6 papers · 1 filter
Generalized Gelfand-Cetlin data and abelianization
Peter Crooks, Mitchell Pound
This manuscript aims to advance existing approaches to the abelianization of symplectic quotients. Two such approaches include the imploded cross-sections of Guillemin-Jeffrey-Sjam…
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…
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…
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…
The Moore-Tachikawa conjecture via shifted symplectic geometry
Peter Crooks, Maxence Mayrand
We use shifted symplectic geometry to construct the Moore-Tachikawa topological quantum field theories (TQFTs) in a category of Hamiltonian schemes. Our new and overarching insight…
Scheme-theoretic coisotropic reduction
Peter Crooks, Maxence Mayrand
We develop an affine scheme-theoretic version of Hamiltonian reduction by symplectic groupoids. It works over or , and is formulated for an aff…