Noah White

University of Califonia,
Los Angeles

Introduction

The motivation for my research comes from representation theory. In particular I am interested in Lie algebras and related objects such as the Weyl groups. One can often make difficult questions in representation theory simpler by reinterpreting them in terms of some geometry. Often this sheds light on the underlying combinatorics. It is this interaction which I find fascinating.

A particularly beautiful example are the Littlewood-Richardson coefficients. On the combinatorial side, these numbers control the multiplication of Schur polynomials. On the algebraic side they are responsible for the decomposition of tensor products of simple $\mathfrak{gl}_n$-modules. And on the geometric side they tell us how Schubert varieties intersect. This correspondence is at the heart of my research.

More specifically I am interested in the relationship between crystal bases, the Gaudin model and the algebraic Bethe ansatz for $\mathfrak{gl}_n$.

I am also working on a project with David Jordan on describing the center of the reflection equation algebra - and the quantum group $U_q(\mathfrak{gl}_n)$ - combinatorially.

Papers and preprints

The center of the reflection equation algebra via quantum minors (jt with D. Jordan)

The Monodromy of real Bethe vectors for the Gaudin model

Calogero-Moser cells in type A and the RSK correspondence (jt with A. Brochier and I. Gordon). In preparation.

Talks

Here is a (incomplete) list of the talks I have given.

 Nov 2017 AMS Western Sectional meeting, The center of the reflection equation algebra (and quantum group) for $GL_n$. Oct 2017 Toronto, Geometric representation theory seminar, The center of the reflection equation algebra (and quantum group) for $GL_n$. Jun 2016 Köln algebra seminar, The cactus group and the Gaudin model. Apr 2016 Max Plank Institute, Oberseminar, The cactus group and RSK. Mar 2016 IMJ Paris Diderot Groupes, Représentations et Géométrie seminar, Monodromy of the Gaudin system in type A. Aug 2015 Melbourne algebra/geometry/topology seminar, Cactus group actions on Young tableaux. Aug 2015 UQ pure maths seminar, Cactus group actions on Young tableaux. Jul 2015 Sydney algebra seminar, Cactus group actions in Schubert calculus, crystals and integrable systems. May 2015 Joint Heriot Watt, Edinburgh, Glasgow, St. Andrews PG Colloquium, Reality in algebraic geometry. Feb 2015 QMUL algebra seminar, Schubert calculus and the cactus group. Dec 2014 GEARS seminar, Glasgow, The representation theory of the symmetric groups via the action of a “maximal torus”. Mar 2014 ARTIN in Newcastle, The center of quantum $GL_n$ Sep 2014 Geometry club, Edinburgh, Galois Theory in Enumerative Geometry. Sep 2013 Geometry club, Edinburgh, Invariants of knots from representation theory.