MS Seminar (Mathematics - String Theory)

Speaker: Andrei Negut (MIT)
Title: W-algebras, moduli of sheaves on surfaces, and AGT
Date: Tue, Aug 22, 2017, 13:15 - 14:45
Place: Seminar Room A
Abstract: To a smooth surface, we associate the W-algebra of type gl_r with two deformation parameters equal to the Chern roots of the cotangent bundle of S. We expect that the resulting algebra acts on the K-theory groups of moduli spaces of semistable rank r sheaves on S, and one can compute commutation relations between the algebra and the Carlsson-Okounkov Ext operator. When the surface is S=A^2, this allows one to present the Ext operator as a vertex operator for deformed W-algebras, thus yielding a mathematical proof of the 5d AGT relations with matter for the gauge group U(r).