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FIELD Math:Geometry
DATE April 08 (Thu), 2021
TIME 16:00-17:00
PLACE Online
SPEAKER Tu, Junwu
HOST Bhamidi, S.S Sreedhar
INSTITUTE Institute of Mathematical Science, ShanghaiTech University
TITLE On the categorical enumerative invariants of a point
ABSTRACT

We briefly recall the definition of categorical enumerative invariants (CEI) first introduced by Costello around 2005. Costello's construction relies fundamentally on Sen-Zwiebach’s notion of string vertices V_{g,n}’s which are chains on moduli space of smooth curves M_{g,n}’s. In this talk, we explain the relationship between string vertices and the fundamental classes of the Deligne-Mumford compactification of M_{g,n}. More precisely, we obtain a Feynman sum formula expressing the fundamental classes in terms of string vertices. As an immediate application, we prove a comparison result that the CEI of the field \mathbb{Q} is the same as the Gromov-Witten invariants of a point.

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