Cohomological DT theory beyond the integrality conjecture

10 May 2016
Ben Davison
The integrality conjecture is one of the central conjectures of the DT theory of quivers with potential, which itself is a key tool in understanding the local calculation of DT invariants on moduli spaces of coherent sheaves, as well as having deep links to geometric representation theory, noncommutative geometry and algebraic combinatorics.  I will explain some of the ingredients of the proof of this conjecture by myself and Sven Meinhardt.  In fact the proof gives much more than the original conjecture, which ultimately concerns identities in a Grothendieck ring of mixed Hodge structures associated to moduli spaces of representations, and proves that these equalities categorify to isomorphisms in the category of mixed Hodge structures.  I'll explain what this all means, as well as giving some applications of the categorified version of the theory.
  • Algebraic and Symplectic Geometry Seminar