K. L. Kirkpatrick

Associate Professor of Mathematics and Physics

Illinois

A note to prospective students:

I'm not teaching during the academic year 2020-2021, but you may click on any of the courses below.

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.
What's new: 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
Here are links to my paper, The Turing Test Relies on a Mistake about the Brain, my 2018 Beckman talk slides, BIO-LOGIC: Biological Computation, and IMCT talk slides, Bose-Einstein Condensation and Biological Machines.

Other Interests

I've mentored Illinois Geometry Lab projects on percolation theory with Michelle Delcourt and Thomas Mahoney, and a project on phase transitions in XY models with Tayyab Nawaz.

My NSF CAREER Award has been providing partial support for Urbana's Kovalevsky Days.

Blog: How to Grad School While Poor.

Teaching

Resources for all students from Saundra Yancy McGuire and Stephanie McGuire's book Teach Students How to Learn: Appendices A and B

Math 442 Partial Differential Equations, Spring 2020

Math 595 Advanced Machine Learning, Spring 2020

Math 490 Mathematics of Machine Learning, Fall 2019

Math 461 Probability, Spring 2019

Math 490 Mathematics of Machine Learning, Fall 2018

Math 595 Special Topics: Interacting Particle Systems, Spring 2017

Math 461 Probability Theory, Spring 2017

Math 564 Applied Stochastic Processes, Fall 2016

People:

Michael Brannan, now at Texas A&M
Tayyab Nawaz, now at Illinois NetMath
Leslie A. Ross
Jing Wang, now at Purdue

Brief Vita

Academic Positions:: Visiting Associate Professor, MIT, Fall 2017; Associate Professor of Physics, Illinois, since 2017; Associate Professor of Mathematics, Illinois, since 2016; Assistant Professor of Mathematics, University of Illinois at Urbana-Champaign, 2011-2016; Visiting Professor, Université de Paris IX Dauphine, June 2012; Courant Instructor/PIRE Fellow, NYU, 2009-2011; NSF Postdoctoral Fellow, MIT, 2007-2009

Education:: Ph.D. in Mathematics, U.C. Berkeley

Honors:: 2020-2021 LAS Study in a Second Discipline Fellowship (Neuroscience); 2017-2018 Simons Fellow in Mathematics; 2016-2018 Blackwell Scholar in Mathematics; 2016-2017 H.C. Petit Scholar; 2016 Tenney Peck Teaching Award; Urbana campus List of Teachers Ranked as Excellent, Springs 2014 and 2015; NSF CAREER Award DMS-1254791, May 2013 - April 2018 (est.); NSF REU supplement DMS-1242731, July 2012 - July 2014 (est.); NSF grant DMS-1106770, Aug. 2011 - July 2014 (est.); Courant/NSF PIRE Fellowship at Université de Paris IX, NSF OISE-0730136, 2010 - 2011; NSF Mathematical Sciences Postdoctoral Fellowship, 2007-2009; AAUW American Dissertation Fellowship, 2006-2007; NSF Graduate Research Fellowship; Phi Kappa Phi, K. Greey Graduate Fellowship; Schafer Prize; Goldwater Scholarship

Articles:: Nonlinear Schrodinger equation and quantum statistical mechanics:; Brannan, M. and Kirkpatrick, K. Quantum groups and generalized circular elements. PJM Vol. 282 (2016), No. 1, 35–61; Ben Arous, G., Kirkpatrick, K., and Schlein, B. A Central Limit Theorem in many-body quantum dynamics. Comm. Math. Phys., 321:2, 2013, 371-417.; Kirkpatrick, K., Schlein, B., and Staffilani, G. Derivation of the two dimensional nonlinear Schrodinger equation from many body quantum dynamics. American Journal of Mathematics, 2009.

Gibbs measures, phase transitions, and classical statistical mechanics:

Kirkpatrick, K. and Nawaz., T. Critical behavior of mean-field XY and related models. To appear in Birkhauser Proceedings of the Conference in honor of Rodrigo Bañuelos.

