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UID:20250717T152643EDT-2898UoUzNf@132.216.98.100
DTSTAMP:20250717T192643Z
DESCRIPTION:Title: Isomonodromic tau functions on Riemann Surfaces through 
 free fermions and four-dimensional QFTs\n\nAbstract: Using arguments from 
 two-dimensional Conformal Field Theory\, Gamayun Iorgov and Lisovyy provid
 ed in 2012 an explicit expression for the tau function of the sixth\n	Painl
 evé equation as a Fourier transform of Virasoro conformal blocks of a free
  fermion CFT\, which has an explicit combinatorial (convergent) expansion 
 as the so-called\n	dual partition function of a corresponding four-dimensio
 nal supersymmetric Quantum Field Theory. This 'Kiev formula' has been late
 r generalized to more general isomonodromic problems on the sphere\, with 
 both regular and irregular punctures\, and the combinatorial expansion has
  been shown to arise from the minor expansion of an associated Fredholm de
 terminant\, in terms of which the tau function can be formulated.\n	\n	In th
 is talk I will show how the above picture can be generalized to the case o
 f Riemann Surfaces with nonzero genus and marked points\, where new featur
 es arise due to the nontriviality of the moduli space of flat connections.
  I will consider in detail the example of the punctured torus\, for which 
 I will show that the tau function can be written as a free fermion conform
 al block from two-dimensional CFT\, and as a Fredholm determinant of Cauch
 y operators\, whose minor expansion reproduces the conformal block itself.
  \n\n \n\nWeb - Please fill in this form: https://forms.gle/S1NcNQ8BxkzfAX
 cj9\n
DTSTART:20210323T193000Z
DTEND:20210323T203000Z
SUMMARY:Fabrizio Del Monte (CRM)
URL:/mathstat/channels/event/fabrizio-del-monte-crm-32
 9594
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