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math.SG2025
Slices for reductive group actions in algebraic and holomorphic symplectic geometry
Peter Crooks, Rebecca Goldin, Yiannis Loizides
Symplectic slice theorems elucidate the local structure of symplectic manifolds carrying Hamiltonian actions of compact Lie groups. We generalize these theorems in two natural sett…
math.SG2025
Grothendieck-Springer resolutions and TQFTs
Peter Crooks, Maxence Mayrand
The Moore-Tachikawa conjecture is that each connected complex semisimple group determines a two-dimensional TQFT in a category of Hamiltonian symplectic varieties. While it wou…
math.SG2025
Some incarnations of Hamiltonian reduction in symplectic geometry and geometric representation theory
Peter Crooks, Xiang Gao, Mitchell Pound +1
In this expository note, we give a self-contained introduction to some modern incarnations of Hamiltonian reduction. Particular emphasis is placed on applications to symplectic geo…