Matthew Nicoletti

I am a 5th year PhD student at MIT, advised by Alexei Borodin. Before that, I was an undergraduate at UC Berkeley. I'm interested in probability, combinatorics, and mathematical physics. Currently, I am mainly studying interacting particle systems and exactly solvable lattice models in statistical mechanics.

Office: 2-333C

Email: mnicolet at mit dot edu

Papers

  1. (with Vadim Gorin) Six Vertex Model and Random Matrix Distributions [arxiv], 2023. (preprint)
  2. (with Amol Aggarwal and Leonid Petrov) Colored Interacting Particle Systems on the Ring: Stationary Measures from Yang-Baxter Equation [arxiv], 2023. (preprint)
  3. (with Tomas Berggren and Marianna Russkikh) Perfect t-embeddings of uniformly weighted Aztec diamonds and tower graphs [arxiv], 2023. (To appear in IMRN)
  4. (with David Keating) Shuffling algorithm for coupled tilings of the Aztec diamond [arxiv], 2023. (To appear in Annales Henri Poincaré)
  5. Local Statistics and Shuffling for Dimers on a Square-Hexagon Lattice [arxiv], 2022. (Under revision in Annales de l'Institut Henri Poincaré B)
  6. (with Leonid Petrov) Irreversible Markov Dynamics and Hydrodynamics for KPZ States in the Stochastic Six Vertex Model [arxiv], 2022. (Electronic Journal of Probability)
  7. (with Sylvie Corteel and David Keating) Arctic curves phenomena for bounded lecture hall Tableaux [arxiv], 2019. (Communications in Mathematical Physics)

Talks and conferences

Seminar talks: Recent or upcoming travel and conferences:

Teaching, mentorship, and organizing

  • Co-organizer of MIT Integrable Probability Seminar (Fall 2023-present).
  • Teaching Assistant and head administrator, Probability and Random Variables (course number 18.600, Spring 2023).
  • Teaching Assistant, Probability and Random Variables (course number 18.600, Fall 2022).
  • Teaching Assistant, Complex Variables with Applications (course number 18.04, Spring 2022).
  • Mentor for the MIT math directed reading program (DRP). Students: Jemma Schroder and Christina Yu (Winter 2021-2022) and Preston Cranford (Winter 2020-2021)
  • Teaching Assistant, Linear Algebra (course number 18.06, Fall 2021).
  • Teaching Assistant, Stochastic Calculus (course number 18.676, Spring 2021).
  • Teaching Assistant, Probability Theory (course number 18.675, Fall 2020).
  • Mentor for Undergraduate Research Project (MIT UROP+). Project: ``Laws of Large Numbers for Eigenvalue Distributions Using Bessel Generating Functions". Student: Andrew Yao

A few simulations

  • Competitive erosion is a model for an evolving interface between two competing species, see https://arxiv.org/abs/1501.03584 and https://arxiv.org/abs/1501.03584 for background. Here are simulations of the model on the cylinder and in a simply connected pill shaped domain. Here are slides from a short talk at Cornell Probability summer school, based on unpublished calculations with a collaborator, Ananth Sridhar, where we heuristically compute the fluctuations of the interface. (Many thanks to my great friend Daniel Lengyel for help with the numerics and simulations).

  • Lecture Hall Tableaux are combinatorial objects which can be viewed as ensembles of non-intersecting lattice paths on a special lattice. Here is a uniformly random sample (with one particular boundary condition), constructed using "coupling from the past".

  • T-embeddings are special graph embeddings which are compatible with the dimer model Boltzmann measures. Below are pictures of t-embeddings for ``uniform Aztec diamond graphs'' and for ``tower graphs'', with the image of the embedded edges under the associated ``origami maps'' in blue. On the right we show a graph of the origami map for the tower graph.

Accessibility