Abstract:
The Painleve equations are one of the most familiar classes of
nonlinear differential equations. In the talk, I will discuss (review)
their difference analogues. First, we discuss their definition as
condition of isomonodromic deformation for a linear equation. Then we
discuss the construction of these equations as de-autonomization of
cluster integrable systems. In the end, I plan to discuss the solution
of these equations with the help of Nekrasov’s partition function for
five-dimensional gauge theories.
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