Mini-Courses
Yoshinori Namikawa (RIMS)
TBA
Lewis Topley (University of Bath)
TBA
Talks
Riccardo Carini (University of Bonn)
TBA
Wahei Hara (Kavli IPMU)
TBA
Zelin Jia (Nagoya University)
TBA
Tasuki Kinjo (RIMS)
BPS cohomology for symplectic quotients
In this talk, we will introduce the BPS cohomology of symplectic varieties arising as Hamiltonian quotients. When the singularities can be resolved via variation of GIT, the BPS cohomology coincides with the cohomology of the corresponding symplectic resolution. I will explain that the BPS cohomology can be used in the formulation of the topological mirror symmetry conjecture for G-Hitchin system, extending the conjecture of Hausel and Thaddeus for type A groups. I will also discuss some speculations about the BPS cohomology, including counting problems of absolutely indecomposable G-bundles on smooth projective curves defined over finite fields. This talk is partially based on joint work with Chenjing Bu, Ben Davison, Andrés Ibáñez Núñez, and Tudor Pădurariu.
Ayako Kubota (Saitama University)
TBA
Dmytro Matvieievskyi (UMass Amherst)
TBA
Raphaël Paegelow (University of Lille)
Gieseker spaces and Ariki-Koike algebras
We will present combinatorial correspondences between the irreducible components of the fixed points locus of the Gieseker space and the block theory of the Ariki-Koike algebra. First, we will describe the locus of fixed points in terms of Nakajima quiver varieties over the McKay quiver of type A. Then, we will present how to recover the combinatorics of cores of charged multipartitions, as defined by Fayers and developed by Jacon and Lecouvey, on the Gieseker side. In addition, we will present a new way to compute the multicharge associated with the core of a charged multipartition. Finally, if time permits, we will also explain how the notion of core blocks, discovered by Fayers, can be interpreted geometrically using a deep connection between quiver varieties and affine Lie algebras.
Benjamin Tighe (University of Oregon)
TBA