Coffee is served between 2.45 and 3.15 outside the lecture hall.

Lecture 2:
Friday, May 25, 3.15-4.15 pm
Lecture hall E3, Osquarsbacke 14

Lecture 3:
Monday, May 28, 3.15-4.15 pm
Lecture hall E3, Osquarsbacke 14

Abstract:

Homogeneous dynamics is another name for the theory of flows
on homogeneous spaces, or homogeneous flows. The study of
homogenous flows has been attracting considerable attention for
at last 40-50 years. During the last three decades, it has been realized
that some problems in number theory and, in particular, in Diophantine
approximation can be solved using methods from the theory of
homogeneous flows. The purpose of the first lecture is to give examples
of interactions between number theory and homogenous dynamics;
mostly only formulations will be given, but there will be also very brief
description of some proofs. The second and third lectures will be the
continuation, on a more technical level, of the first lecture. Topics to be
(very briefly) covered include: (1) recurrence to compact sets and Diophantine
approximation on manifolds; (2) orbit closures, the Oppenheim conjecture and the
Littlewood conjecture; (3) classification of ergodic invariant measures and
equidistribution; (4) quantitative Oppenheim conjecture and counting of integral
points on homogenous varieties; (5) effective results in homogeneous dynamics.

Sponsored by the Göran Gustafsson Foundation

2012-05-11