Kirkpatrick, K. and Nawaz., T. Asymptotics of mean-field O(N) models. To appear in J. Stat. Phys.

Kirkpatrick, K. and Meckes, E. Asymptotics of the mean-field Heisenberg model. J. Stat. Phys., 152:1, 2013, 54-92.

Kirkpatrick, K. Solitons and Gibbs measures for nonlinear Schrodinger equations, invited article for a special issue of MMNP.

Chatterjee, S. and Kirkpatrick, K. Probabilistic methods for discrete nonlinear Schrodinger equations. Comm. in Pure and Appl. Math., 65:5, 2012, pp. 727-757.

Kirkpatrick, K. Rigorous derivation of the Landau equation in the weak coupling limit (updated April, 2009) Communications in Pure and Applied Analysis, 2009.

Applications to computational biology:

Sun, D., Wang, Z., and Yu, S. Kinship accuracy: Comparing algorithms for large pedigrees. Stanford Undergraduate Research Journal, Vol. 13, 2014, 97-102.

Kirkpatrick, K. and Zhang, Y. Fractional Schrodinger dynamics and decoherence.

Kirkpatrick, B. and Kirkpatrick, K. Optimal State-Space Reduction for Pedigree Hidden Markov Models.

Kirkpatrick, K., Lenzmann, E., and Staffilani, G. On the continuum limit for discrete NLS with long-range lattice interactions. Comm. Math. Phys., 317:3, 2013, 563-591.

Bortz, D.; Guy, B.; Hood, J.; Kirkpatrick, K.; Nguyen, V.; and Shimanovich, V. Modeling HIV infection dynamics using delay differential equations. CRSC Technical Report (Pierre A. Gremaud, Zhilin Li, Ralph C. Smith, and Hien T. Tran, eds.) CRSC-TR00-24, October 2000.

Also:; Blecher, D., Kirkpatrick, K., Neal, M., and Werner, W. Ordered involutive operator spaces. Positivity, vol. 11, 2007, 497-509.; Teppo, A. R., Esty, W. W., and Kirkpatrick, K. The Assessment of Mathematical Logic: Abstract Patterns and Familiar Contexts. Psychology in Mathematics Education, Proceedings, 2003.

Past Teaching:
: Math 461 Probability Theory, Spring 2014; Math 562 Probability Theory II, Fall 2013; Math 561 Probability Theory I, Spring 2013; Math 461 Probability & Mathematica, Fall 2012; Math 461 Probability Theory, Spring 2012; Math 286 Differential Equations Plus Linear Algebra, Fall 2011; Courant instructor, Analysis I (V63.0325), spring 2010.; Courant instructor, Calculus II (V63.0122-8), fall 2009.

Resources for improving writing skills and presenting skills.

