Nic Brody

Mathematics student


I am a second year Master's student in the math department at UCSB. My advisor is Jon McCammond, with whom I am studying Coxeter groups. I was previously a student of the College of Creative Studies, and as an undergraduate, I worked closely with Jordan Schettler. With Jordan, I studied a connection between hyperbolic triangles and elliptic curves.

My CV can be downloaded from this link.

My interests include playing guitar and watching live music. I have seen my favorite band this many times, and I also really like these bands. I am poorly-versed in computers, physics, philosophy, linguistics, biology, and psychology but am curious about these topics as well.



Limit Roots of Lorentzian Coxeter Systems (in progress)

Rational Hyperbolic Triangles and a Quartic Model of Elliptic Curves


The Numbers Game for solving the word problem in Coxeter groups

Hyperbolic Triangles for drawing triangles in the upper half plane in Geogebra


These are some topics I am interested in, but may or may not know much about. The items in this list range from specific objects to broad fields of mathematics. I am interested in: Coxeter groups, Artin groups, buildings, L-functions, automorphic forms, noncrossing partitions, regular polytopes, the word problem for groups, path algebras, representation theory, invariant theory, boundaries of groups, Garside structures, incidence/category algebras, noncommutative algebra, braid groups, knot theory, rational points on elliptic curves, generating functions, finite geometries, Klein's solution of the quintic, Diophantine equations, and every topic in the list below.

Expository writing (many of the links are under construction)

Classification of Finite Reflection Groups

Dehn Functions

Banach-Tarski Paradox

Non-Hopfian Groups

Automatic Groups

Mobius Functions

Adjoint Functors

Regular Polygonomials




I am currently the TA for Math 6A (Vector Calculus) and Math 201A (Real Analysis).

In Summer 2015, I was the TA for Math 4A (Linear Algebra).

In Spring 2015, I was the TA for Math 4A (Linear Algebra).

In Winter 2015, I was the TA for Math 118B (Real Analysis).

In Fall 2014, I was the TA for Math 118A (Real Analysis).

In Spring 2014, I was the TA for Math 115B (Number Theory).

In Winter 2014, I was the TA for Math 115A (Number Theory).