Cohomological Donaldson—Thomas invariants for 3-manifolds

Cohomological Donaldson—Thomas theory associates cohomology groups to various moduli spaces in algebraic geometry, such as the moduli space of coherent sheaves on a Calabi—Yau 3-fold. In this talk I will explain some recent results on cohomological DT invariants in the setting of a real 3-manifold $M$. In terms of string theory it corresponds to counting D3 branes in the compactification of a type IIB string theory on $T^* M$. This setting of DT theory is particularly interesting due to its connections to topology (via skein modules), geometric representation theory (geometric Langlands program), and mathematical physics (analytic continuation of Chern—Simons theory). This talk is based on papers joint with Gunningham, Kinjo, Naef, and Park.