Trung Vu
University of Illinois at UrbanaChampaign
My name is Trung Vu. I am a fifthyear mathematics Ph.D. student at the University of Illinois UrbanaChampaign. My advisors are Professor Philippe Di Francesco and Professor Rinat Kedem. I am currently on the job market Fall 2024.
I am interested in statistical mechanics and its interaction with other areas such as algebraic combinatorics, probability, discrete complex analysis, and representation theory. Specifically, I like to think about statistical mechanics models such as vertex models, dimer models and Ising models. Currently, I am studying the Tsystems, the Qsystems, domino tiling of graphs arising from the discrete stepped initial data surface of these systems, limit shapes, embedding and the artic curve phenomena. I put down some short introductory ideas from my own notes to each of these topics on the "Topics" tab above along with references for more details.
I am the organizer of University of Illinois UrbanaChampaign Integrability & Representation Theory Seminar in 20242025 academic year with Philippe Di Francesco, Rinat Kedem, David Keating, Wonwoo Kang.
Publication

Trung Vu (joint with Kosmas Diveris), Matrix Square Roots of Polynomials, Pi Mu Epsilon Journal, 2018, [preprint]

Trung Vu (joint with Philippe Di Francesco), Arctic curves of Tsystem with slanted initial data, Journal or Physics A: Mathematical and Theoretical, 57 335201, [journal] [arXiv]
Submitted and Preprints
Ongoing project
tembedding of the Tsystem dimer.

Tsystem dimer density and height fluctuation.

Tsystem dimer integrable system and spectral Harnack curves.
Update
 October 25th, 2024: University of Michigan Combinatorics Seminar, Ann Arbor, Michigan
 October 10th, 2024: Purdue University Mathematical Physics Seminar, West Lafayette, Indianna
 July 6th  July 21st, 2024: Integrable Probability Summer School, University of Virginia, Charlottesville, VA
 June 25th  30th June 2024: Jim Propp's 60th Birthday Conference, Statistical and Dynamical Combinatorics, MIT, Cambridge, Massachussett
 March 2024June 2024: Visiting researcher/participant of Geometry, Statistical Mechanics, and Integrability Long Program at Institute for Pure and Applied Mathematics, Los Angeles
 August 2023, 1424th: Dimers: Combinatorics, Representation Theory and Physics at CUNY, NYC
 Fall 2022  Fall 2023: I am supported by Bourgin fellowship and University of Illinois at UrbanaChampaign Research Board
 April 2022: Analytic Conbinatorics in Several Variables Workshop at American Institute of Mathematics
 June 2125, 2021: 9th International Conference on Lattice Path Combinatorics & Applications