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A.Katok

Selected topics in modern dynamics and its applications

My plan is to schedule four sessions at IUM on June 3, 5, 9, and 10, room 310.

Each seminar will be dedicated to a separate topic; there are connections betweent topics 3 and 4 (see below), otherwise the seminars will be totally independent. Each seminar (including the last one) may be attended independently of the others. The presentation of both the introductory part and the discussion will be shared between myself and other mathematicians. I welcome any suggestions to that extent. So far Y.S. Ilyashenko agreed to make a presentation at Seminar 1 and MIsha Kulikov agreed to present a part of the introduction at the Seminar 3.

I am trying to emphasize areas which are not strongly reperesented in Moscow by resident mathematicians.

1. Tuesday June 3, 4PM
Selected topics in partial hyperbolicity
(After Pugh, Shub, Wilkinson, Dolgopyat, Pesin, Brin, D. Burago, S.Ivanov and others)

2. Thursday June 5, 4pm
Mechanisms of slow mixing and new uses of approximations in ergodic theory
(After Fayad, Katok, Kochergin)

3. Monday June 9, 4pm
Appplications of measure rigidity to diophantine approximation
(After Dani, Margulis, Einsiedler, Katok, Lindenstrauss, Spatzier, Kalinin)

4.Tuesday June 10, 4pm
Appplications of measure rigidity to quantum unique ergodicity
(After Lindenstrauss, Bourgain, Sarnak and others)

The format of each seminar is as follows: about 90 minutes of introductory presentation, a break (20-30 minutes), and the second part of indefinite length with a discussion of recent results and open problems. Expected end of each seminar is between 7:30 and 8pm. Both parts will include presentations by various mathematicians.

All seminars will be conducted in Russian.