Conférence GAGC 2015

Cohomological Hall modules and Donaldson-Thomas theory with classical structure groups

24 nov. 2015, 17:00

50m

CIRM, Luminy

Orateur

M. Matt Young (Texas University)

Description

Given a complex reductive group $G$, there is expected to be a generalization of Donaldson-Thomas theory whose goal is to count, in an appropriate sense, stable principal $G$-bundles over a Calabi-Yau threefold. The standard Donaldson-Thomas theory arises when $G$ is a general linear group. I will present some recent results on such a generalization when $G$ is a classical group using the framework of quiver representations. The key new tool is a representation of Kontsevich and Soibelman's cohomological Hall algebra which is constructed from the cohomology of moduli stacks of quiver theoretic analogues of $G$-bundles. Conjecturally, the desired $G$-Donaldson-Thomas invariants are encoded in degrees of the generators of this representation. I will describe a number of situations where this conjecture has been confirmed.

Documents de présentation

summary

Resume_Young.pdf