I am a Research Fellow in the School of Mathematics and Statistics at the University of Sydney. I was a graduate student at MIT under the supervision of Prof. Roman Bezrukavnikov, and a post-doc at the University of Utah from 2015-2016. Here is my CV.

My interests are in representation theory, using techniques from categorification, geometry and combinatorics.

See here for my new webpage (sites.google.com/view/vinothmn/)

**Equivariant coherent sheaves on the exotic nilpotent cone**. pdf arxiv * Represent. Theory 17 (2013), 663-681 *

We construct a version of the Lusztig-Vogan bijection for the exotic nilpotent cone following techniques used by Bezrukavnikov in the classical case; the bijection is between dominant weights, and the set of pairs consisting of a nilpotent orbit and a finite-dimensional irreducible representation of the isotropy group of the orbit.

**Quiver varieties and crystals for symmetrizable Kac-Moody algebras.** (joint w/ Peter Tingley) arxiv

* Math. Res. Letters (to appear, 2018) *

We extend Kashiwara and Saito's geometric realization of the B(\infty) crystal for a simply-laced Kac-Moody algebra using irreducible components of Lusztig's quiver varieties to the symmetrizable case.

** Stability conditions for Gelfand-Kirillov sub-quotients of category O ** arxiv * Int. Math. Res. Not. (2016), No. 00, pp. 1–33 *

We construct an example of "real variation of stability conditions" (a notion developed by Anno, Bezrukavnikov and Mirkovic, building on Bridgeland's stability conditions), using certain sub-quotients of category O with a fixed Gelfand-Kirillov dimension.

**Exotic t-structures for two-block Springer fibers.** (pre-print, joint w/ Rina Anno) arxiv

Bezrukavnikov-Mirkovic introduced exotic t-structures on Springer fibers to study representations of Lie algebras in positive characteristic. When the nilpotent has Jordan type *(m+n, n)*, we give a description of the irreducible sheaves and Ext spaces, using Cautis-Kamnitzer's tangle categorification results.

** Modular representations in type A with a two-row nilpotent central character (pre-print, joint w/ David Yang) ** arxiv

We study the category of modular representations of sl_{m+2n} with two-row nilpotent p-character, using the geometric approach from our work with Anno. We give combinatorial formulae for the dimensions of the simple objects, and the multiplicities of the simples in the baby Vermas.

**Irreducible components of exotic Springer fibres. ** (pre-print, joint w/ Daniele Rosso and Neil Saunders) arxiv

We show that irreducible components of exotic Springer fibers are naturally in bijection with standard Young bitableaux.

** Irreducible components of exotic Springer fibres II: exotic Robinson-Schensted algorithm (pre-print, joint w/ Daniele Rosso and Neil Saunders) ** arxiv

We give a combinatorial description of the geometric Robinson-Schensted algorithm obtained using the exotic nilpotent cone.

** Categorification via blocks of modular representations of sl(n) (pre-print, joint w/ Gufang Zhao) ** arxiv

We show that the categorical sl_2 action constructed in Cautis-Kamnitzer-Licata, using coherent sheaves on cotangent bundles to Grassmanians, is equivalent to a positive characteristic version of the sl_2 action constructed by Bernstein, Frenkel, Khovanov using singular blocks of category O.

**An introduction to nilpotent cones.** (pdf)

My honors thesis at the University of Sydney, supervised by Anthony Henderson.