**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.)

- Cluster modular group of the dimer model. (in
preparation; with an appendix by Giovanni
Inchiostro.)** **

- 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**

- 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.