David Keating

I am currently a RTG Postdoctoral Research Associate in the combinatorics group at the University of Illinois Urbana-Champaign. My postdoc advisor is Philippe Di Francesco. I am interested in statistical mechanics of two-dimensional lattice models, integrable probability, and combinatorics.

Previosly, I was a Van Vleck visiting assistant professor at UW Madison in the probability group, advised by Vadim Gorin.

In 2021, I recieved my Phd in mathematics from UC Berkeley. My advisor was Nicolai Reshetikhin. The title of my thesis was "Limit shapes in two-dimensional lattice models arising from physics and combinatorics". It recieved a 2021 Herb Alexander Prize from the Berkeley math department.

CV

Contact

• Email: (first initial)(last name)@illinois.edu
• Office: 109 Altgeld

Papers and preprints

• Asymptotics of Bounded Lecture-Hall Tableaux, with Z. Li and I. Prause.
• Shuffling algorithm for coupled tilings of the Aztec diamond, with M. Nicoletti.
• Colored vertex models and k-tilings of the Aztec diamond, with S. Corteel and A. Gitlin.
• A vertex model for supersymmetric LLT polynomials, with A. Gitlin.
• Equivalences of LLT polynomials via lattice paths.
• A vertex model for LLT polynomials, with S. Corteel, A. Gitlin, and J. Meza.
• Area statistics of large oscillating tableaux.
• Integrability of limit shapes of the inhomogeneous six vertex model, with N. Reshetikhin and A. Sridhar.
• Arctic curves phenomena for bounded lecture hall tableaux, with S. Corteel and M. Nicoletti.
• Conformal limit for dimer models on the hexagonal lattice, with N. Reshetikhin and A. Sridhar.
• Random tilings with the GPU, with A. Sridhar.

Gallery of Simulations

A gallery of simulations of the six vertex model, tilings, etc.

Teaching

At UIUC:

• Fall 2024: Instructor for Math 441 "Differential Equations." Syllabus

At UW Madison:

• Fall 2022, Spring and Fall 2023, Spring 2024: Instructor for Math 632 "Introduction to Stochastic Processes."
• Spring 2022: Instructor for Math 475 "Introduction to Combinatorics."
• Fall 2021 and Spring 2024: Instructor for Math 431 "Introduction to Probability."

At UC Berkeley:

• Spring 2020: GSI for Math 128A "Numerical Analysis."
• Spring 2019: GSI for Math 54 "Linear Algebra and Differential Equations."
• Fall 2018: GSI for Math 54 "Linear Algebra and Differential Equations."
• Fall 2017: GSI for Math 53 "Multivariable Calculus."
• Spring 2017: GSI for Math 53 "Multivariable Calculus."
• Fall 2016: GSI for Math 54 "Linear Algebra and Differential Equations."
• Spring 2016: GSI for Math 1B "Calculus II."
• Fall 2015: GSI for Math 1A "Calculus I."

Slides

Some slides from my talks:

• Random tilings on the gpu
• Arctic curves for bounded lecture hall tableaux
• Coupled tilings of the Aztec diamond

Miscellaneous

• A library for generating random tilings with Markov chain Monte Carlo on the GPU.