# Mathematics Colloquia and Seminars

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### 4-manifold invariants and 2d CFT

**QMAP Seminar**

Speaker: | Mykola Dedushenko, Caltech |

Location: | 2112 MSB |

Start time: | Fri, May 19 2017, 1:15PM |

Recently, there has been a hope that there exists a class of 2d N=(0,2) SCFTs T[M_4, G] labelled by a 4-manifold M_4 and a Lie group G which could provide a new type of smooth structure invariants for M_4. Such theories are given by twisted compactifications of the 6d (2,0) theory on M_4.

We study one of the simplest cases when G=U(1). Even though such T[M_4, U(1)] looks trivial (in particular, it is free), from the string theory point of view, it is natural to include certain local defect operators in this theory. The resulting vertex operator algebra (VOA) encodes Seiberg-Witten (SW) invariants of M_4 and their equivariant multi-monopole generalization. We investigate such equivariant multi-monopole invariants from several points of view, including the 4d gauge theoretic approach, and identify the structure of the VOA encoding them. We also propose some further directions for generalizations, including the case of non-abelian G.

Coffee and Pastries served at 1pm.