Schlesinger Transformations and Difference Painlevé Equations

03/24/2016 - 16:00
03/24/2016 - 17:30
Anton Dzhamay
Concordia University, Math Help Center, room 912.00 / Library Building, 1400 de Maisonneuve Blvd. West, Montréal

The main goal of this talk is to explain an isomonodromic approach to the theory of difference Painlevé equations. We first briefly outline the theory of elementary Schlesinger transformations of Fuchsian systems. Next, we study such transformations for systems that have two-dimensional space of accessory parameters and show that these transformations can be expressed via difference Schlesinger equations. We consider in detail one example of such  reductions that corresponds to the equation with the E_6 affine Weyl symmetry group.  If time permits, we will show how the resulting equation can be analyzed using the geometric framework of H. Sakai.

Last edited by on Thu, 03/17/2016 - 13:31