Casey Blacker


Casey Blacker at Peterhof Palace, Saint Petersburg.

I am an Assistant Professor of Mathematics at Augusta University.

My interests include moment maps, Lie groupoids, bundle gerbes, and quantization. More recently, I have become interested in higher geometry, including (higher) stacks and gerbes.


Publications

  1. Reduction of L∞-algebras of observables on multisymplectic manifolds (with Antonio Miti and Leonid Ryvkin), SIGMA, 2024,
    https://doi.org/10.3842/SIGMA.2024.061p
  2. Reduction of multisymplectic manifolds, Lett. Math. Phys., 2021,
    https://doi.org/10.1007/s11005-021-01408-y
  3. Quantization of polysymplectic manifolds, J. Geom. Phys., 2019,
    https://doi.org/10.1016/j.geomphys.2019.103480
  4. Polysymplectic reduction and the moduli space of flat connections, J. Phys. A, 2019,
    https://doi.org/10.1088/1751-8121/ab2eed
  5. First eigenvalue of the p-Lapacian on Kähler manifolds (with Shoo Seto), Proc. Amer. Math. Soc., 2019, https://doi.org/10.1090/proc/14395
  6. The Moduli Space of Flat Connections over Higher Dimensional Manifolds (PhD Thesis), 2018, https://escholarship.org/uc/item/0535z0rb

Student Research

  1. Logarithmic spirals on surfaces of constant Gaussian curvature (with Pavel Tsyganenko), Involve, 2024, https://doi.org/10.2140/involve.2024.17.689

Events Organized

  • Multisymplectic Structures in Geometry and Physics 2024
  • Young Researchers' Virtual Multisymplectic Geometry Conference 2021
  • Young Researchers' Virtual Multisymplectic Geometry Conference 2020

Selected Notes and Slides

Reduction of multisymplectic manifolds



Quantization of polysymplectic manifolds



Simplicial sets



Quantum computing



Curvature and holonomy on double Lie groupoids