Hamiltonian actions on stacks, equivariant cohomology and localization

• Grant number: 22/09234-3
• Support Opportunities: Regular Research Grants
• Start date: November 01, 2022
• End date: October 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Cristián Andrés Ortiz González
• Grantee: Cristián Andrés Ortiz González
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this project we are concerned with an extension of the Localization Theorem of Atiyah-Bott and Berline-Vergne for the equivariant cohomology of a Lie 2-group acting on a stack/Lie groupoid. We also study Hamiltonian actions of 2-groups on both 0-shifted and 1-shifted symplectic stacks with the aim of describing their equivariant cohomology. Also, in the 1-shifted case we plan to describe the corresponding Marsden-Weinstein reduction procedure. (AU)