**Graduate Student**

** **

** Office:** Room 019, Kassar House

** Mailing Address:** Department
of Mathematics

019 Kassar House

Box 1917

151 Thayer Street

Providence, RI 02912

**Email: **gterrence at math dot brown dot edu

** **

I am a fifth year graduate student interested in mathematical physics. I work on problems in the intersection of combinatorics, algebraic geometry and probability. I am visiting Yale for the academic year 2019-2020. My advisor is Rick Kenyon.

I am an organizer for the Brown discrete math seminar with Rick Kenyon and Sam Watson. I am also an organizer for the AMS annual grad student math conference at Brown with Victoria Gras Andreu and Max Weinreich.

**Research**

- Dimers and Beauville systems. (in preparation; with Alexander Goncharov and Rick Kenyon.)

Given
a convex integral polygon, we can construct a dimer integrable system
and a toric surface. We show that the spectral transform is a birational
isomorphism of the dimer integrable system with the Beauville integrable
system associated to the toric surface.

- Cluster modular groups of dimers and networks. (with an appendix by Giovanni Inchiostro.)

We compute the group of symmetries of the dimer integrable system. Each element of the group gives a way to shuffle the dimer model, generalizing domino-shuffling.

- Spectra of biperiodic planar networks.

Associated to the Laplacian on a biperiodic planar network is its spectrum, a curve and a certain divisor on it (see image below for an example depicting the divisor on the amoeba of a spectral curve). We provide a classification of biperiodic planar networks in terms of their spectrum.

- Grove
arctic curves from periodic cluster modular transformations.

Cube groves are a model for random surfaces. In the scaling limit, they exhibit phase transitions where the phase boundary is a deterministic algebraic curve (see image below).

**Invited talks**

**Upcoming:**

- January 28, 2020 - Dartmouth.

**Past:**

- November 15, 2019 - Combinatorics seminar, University of Michigan.

- November 8, 2019 - Integrable probability seminar, Columbia University.

- September 19, 2019 - Combinatorics seminar, Yale University.

- August 7, 2019 - Algebra and Combinatorics seminar, Indian Institute of Science.

- January 23, 2019 - ICTS-TIFR conference (Universality in random structures: Interfaces, matrices, sandpiles.)

- August 8, 2018 - Indian Institute of Science.

- July 23, 2018 - Bangalore probability seminar, Indian Statistical Institute (ISI), Bangalore.

- April 10, 2018 - Discrete math seminar, Brown University.

**Slides from talks**

**Teaching
**

- Fall 2018 - Math 90: Introductory Calculus I (Instructor).

- Fall 2017 - Math 200: Intermediate Calculus (for Physics/Engineering) (Instructor).- Spring 2017 - Math 200: Intermediate Calculus (for Physics/Engineering) (TA).

- Fall 2016 - Math 100: Introductory Calculus II (TA).

Directed reading program:

-Spring 2018 - I mentored Jackson Markey. We read portions of
"Enumerative geometry and string theory" by Sheldon Katz.