Venue: HIM lecture hall, Poppelsdorfer Allee 45 (unless stated otherwise)

Minicourse: Parabolic Higgs Bundles and Hyperpolygons

Speaker: Alessia Mandini

Tuesday, September 27, 11:00-12:00

Friday, September 28, 11:00-12:00 and 14:00-15:00

Venue: HIM, Discussion Room 20

Minicourse: GMN Theory and hyperKähler geometry

Speaker: Mario Garcia-Fernandez

Friday, November 2, 15:00-16:00

Friday, November 9, 15:00-16:00

Friday, November 23, 15:00-16:00

Wednesday, December 19, 15:00-16:00

Venue: HIM lecture hall

Abstract: In these series of lectures we discuss the conjectural application of GMN theory to hyperKähler geometry. We will essentially follow these notes of Neitzke but try to give insight from other references, like the original or the work of Gross and Wilson.

Minicourse: Vortices and Quantum Kirwan Maps

Speaker: Fabian Ziltener (KIAS, Seoul)

Tuesday, December 11, 10:00-11:00 and 11:15-12:00

Wednesday, December 12, 14:00-15:00 and 15:15-16:00

Venue: HIM lecture hall

Abstract: Given a Hamiltonian Lie group action on a symplectic manifold, the Kirwan map is a natural ring homomorphism from the equivariant cohomology of the manifold to the cohomology of the symplectic quotient. By counting symplectic vortices over the plane, one obtains a quantum deformation of this homomorphism. The map relates the equivariant Gromov-Witten theory of the symplectic manifold with the Gromov-Witten theory of the symplectic quotient. On Tuesday, I will give some geometric background on the Kirwan map, vortices and Gromov-Witten theory, and motivate the construction of a quantization of the Kirwan map. On Wednesday, I will discuss a relevant bubbling result, Fredholm theory, and decay at infinity for vortices over the plane.