K. L. Kirkpatrick

Blue light trail of the tip of the second part of a double pendulum, with the path looking chaotic and somewhat uniformly spread out over an annulus

Associate Professor of Mathematics and Physics

University of Illinois



Math 490 Mathematics of Machine Learning in Fall 2022 is online and on Canvas. Zoom info will be posted on Canvas and sent before the first class meeting to everyone who is registered and to auditors who email with enough time for my response. For exact details about this course, please refer to Canvas. For an approximate sense of how this course will go, you can look at the public Fall 2019 Math 490 webpage: https://faculty.math.illinois.edu/~kkirkpat/490fall2019.html

(Exam dates are likely to be around October 12 and December 7, times flexible.)

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


Research Interests: quantum and statistical mechanics, condensed and dark matter, foundations of neuroscience and computer science.


Here's a description of my dark matter interests for a broad audience.

What's new:
  • My paper, Biological computation: hearts and flytraps, in the Journal of Biological Physics.
  • Microtubules as electron-based topological insulators, with Varsha Subramanyan, Saraswathi Vishveshwara, Smitha Vishveshwara: https://arxiv.org/abs/2112.12203.
  • Analysis of Bose-Einstein condensation times for self-interacting scalar dark matter, with Anthony E. Mirasola and Chanda Prescod-Weinstein: arxiv:2110.08921 in PRD.
  • Relaxation times for Bose-Einstein condensation in axion miniclusters, with Anthony E. Mirasola and Chanda Prescod-Weinstein: arxiv:2007.07438
  • A large deviation principle in many-body quantum dynamics, with Simone Rademacher and Benjamin Schlein: arxiv.org/abs/2010.13754
  • Limiting Behaviors of High Dimensional Stochastic Spin Ensemble, with Gao, Marzuola, Mattingly, and Newhall: arxiv.org/abs/1806.05282
  • 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 2018 Beckman talk slides, BIO-LOGIC, and IMCT talk slides, Bose-Einstein Condensation and Biological Machines.

    I'm also interested in:
  • Working with a student who is fluent in quantum mechanics and German.
  • 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.

    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 provided partial support for Urbana's Kovalevsky Days.

    Blog: How to Grad School While Poor.

    People:
    Shubhang Goswami
    Daniel Inafuku
    Kesav Krishnan
    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:
    Simons Professor, CRM, Montréal, June 2022
    Visiting Associate Professor, MIT, Fall 2017
    Associate Professor of Mathematics and Physics, Illinois, since 2017
    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
    B.S. in Mathematics, Montana State University
    Honors:
    College of LAS Study in a Second Discipline Fellowship, Neuroscience, 2020 - 2021
    Simons Fellow in Mathematics, 2017 - 2018
    Blackwell Scholar in Mathematics, 2016 - 2018
    H.C. Petit Scholar, 2016 - 2017
    Tenney Peck Teaching Award, 2016
    Urbana campus List of Teachers Ranked as Excellent, e.g., Springs 2014 and 2015
    NSF CAREER Award DMS-1254791, 2013 - 2020
    NSF REU supplement DMS-1242731, 2012 - 2014
    NSF grant DMS-1106770, 2011 - 2015
    Courant/NSF PIRE Fellowship at Université de Paris IX, NSF OISE-0730136, 2010 - 2011
    NSF Mathematical Sciences Postdoctoral Fellowship
    AAUW American Dissertation Fellowship
    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.

    Teaching:
    Math 442 in 2022 public webpage only (remainder was on Canvas)
    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
    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 organized the 2nd Conference on New Developments in Probability, May 2021.
    Spring 2020: Brief CV