Brief Bio

I am a Visiting Lecturer in the Department of Mathematics and Statistics at Mount Holyoke College. Before that, I was a graduate student at the University of Minnesota-Twin Cities, where I obtained my PhD in 2017 under the advising of Benjamin Brubaker.

Beginning in Fall 2020, I will be a Visiting Assistant Professor in the Mathematics Department at Oberlin College.

Research

My research interests lie primarily in representation theory and number theory. In the majority of my current research, I use techniques of statistical mechanics (an area of physics), such as statistical-mechanical models and the Yang–Baxter equation, to study interesting objects in the representation theory of algebraic groups with connections to number theory. I have used such techniques to present new formulas for some nonarchimedean metaplectic Whittaker functions, which arise in the local theory of automorphic forms.

I have continued to study further connections between these "ice models," Whittaker functions, and Eisenstein series. I have taken an interest in colored ice models, which have surprising connections to Demazure operators and Kashiwara crystals. Another recent interest (albeit unrelated) involves staircase tableaux and the cyclic sieving phenomenon (seen in combinatorics).

Teaching

Fall 2020 (Oberlin College):

Past (Mount Holyoke College):

Past (University of Minnesota):

Some Papers

Duality for metaplectic ice (with Ben Brubaker, Valentin Buciumas, and Dan Bump). Commun. Number Theory Phys., volume 13, number 1 (2019). arXiv:1709.06500v3.

(submitted) Metaplectic ice for Cartan type C. (2017) arXiv:1709.04971v2.

(in preparation) Colored non-nested five-vertex models and Demazure atoms.

(in preparation) A comparison theorem for local Whittaker functions and global Eisenstein series.

Contacting Me

Office: 417 Clapp Lab
Email: ngray (at) mtholyoke.edu
Phone: (413) 538-2341

Department of Mathematics and Statistics
Mount Holyoke College
50 College Street
South Hadley, MA 01075