## Sam Gunningham's Homepage

I am a postdoc at the Department of Mathematics, UT Austin.

**Mailing address**:

Department of Mathematics

University Station C1200

Austin, TX 78712-0257

**E-mail address**: `gunningham[at]math[dot]utexas[dot]edu`

**Office**: RLM 11.166

Curriculum Vitae

** 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 **:

*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*

arXiv:1705.04266 (preprint).
*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)

Link to Arxiv papers
**Useful Links:**

Arxiv
Mathscinet

Image credit: Anna Dabrowski

**Teaching**

Representation Theory, Spring 2017

Notes from my D-modules class, Spring 2015

For undergraduate classes, check Canvas.