14:00 Kai Behrend (Vancouver): The spectrum of the inertia operator on the motivic Hall algebra
Following an idea of Bridgeland, we study the operator on the K-group of algebraic stacks, which takes a stack to its inertia stack. We prove that the inertia operator is diagonalizable when restricted to nice enough stacks, including those with algebra stabilizers. We use these results to prove a structure theorem for the motivic Hall algebra of a projective variety, and give a more conceptual definition of virtually indecomposable stack function. This is joint work with Pooya Ronagh.
15:20 Behrang Noohi (London QMUL): String operations on stacks
I begin with a quick review of the Goldman bracket and Turaev cobracket on oriented surfaces, the subsequent generalisation to higher dimension by Chas-Sullivan, and the recent work of Chas-Gadgil for orbifold surfaces (via Fuchsian groups). I will explain how this all can be extended to differential stacks. An important role is played here by the inertia stack. Time permitting, I will discuss a conjectural connection with shifted symplectic structures. This is joint work with Greg Ginot.
17:00 Travis Schedler (London IC): Symplectic resolutions of quiver and character varieties
I will explain joint work with Bellamy classifying those Nakajima quiver varities admitting symplectic resolutions. Although, as we explain, these are always symplectic singularities in the sense of Beauville, they do not always admit symplectic resolutions. They are product of ‘irreducible’ ones, of which those admitting resolutions come in three types: symemtric powers of du Val singularities, varieties for indivisible dimension vectors, and varieties related to O’Grady’s example, where the resolution strangely does not come from GIT. The technique, involving Drezet’s theorem on factoriality, extends to character varieties, which we show that, for a closed Riemann surface of genus at least two, do not admit a symplectic resolution.
The talks will be in Room 3.27 of the Bancroft Building (#31 in the QMUL campus map). The entrance to the campus (East Gate) is a 4 minute walk from Mile End tube station. An additional 3 minute walk from there takes you to the Bancroft Building.
Social programme
The “ground” coffee shop is #33 on the campus map. It is 2 minutes away from the Bancroft Building. There is also a canteen (which has a small Starbucks in it) in #47. It is called “The Curve”.
Further information can be found on the COW webpage here