# William Hardesty

## Contact Information

** Office:** 489 Carslaw Building

** Email: ** william dot hardesty at sydney dot edu dot au

** Postal Address: **

## About Me

I am a Research Fellow in the School of Mathematics and Statistics at the University of Sydney.
Prior to this, I was a Postdoctoral Researcher at
Louisiana State University from 2016 to 2019.
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) Integral exotic sheaves and the modular Lusztig-Vogan bijection.

Preprint **arXiv:1810.08897**, 46 pp. (submitted)
- On the centralizer of a balanced nilpotent section.

Preprint **arXiv:1810.06157**, 21 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) Representation theory of disconnected reductive groups.

To appear in **Documenta Mathematica**, 23 pp.
- (with P. Achar, S. Riche)
Conjectures on tilting modules and antispherical $p$-cells.

To appear in **RIMS Kôkyûroku Bessatsu**, 20 pp.
- (with P. Achar) Calculations with graded perverse-coherent sheaves.

To appear in **The Quarterly Journal of Mathematics**, 23 pp.
- (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.