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.
