**Prof. Anatoly Vershik**

**Steklov Institute of Mathematics, St. Petersburg**

**Lecture 1: April 29, 2019 at 15:30 at Amado 232**

**Title**: *Graded graphs and central measures*

**Abstract**: Graded graphs (Bratteli diagrams) as dynamical language; Markov compact of paths, central measures. connection to asymptotic representation theory of locally finite groups, characters as a central measures. limit shape type theorems and generalized law of large numbers.

**Lecture 2: May 1, 2019 at 14:30 at room 814**

**Title**: *Ergodic theory of graded graphs*

**Abstract**: Principal cocycle, adic structure, theorem of adic realization, absolute (boundaries) for random walks on the groups, combinatorial coding of dynamical systems.

**Lecture 3: May 2, 2019 at 14:30 in room 814** (Amado Building)

**Title**: *Theory of filtrations and applications*

**Abstract**: Metric and combinatorial invariants of the filtrations standartness, criteria of standartness, and secondary entropy of automorphisms. boundaries and invariant measures for filtrations; projective limits of the simplices.