##### Department of Mathematics,

University of California San Diego

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### Special Colloquium

## Ilya Kossovskiy

#### University of Vienna

## Dynamical Approach in Cauchy-Riemann Geometry and Applications

##### Abstract:

The subject of Cauchy-Riemann Geometry (shortly: CR-geometry), founded in the research of Henri Poincare, is remarkable in that it lies on the border of several mathematical disciplines, among which we emphasize Complex Analysis and Geometry, Differential Geometry, and Partial Differential Equations. Recently, in our research, we have discovered a new face of CR-geometry. This is a novel approach of interpreting objects arising in CR-geometry (called CR-manifolds) as certain Dynamical Systems, and vice versa. It turns out that geometric properties of CR-manifolds are in one-to-one correspondence with that of the associated dynamical systems. In this way, we obtain a certain vocabulary between the two theories. The latter approach has enabled us recently to solve a number of long-standing problems in CR-geometry. It also has promising applications for Dynamical Systems. We call this method the CR (Cauchy-Riemann manifolds) - DS (Dynamical Systems) technique. In this talk, I will outline the CR - DS technique, and describe its recent applications to Complex Geometry and Dynamics.

Host: Peter Ebenfelt

### January 11, 2016

### 3:00 PM

### AP&M 6402

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