On the categorical enumerative invariants of a point

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.