Noah White

Mathematical Sciences Institue
Australian National University
Canberra, ACT, Australia

noah.white@anu.edu.au
Office 2.70, Hanna Neumann Building 145

It's me!

Background

I am a representation theorist interested in problems that have some connection to combinatorics, algebraic geometry and integrable systems. I arrived at ANU in 2020 after being a postdoc at University of California, Los Angeles and obtaining my PhD at the University of Edinburgh.

Research

My research has many interconnections however it can be broadly split into several areas:

Bethe ansatz in representation theory

The Bethe ansatz is a method used to construct eigenvectors for Hamiltonians in some quantum mechanical systemns such as Gaudin spin chains. It has found wide application in representation theory and helped resolve several conjectures (famously the Shapiro-Shapiro conjecture). My research concerns the specific case of the Gaudin model for (\mathfrak{gl}_n)) which I used to prove a conjecture of Etingof, showing that the monodromy of the Bethe eigenvectors recovers an action of the cactus group coming from crystal graphs. The same setting was used to resolve a conjecture of Bonnaf'e-Rouqiuer concerning a reinterpretation of Kazhdan-Lusztig cells for the symmetric group in terms of the rational Cherednik algebra and Calogero-Moser space.

Cactus group actions

Actions of the braid group play an important role in representation theory. Often these actions come with a parameter that one can send to zero. In this limit, one recovers an action of the associated cactus group. I am interested in both calculating specific examples of these actions, and understanding more precisely the relation between the braid group and the cactus group actions.

Generalised Jucys-Murphy elements

The classical Jucys-Murphy elements of the symmetric group arise from the restriction to smaller symmetric subgroups and are used to construct the irreducible representations. From many points of view, there is nothing special about the symmetric subgroups considered and one can defined generalised Jucys-Murphy elements for any chain of parabolic subgroups. I show how to calculate the eigenvalues of these operators, and how to find additional operators to diagonalise the multiplicity spaces that arise from more general restrictions. This is research in progress.

Invariants for the reflection equation algebra

Invariant functions for the general linear group in its regular representation are given by the coefficients of the characteristic polynomial (e.g. the trace and the determinant). With David Jordan I investigated the analgous problem for the reflection question algebra, a quantisation of the general linear group. Various implicit descriptions of the invariants have been given, however we were able to write down explicit formulas. This also yielded a new description of the centre of the Drinfeld-Jimbo quantum group.

Teaching

My current teaching:

My previous teaching at ANU:

My previous teaching at UCLA:

Software and other