Schmidt's game, its modifications, and a conjecture of Margulis

Barak Weiss

Ben-Gurion University and Yale

Brandeis University

Thursday, October 26, 2006

Talk at 4:30 p.m. in 317 Goldsmith Hall

Tea at 4:00 p.m. in 300 Goldsmith Hall

Abstract: Let BA denote the set of real numbers with bounded continued fraction coefficients. This is a set of zero Lebesgue which is also meager (small in the sense of category). Nevertheless it was shown by W. Schmidt in 1966 that for any sequence a_1, a_2, ... of reals, the countable intersection of BA + a_i is nonempty. In proving this result Schmidt introduced a powerful (yet amusing) method based on a game for two players, which can be played on any complete metric space. In recent work with Dmitry Kleinbock we describe variants of Schmidt's game which make it possible to show that certain dynamically defined sets have nonempty intersection. As a consequence we verify a conjecture of Margulis from 1990.

Home Web page: Alexandru I. Suciu Posted: October 20, 2006
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