# William Hardesty

## Contact Information

** Office:** 147 Lockett Hall

** Email: ** whardesty at math dot lsu dot edu

** Postal Address: **

## About Me

I am a Postdoctoral Researcher in the Department of Mathematics at Louisiana State University, working with
Pramod Achar.
I recieved my Ph.D. from the
University of Georgia in 2016 under the supervision of
Daniel Nakano.

My research is in geometric representation theory, with an emphasis on the modular representation theory of reductive algebraic groups, and in related areas of geometry and combinatorics.

### Additional Resources

## Research

### Preprints

- (with P. Achar)
* Co-t-structures on derived categories of coherent sheaves and the cohomology of tilting modules*.

In preparation
- (with P. Achar, S. Riche)
Conjectures on tilting modules and antispherical $p$-cells.

Preprint **arXiv:1812.09960**, 16 pp.
- (with P. Achar, S. Riche) Integral exotic sheaves and the modular Lusztig-Vogan bijection.

Preprint **arXiv:1810.08897**, 46 pp. (submitted)
- (with P. Achar, S. Riche) Representation theory of disconnected reductive groups.

Preprint **arXiv:1810.06851**, 23 pp. (submitted)
- On the centralizer of a balanced nilpotent section.

Preprint **arXiv:1810.06157**, 21 pp. (submitted)
- (with P. Achar) Calculations with graded perverse-coherent sheaves.

Preprint ** arXiv:1806.07780**, 23 pp. (submitted)
- Explicit calculations in an infinitesimal singular block of $SL_n$.

Preprint **arXiv:1805.04614**, 25 pp. (submitted)

### Published/Accepted

- (with P. Achar, S. Riche) On the Humphreys conjecture on support varieties of tilting modules.

To appear in **Transform. Groups**, 54 pp.

- On support varieties and the Humphreys conjecture in type $A$.

**Adv. Math.** 329 (2018), 392-421

- (with D. Nakano, P. Sobaje) On the Existence of Mock Injective Modules for Algebraic Groups.

**Bull. Lond. Math. Soc.** 49 (2017), 806-817

- Support varieties of line bundle cohomology groups for $G=SL_3(k)$.

**J. Algebra** 448 (2016), 127-173

## Collaborators

Pramod Achar, Daniel Nakano, Simon Riche, Paul Sobaje

## Teaching

- MATH 2065: Ordinary Differential Equations (Spring 2018, LSU)
- MATH 1551: Honors Calculus I (Fall 2016, LSU)
- MATH 2250: Calculus I (Fall 2015, UGA)
- MATH 1113: Pre-Calculus (Fall 2014, UGA)
- MATH 2250: Calculus I (Spring 2014, UGA)
- MATH 1113: Pre-Calculus (Fall 2013, UGA)

Copyright © 2018 William Hardesty. All Rights Reserved.