Kay Kirkpatrick

Biography

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/