Brief Bio

I am a Visiting Assistant Professor in the Mathematics Department at Oberlin College. Before that, I was a Visiting Lecturer for three years at Mount Holyoke College. I obtained my PhD at the University of Minnesota-Twin Cities under the advising of Benjamin Brubaker.

In Summer 2020, I joined other early-career mathematicians by becoming a member of the 2020 cohort for Project NExT, a professional development program sponsored through the MAA for new or recent PhDs in the mathematical sciences.

In Summer 2021, I participated in the Park City Mathematics Institute's Undergraduate Faculty Program (UFP), a program that is aimed at faculty members from all types of colleges and universities who have strong interests in undergraduate teaching and research. UFP 2021 focused on motivic Milnor numbers.

Research

My research interests lie primarily in representation theory and number theory. In the majority of my current research, I use techniques from statistical mechanics, 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. More recently, I have been studying colored ice models, which have surprising connections to Demazure operators and Kashiwara crystals. Even more recently, I have been studying $\mathbb{A}^1$-Milnor forms and algebraic singularities and their connections to Puiseux series and Newton polygons.

Teaching

Spring 2023:

Past:

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: King Building 204
Email: ngray (at) oberlin.edu
Phone: (440) 775-8972

Mathematics Department
King Building 205
10 N. Professor Street
Oberlin, OH 44074