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.
I am co-organizing the Learning Seminar in Algebraic Combinatorics.
I am on the job market this Fall. Here is my CV.
8. Discrete dynamics in cluster integrable systems from geometric R-matrix transformations. (with Sanjay Ramassamy.)
We classify the discrete dynamics in cluster integrable systems that arise from sequences of elementary transformations and geometric R-matrix transformations.
7. Dimers and Beauville integrable systems. (with Giovanni Inchiostro.)
show that the dimer integrable system on the honeycomb lattice is
isomorphic to the Beauville integrable system on the projective plane.
6. The inverse spectral map for dimers. (with Alexander Goncharov and Rick Kenyon.)
proved that the spectral transform of the dimer integrable system is
birational by constructing an inverse map using theta functions on
Jacobians of spectral curves. We provide an alternate construction of
the inverse map that involves only rational functions in the spectral
5. 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.
4. 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.3. The cluster modular group of the dimer model. (with Giovanni Inchiostro.) To appear in Ann. Inst. Henri Poincare D.
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.
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).
- August 8, 2022 - TIFR-CAM.
- August 2, 2022 - Colloquium, ISI Bangalore.
- July 6, 2022 - ICTS conference (Combinatorial algebraic geometry- real and tropical) (slides, video).
- April 28, 2022 - Integrable probability seminar, MIT.
- April 7, 2022 - JMM (Combinatorial applications of computational geometry and algebraic topology).
- February 11, 2022 - Combinatorics seminar, University of Minnesota.
- 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 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.
- Parking functions and LLT polynomials (Combinatorics learning seminar, notes).
- Positroid varieties (Combinatorics learning seminar, notes).
- Winter 2022- MATH 465 - Introduction to Combinatorics (both sections).
- 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.
- 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.