Terrence George

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

Limit shapes for cube groves.


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.