3 papers
math.DG2019
Quantization of Polysymplectic Manifolds
Casey Blacker
We adapt the framework of geometric quantization to the polysymplectic setting. Considering prequantization as the extension of symmetries from an underlying polysymplectic manifol…
math.DG2018
Polysymplectic Reduction and the Moduli Space of Flat Connections
Casey Blacker
A polysymplectic structure is a vector-valued symplectic form, that is, a closed nondegenerate 2-form with values in a vector space. We first outline the polysymplectic Hamiltonian…
math.DG2018
First eigenvalue of the -Laplacian on Kähler manifolds
Casey Blacker, Shoo Seto
We prove a Lichnerowicz type lower bound for the first nontrivial eigenvalue of the -Laplacian on Kähler manifolds. Parallel to the case, the first eigenvalue lower boun…