Vinoth Nandakumar's Homepage

me

About me


I am post-doc in mathematics at the University of Utah working in representation theory. Here is my CV and my Research Statement.

This semester I'm teaching MATH2210; see here for the course webpage.

Research

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

Following techniques used by Bezrukavnikov to establish a bijection between the dominant weights for a simple algebraic group, and O, the set of pairs consisting of a nilpotent orbit and a finite-dimensional irreducible representation of the isotropy group of the orbit, we prove an analogous statement for Kato's exotic nilpotent cone. We do this by studying a certain t-structure on the derived category of equivariant coherent sheaves on the exotic nilpotent cone.

Exotic t-structures for two-block Springer fibers. (pre-print, joint w/ Rina Anno) pdf
Exotic t-structures were introduced by Bezrukavnikov and Mirkovic in order to study representations of Lie algebras in positive characteristic. Here we study the exotic t-structure on Dn, the derived category of coherent sheaves on a two-block Springer fibre (i.e. for a nilpotent matrix of type (m+n, n)). Using work of Cautis and Kamnitzer, we give a description of the irreducible objects in the heart of this exotic t-structure, and compute the Ext's between these.

Quiver varieties and crystals for symmetrizable Kac-Moody algebras. (pre-print, joint w/ Peter Tingley) pdf
Kashiwara and Saito constructed a geometric realization of the B(\infty) crystal for a simply-laced Kac-Moody algebra, by using irreducible components of Lusztig's quiver varieties (which are representation varieties of the corresponding pre-projective algebra). We generalize this construction to symmetrizable Kac-Moody algebras.

Stability conditions for category O (pre-print) pdf
Recently, Anno, Bezrukavnikov and Mirkovic have introduced the notion of a real variation of stability conditions (which is related to Bridgeland's stability conditions), and construct an example using categories of coherent sheaves on Springer fibers. Here we construct another example, by studying certain sub-quotients of category O with a fixed Gelfand-Kirillov dimension. We use the braid group action on the derived category of category O, and certain leading coefficient polynomials coming from translation functors.

Expository articles

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

Talks

Exotic t-structures for two-block Springer fibres. (Slides)
A description of the irreducible objects in the heart of the exotic t-structure corresponding to a 2-block Springer fibre, for the Usyd Algebra Seminar (in July, 2012).

Gelfand-Tsetlin bases and crystals. (pdf)
An exposition of the theory of Gelfand-Tsetlin bases and crystal, for this seminar.

Cluster algebras, and representations of quantum affine algebras. (pdf)
An exposition of some work by Hernandez and Leclerc which constructs a monoidal categorification of cluster algebras of finite type via a certain subcategory of representations of the quantum affine algebras, for this seminar.


The format for this webpage was stolen from Yi Sun's webpage.