65 KAM Mathematical Colloquium

65 KAM Mathematical Colloquium

Vitaly Bergelson

(University of Ohio, Columbus)

ERGODIC THEOREMS ALONG POLYNOMIALS: FROM COMBINATORIAL APPLICATIONS TO CHALLENGES FOR PHYSICISTS


ctvrtek 25. ledna 2007 ve 14:00, poslucharna S5, druhe patro
KAM MFF UK
Malostranske nam. 25
118 00 Praha 1

Abstract

Various recurrence and convergence results obtained in recent years indicate that dynamical systems exhibit regular behavior along polynomial times. While these results were mainly motivated by applications to number theory and combinatorics, such as the polynomial extension of Szemeredi's theorem on arithmetic progressions, this phenomenon also deserves attention from the point of view of potential applications to physics. For example, the Poincare recurrence theorem, as well as convergence theorems of the von Neumann and Birkhoff type, hold along any sequence of the form p(n), n=1,2, ... where p(n) is a polynomial with integer coefficients satisfying p(0) = 0, and it would be of interest to give a physical interpretation of these facts. After reviewing some known results, we will discuss the intriguing dichotomy between the theorems related to polynomial and exponential behavior. The last part of the talk will be devoted to open problems and conjectures.
 


V patek 26. 1. 2007 v poslucharne S5 v 10:40 prednese V. Bergelson navazujici druhou prednasku The Early results of Ramsey theory and their modern counterparts, ktera bude prvni prednaskou MiniDocCoursu (podrobnosti viz minidoc)
 

O přednášejícím

Vitaly Bergelson studoval v Rusku a Izraeli. Jeho dizertace (vypracovana pod vedenim prof. H. Furstenberga na Jeruzalemske univerzite) ziskala Landauovu cenu. Od roku 1984 je zamestnan na University of Ohio v Columbusu, kde je v soucasnosti radnym profesorem. Prof. Bergelson je mezinarodne uznavanym pracovnikem v ergodicke teorii a jejich aplikacich, zvlaste v kombinatoricke teorii cisel. Spolecne se svym studentem A. Leibmanem dokazal napriklad zname polynomialni verze Van der Waerdenovy vety a Szemerediho vety. Vitaly je znamym prednasejicim a oblibenym ucitelem. V letosnim roce prednesl zvanou prednasku na Mezinarodnim kongresu matematiku v Madridu a rovneďż˝ Mordellovu prednasku v Cambridgi. Jeho praďż˝ske kolokvium je venovano hlavni oblasti jeho zajmu a je urceno siroke matematicke a informaticke verejnosti.