Victor Novokshenov (Institute of Mathematics, Ufa Science center RAS, Ufa, Russia)
  Orthogonal polynomials and Painleve' equations.

Asymptotics of the orthogonal polynomials constitute a classic analytic problem. A distribution of zeroes to generalized Hermite polynomials is studied in some scaling limit. These polynomials defined as Wronskians of classic Hermite polynomials appear in a number of mathematical physics problems as well as in the theory of random matrices. Calculation of asymptotics is based on Riemann — Hilbert problem for Painlev'e IV equation which has solutions expressed in terms of these polynomials. In this scaling limit the Riemann — Hilbert problem is solved in elementary functions. As a result, we come to analogs of Plancherel — Rotach formulas for asymptotics of classical Hermite polynomials.