William Hardesty


Myself.

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

  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) Integral exotic sheaves and the modular Lusztig-Vogan bijection.
    Preprint arXiv:1810.08897, 46 pp. (submitted)

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

  4. 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) Representation theory of disconnected reductive groups.
    To appear in Documenta Mathematica, 23 pp.

  2. (with P. Achar, S. Riche) Conjectures on tilting modules and antispherical $p$-cells.
    To appear in RIMS Kôkyûroku Bessatsu, 20 pp.

  3. (with P. Achar) Calculations with graded perverse-coherent sheaves.
    To appear in The Quarterly Journal of Mathematics, 23 pp.

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

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

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

  7. 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


Copyright © 2018 William Hardesty. All Rights Reserved.