学术报告（唐鑫星 6.30）
Monodromy dependence and connection problem for Painlevé VI tau function
It is well known that Painlevé VI equation describes the first nontrivial example of Fuchsian (rank 2 with 4 regular singular points) isomonodromic deformation. There is a corresponding isomonodromic tau function, which could be regarded as the generating function of certain hamiltonians, or in terms of Painlevé/CFT correspondence, as a sum of c=1 conformal blocks. In this survey talk, I will focus on two questions of isomonodromic tau functions (defined by Jimbo-Miwa-Ueno). First, based on RiemannHilbert correspondence, one can discuss the extension of JMU tau function by changing monodromy (M. Bertola, Lisovyy-Prokhorov).
Second, such an extension can be used to solve a long-standing problem of evaluation of the connection formulae for the Painlevé VI tau functions. We will sketch the computation idea in this talk.
