Global asymptotic analysis of the Painleve transcendents. The Riemann-Hilbert Approach

Series: 
School of Mathematics Colloquium
Thursday, January 22, 2009 - 11:00
1 hour (actually 50 minutes)
Location: 
Skiles 269
,  
Indiana University-Purdue University Indianapolis
In this talk we will review some of the global asymptotic results obtained during the last two decades in the theory of the classical Painleve equations with the help of the Isomonodromy - Riemann-Hilbert method. The results include the explicit derivation of the asymptotic connection formulae, the explicit description of linear and nonlinear Stokes phenomenon and the explicit evaluation of the distribution of poles. We will also discuss some of the most recent results emerging due to the appearance of Painleve equations in random matrix theory. The Riemann-Hilbert method will be outlined as well.