Vinoth Nandakumar

me

About me


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/)

Research

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. 133

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.

Expository articles

An introduction to nilpotent cones. (pdf)
My honors thesis at the University of Sydney, supervised by Anthony Henderson.