Research Interests: quantum and statistical mechanics, condensed matter, and machine learning.
Here's a general description of some of my results and aims. Specifically, I'm interested in:
- Working with a student who is fluent in quantum mechanics and German and/or French.
- Quantum groups as models of freely independent random variables, especially in non-tracial von Neumann algebras.
- Quantum statistical mechanics models: Bose-Einstein condensation and nonlinear Schrödinger equations (NLS), discrete NLS and other lattice systems with noise or long-range interactions, and fractional NLS models of energy transport in biopolymers like DNA. Terry Tao's blog entry about some of my BEC work.
- Classical statistical mechanics: soft-sphere models of plasmas, and the Landau equation in the weak coupling limit.
- Computational probability, algorithms, and family genetic data analysis.
- Spin models of ferromagnets and superconductors: Heisenberg model, XY model, coupled XY models, Toy Higgs model, other O(N) models, and connections with macroscopic equations for magnets and superconductors, especially critical behavior.
- Foundations of computer science, cognitive science, and artificial intelligence.
- Recent paper: Limiting Behaviors of High Dimensional Stochastic Spin Ensemble, with Gao, Marzuola, Mattingly, and Newhall: arxiv.org/abs/1806.05282
- Recent paper: Transport of a quantum particle in a time-dependent white-noise potential, with Hislop, Olla, and Schenker: arxiv.org/abs/1807.08317
- My new paper, The Turing Test Relies on a Mistake about the Brain. My recent Beckman talk slides, BIO-LOGIC: Biological Computation.
Read more about Kay at https://faculty.math.illinois.edu/~kkirkpat/
Recent Courses Taught
- MATH 442 - Intro Partial Diff Equations
- MATH 461 - Probability Theory
- MATH 490 - Mathematics of MachineLearning
- MATH 492 - Foundations of Quantum Mechani
- MATH 564 (STAT 555) - Applied Stochastic Processes
- MATH 595 - Interacting Particle Systems