Sam Gunningham's Homepage
I am a postdoc at the Department of Mathematics, UT Austin.
Department of Mathematics
University Station C1200
Austin, TX 78712-0257
E-mail address: gunningham[at]math[dot]utexas[dot]edu
Office: RLM 11.166
Research Interests :
I work in an area called Geometric Representation Theory, which involves aspects of Algebraic Geometry, Algebraic Topology, Representation Theory, and Mathematical Physics. Some particular interests include D-modules, topological field theory, and (higher) categorical structures.
My current projects include:
- Generalized Springer Theory for adjoint equivariant D-modules on reductive groups and Lie algebras via parabolic induction and restriction.
- Quantization of the group scheme of regular centralizers (with David Ben-Zvi and David Nadler)
- Character sheaves and the topology of character varieties (with David Ben-Zvi and David Nadler).
- Mirabolic D-modules via parabolic induction and restriction (with Travis Schedler and Gwyn Bellamy)
- Principal bundles on elliptic curves and elliptic character sheaves (with Dragos Fratila and Penghui Li)
- Springer Theory for Quantum D-modules (with David Ben-Zvi, David Jordan, and Pavel Safranov)
- Understanding Topological K-theory via Clifford modules.
- String topology for stratified spaces (with David Treumann).
- Spin topological field theories and Hurwitz numbers.
Papers and Preprints :
Link to Arxiv papers
- Spin Hurwitz numbers and topological quantum field theory,
Geometry & Topology 20-4 (2016), 1859--1907. DOI 10.2140/gt.2016.20.1859
- A Derived Generalized Springer Decomposition for D-modules on a Reductive Lie Algebra
arXiv:1705.04297 (preprint, submitted)
- The Character Field Theory and Homology of Character Varieties
- A Generalized Springer Decomposition for D-modules on a Reductive Lie Algebra
arXiv:1510.02452 (preprint, submitted).
- Highest Weights for Categorical Representations
(joint with David Ben-Zvi and Hendrik Orem)
arXiv:1608.08273 (preprint, submitted)
Image credit: Anna Dabrowski
Representation Theory, Spring 2017
Notes from my D-modules class, Spring 2015
For undergraduate classes, check Canvas.