Talks:: Banff Conference on Advances in Dispersive Equations, July 2019; Keynote at the Seminar on Stochastic Processes (SSP), Utah, Mar 2019; Birthday conference for Thomas Liggett, Interacting Particle Systems and Statistical Mechanics, IPAM, Mar 2019; AWM Mini-Symposium talk on Math Communication, Feb 2019; Institute for Condensed Matter Theory seminar at University Illinois, Dec 2018; SIAM Conference on Nonlinear Waves and Coherent Structures, Anaheim, June 2018; AMS Annual Colloquium at University of Nebraska, Lincoln, Apr 2018; Logic seminar at University of Illinois at Urbana-Champaign, Jan 2018; Random matrices seminar at Harvard, Nov 2017; Physics of Living Systems seminar at MIT, Nov 2017; PDE and Probability seminars at MIT, Nov 2017; Analysis seminar at McGill, Oct 2017; Colloquium and Math Physics Seminar at Purdue, 2017; SIAM Conference on Nonlinear Waves and Coherent Structures mini-symposium "Quantum Many-Body Dynamics: Analysis, Modeling And Computation" in Philadelphia, PA, August 8-11, 2016; Plenary talk at the first Great Lakes Mathematical Physics Meeting, June 17-19, 2016; Plenary talk at Frontier Probability Days, May 9-11, 2016; Colloquium at Bradley University, Feb. 11, 2016; Plenary talk at the Texas Analysis and Mathematical Physics Symposium (TexAMP 2015), Nov. 6-8, 2015; Colloquium at UC Berkeley, Sept. 10, 2015, blogged about here.; Conference in Stochastic Analysis and Related Topics in honor of Rodrigo Banuelos at Purdue, May 20-22, 2015; Colloquium at UW-Madison, April 17, 2015; Colloquium at Southern Illinois University, April 2, 2015, videorecorded and available on youtube here.; Plenary talk at the 5th Ohio River Analysis Meeting, University of Cincinnati, February 28 - March 1, 2015; 36th Midwest Probability Colloquium at Northwestern, October 2014; Keynote for Illini Math PhD reunion, Sept. 2014; BIRS Workshop "Spin Glasses and Related Topics," at Banff, July 2014; "Recent advances in non-local and non-linear analysis: theory and applications," at ETH Zurich, June 2014.; Ki-Net workshop "Mathematical and Numerical Methods for Complex Quantum Systems" at UIC, March 2014; University of Minnesota Probability seminar, Oct. 2013; Illinois Probability seminar, Sept. 2013; Illinois IMSE (Initiative for Mathematical Sciences and Engineering) Summer School on Multi-Agent Networked Systems talk, Aug. 2013; 71st Midwest PDE seminar, May 2013; IMSE brown bag lunch seminar, Apr. 2013; University of Colorado at Boulder Probability seminar, Apr. 2013; Purdue University Probability seminar, Apr. 2013; Illinois Computational Science and Engineering seminar, Mar. 2013; SIDIM conference in San Juan, Puerto Rico, Mar. 2013; University of Puerto Rico at Mayaguez, PDE lecture, Mar. 2013; Stanford Analysis/PDE seminar, Jan. 2013; Illinois Math 499 Introductory talk for the new math graduate students, Nov. 2012; ICERM Conference on Monte Carlo Methods in Physics and Biology, Nov. 2012; IMSE (Initiative for Mathematical Sciences and Engineering) Kickoff Symposium: Critical Challenges at the Interface of Mathematics and Engineering, Sept. 2012; Banff workshop, Evolution equations of physics, fluids, and geometry, Sept. 2012; UCSD probability seminar, Mar. 2012; UNC Chapel Hill applied math seminar, Feb. 2012; SAMSI Uncertainty Quantification: Simulation of Rare Events workshop, Feb. 2012; UIUC Aerospace Engineering workshop on Random Dynamical Systems, Nov. 2011; University of Bonn PDE seminar, July 14, 2011; University of Edinburgh analysis seminar, May 9, 2011; AWM special Schafer-prize session, Jan. 6, 2011; University of Milan Solitary and Dispersive Days, Dec. 13, 2010; University of Cambridge analysis seminar, Nov. 22, 2010; Oberwolfach workshop on interacting particle systems, Nov. 8, 2010; Budapest Technical University probability seminar, Oct. 21, 2010; Université Paris IX, Séminaire du CEREMADE Analyse-Probabilités, Sept. 28, 2010; CIME Summer School on Quantum Many-Body Systems, Sept. 2, 2010

I organized the MSRI semester PDE, dynamics, and randomness in high dimensions in Fall 2015.
I organized the Conference on New Developments in Probability at Northwestern University, May 6-8, 2016.
I organized the 39th Midwest Probability Colloquium at Northwestern, Oct 14-16, 2017.
I'm organizing the 2nd Conference on New Developments in Probability, postponed to May 2021.

Spring 2020: Brief CV