ever since, the exciting development of the Boltzmann-Sinai ergodic hypothesis has required ideas from the theory of dynamical systems, from geometry and from algebra, not mentioning deep intuitions from physics. Beyond ergodicity, mathematical billiards may also exhibit delicate stochastic behavior like exponential correlation decay. Moreover, constructions arising from mathematical billiards serve as instructive, realistic mechanical models of the Brownian motion, of heat construction, etc. The lecture will present a brief survey of some recent breakthroughs in the theory of mathematical billiards which - though for a long time was considered a bit mystic - now is becoming accessible for a wider circle of experts coming from different branches of mathematics.

Alle Interessierten sind hiermit herzlich eingeladen. Eine halbe Stunde vor
dem Vortrag gibt es Kaffee und Tee im Raum 349 im 3. Stock.

Treffpunkt zum Abendessen wird noch bekannt gegeben.

Für die Mathematischen Fachbereiche der LMU und der TUM, die Dekane

**Prof. Stefan Mittnik, Ph. D. (LMU)** und **Prof. Dr. M. Brokate (TU)**.