Terrence George

Postdoctoral assistant professor


   

 
     Office: East Hall 4860.

     Email: georgete at umich dot edu

    

I am a postdoc at the University of Michigan where my mentor is David Speyer. I work on problems in the intersection of combinatorics, algebraic geometry and probability. I received my PhD from Brown University in 2020 advised by Rick Kenyon.



Research

6. Cross-ratio dynamics and the dimer cluster integrable system. (with Niklas Affolter and Sanjay Ramassamy)

We relate the cross-ratio dynamics integrable system of Arnold et al. to the dimer integrable system. In particular, we find a cluster algebra structure describing cross-ratio dynamics.

5. Electrical networks and Lagrangian Grassmannians. (with Sunita Chepuri and David Speyer.)

We show that Thomas Lam's space of cactus networks is the totally nonnegative Lagrangian Grassmannian.

4. 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.


3. The cluster modular group of the dimer model. (with 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.

2. 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.

1. Grove arctic curves from periodic cluster modular transformations. International Mathematics Research Notices (2020).

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).

 


Talks

- November 4, 2021 - Combinatorics seminar, UCLA (slides, video).

- October 26, 2021 - Random matrix theory seminar, KTH (slides).

- October 1, 2021 - Combinatorics seminar, University of Michigan.

- June 24, 2021 - Algebraic and enumerative combinatorics seminar, University of Waterloo (slides).

- April 4, 2021 - Clusters and geometry seminar, Yale (video).

- November 20, 2020 - Oberwolfach.

- September 18, 2020 - Combinatorics seminar, University of Michigan.

- February 3, 2020 - Probability seminar, Cornell.

- January 28, 2020 - Combinatorics seminar, Dartmouth.

- 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.

Expository talks

- Parking functions and LLT polynomials (Combinatorics learning seminar, notes).
 


Teaching

Michigan:

- Fall 2021 - MA 115 -  Calculus 1, sections 041 and 061.

- Winter 2021 - MATH 465 - Introduction to Combinatorics (both sections).

- Fall 2020 - MA 115 - Calculus 1, sections 032 and 052.

Brown:

- 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.