# William Hardesty

## Contact Information

Office: 147 Lockett Hall
Email: whardesty at math dot lsu dot edu

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.

## Research

### Preprints

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

2. (with P. Achar, S. Riche) Conjectures on tilting modules and antispherical $p$-cells.
Preprint arXiv:1812.09960, 16 pp.

3. (with P. Achar, S. Riche) Integral exotic sheaves and the modular Lusztig-Vogan bijection.
Preprint arXiv:1810.08897, 46 pp. (submitted)

4. (with P. Achar, S. Riche) Representation theory of disconnected reductive groups.
Preprint arXiv:1810.06851, 23 pp. (submitted)

5. On the centralizer of a balanced nilpotent section.
Preprint arXiv:1810.06157, 21 pp. (submitted)

6. (with P. Achar) Calculations with graded perverse-coherent sheaves.
Preprint arXiv:1806.07780, 23 pp. (submitted)

7. Explicit calculations in an infinitesimal singular block of $SL_n$.
Preprint arXiv:1805.04614, 25 pp. (submitted)

### Published/Accepted

1. (with P. Achar, S. Riche) On the Humphreys conjecture on support varieties of tilting modules.
To appear in Transform. Groups, 54 pp.

2. On support varieties and the Humphreys conjecture in type $A$.
Adv. Math. 329 (2018), 392-421

3. (with D. Nakano, P. Sobaje) On the Existence of Mock Injective Modules for Algebraic Groups.
Bull. Lond. Math. Soc. 49 (2017), 806-817

4. Support varieties of line bundle cohomology groups for $G=SL_3(k)$.
J. Algebra 448 (2016), 127-173

## 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)