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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.