Asymptotic Geometric Analysis is concerned with geometric and linear properties of finite dimensional objects, normed spaces and convex bodies, especially with asymptotics of their various quantitative parameters as the dimension tends to infinity. Deep geometric, probabilistic and combinatorial methods developed here are used outside the field in many areas, related to the subject of the program.

One of the main tools of the theory are concept of concentration phenomenon and large deviation inequalities. The concentration of measure is, in fact, an isomorphic form of isoperimetric problems. It was first developed inside the asymptotic geometric analysis and then became pertinent to other branches of mathematics as an efficient tool and useful concept. Some new techniques of the theory are connected with measure transportation methods and with related PDE's. The concentration phenomenon is well-known to be closely linked with combinatorics (Ramsey theory), and such links have been recently better understood in the setting of infinite-dimensional transformation groups.

The achievements of Asymptotic Geometric Analysis demonstrate new and unexpected phenomena characteristic for high dimensions. These phenomena appear in a number of domains of mathematics and adjacent domains of science dealing with functions of infinitely growing numbers of variables.

Main Directions of Research:

* Asymptotic theory of Convexity and Normed spaces
* Concentration of measure and isoperimetric inequalities, optimal transportation approach
* Applications of the concept of concentration
* Connections with transformation groups and Ramsey theory
* Geometrization of Probability
* Random matrices
* Connection with Asymptotic Combinatorics and Complexity Theory