Geometry and String Theory Seminar

Dr. Peter Koroteev, Perimeter Institute

"Large-n limit of Seiberg-Witten theories"

12:00pm, RLM 8.136

Abstract: We study moduli space of U(n) instantons with ramification. It can be argued that the instanton partition function (holomorphic equivariant Euler characteristic) satisfies a system of differential or difference equations which coincide with energy equation for some integrable n-body system of Calogero-Moser or Ruijsenaars type. We then take a limit, when the number of particles becomes large, and recover a different effective integrable model — intermediate long wave hydrodynamics. Spectrum of this model describes quantum multiplication in the small cohomology ring of the moduli space of non-commutative instantons on C^2 and ALE spaces. We shall formulate some results and conjectures on related topics.