# Minicourses

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 http://www.ma.utexas.edu/users/neitzke/expos/gmn-1.pdf but try to give insight from other references, like the original http://arxiv.org/abs/0807.4723 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.