Welcome

(New: daily meditations.)

I'm an assistant professor at the University of Georgia. I'm part of the algebra research group.

My research lies in an area of algebra called geometric representation theory. I enjoy thinking about categories of perverse and coherent sheaves coming from some Lie theoretic data. Keywords related to things I've been thinking about include affine Grassmannian, affine flag manifold, exotic sheaves on the Springer resolution, generalized Springer correspondence, geometric Satake, Lusztig's character sheaves, modular representation theory, and Whittaker sheaves.. 

I completed my Ph.D (08.09.13) under the direction of Pramod Achar at Louisiana State University. My thesis work involved proving formality for the Springer block of (constructible) sheaves on the nilpotent cone. This required the construction of a suitable mixed version of the (equivariant, l-adic) category of sheaves on the nilpotent cone. You can find a copy of my thesis here.

Past Conferences:

Upcoming Travel/Conferences/Seminars:

Papers:

Formality for the nilpotent cone and a derived Springer correspondence, Adv. Math. 235 (2013), 208-236. 
arXiv

(with P. Achar) Parity Sheaves on the Affine Grassmannian and the Mirković–Vilonen Conjecture, Acta Math. 215, no. 2 (December 2015), 183-216.
arXiv

(with P. Achar, and an appendix joint with S. Riche) The affine Grassmannian and the Springer resolution in positive characteristic,  Compos. Math. 152 (2016), no. 12, 2627-2677.
arXiv

(with A. Russell) Perverse Sheaves on the Nilpotent Cone and Lusztig's Generalized Springer Correspondence, in Lie algebras, Lie superalgebras, vertex algebras and related topics, 273-292, 
Proc. Sympos. Pure Math., 92, Amer. Math. Soc., Providence, RI, 2016.
arXiv

(with A. Russell) Formality and Lusztig's generalized Springer correspondence, Algebr. Represent. Theory (2020). 
arXiv

(with R. Bezrukavnikav, D. Gaitsgory, I. Mirković, S. Riche) An Iwahori-Whittaker model for the Satake category, J. Éc. polytech. Math. 6 (2019), 707-735.
arXiv, hal

(with P. Achar) Nearby cycles for parity sheaves on a divisor with simple normal crossings, J. of Singularities 20 (2020), 311-341.
arXiv 

(with R. Bezrukavnikov and S. Riche) Modular affine Hecke category and regular unipotent centralizer, I
arXiv

(with K. Y. Chan and P. Sobaje) Exotic t-structure for partial resolutions of the nilpotent cone
arXiv

 

Because everyone needs some poetry in their life: