PIRSA:25100155 Scientific Series Mathematical physics

DOI10.48660/25100155

Series: Mathematical Physics

(2025). Relative Quasimaps and Tilting Modules. Perimeter Institute. https://pirsa.org/25100155

Relative Quasimaps and Tilting Modules. Perimeter Institute, Oct. 17, 2025, https://pirsa.org/25100155 

@misc{ pirsa_PIRSA:25100155,
  doi = {10.48660/25100155},
  url = {https://pirsa.org/25100155},
  author = {},
  keywords = {Mathematical physics},
  language = {en},
  title = {Relative Quasimaps and Tilting Modules},
  publisher = {Perimeter Institute},
  year = {2025},
  month = {oct},
  note = {PIRSA:25100155 see, \url{https://pirsa.org}}
}

Abstract

The moduli space of quasimaps gives a partial compactification of maps from an algebraic curve to a variety. In physics, the cohomology of this moduli space can be viewed as the state space of a (twisted) supersymmetric gauge theory. It is shown by Bullimore-Dimofte-Gaiotto-Hilburn-Kim that when the target space is a flag variety, this cohomology admits an action of the Lie algebra gl_n and can be identified with the Verma module for generic parameters. I will describe a further compactification of these moduli spaces called relative quasimaps, first introduced by Ciocan-Fontanine-Kim-Maulik, and explain how their cohomology is related to the tilting module of gl_n.

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