K. L. Kirkpatrick
Associate Professor of
Mathematics and Physics
University of Illinois
My courses (Math 442 Partial Differential Equations in Spring 2023)
are online in Canvas. Zoom info and other details are in Canvas, and
an informational email will be sent before the first class meeting
to everyone who is registered and to auditors who email me with enough
advance notice. For an idea of how this course will start,
you can look at the public Spring 2022 webpage:
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
Here's a description of my dark matter interests for a broad
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
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
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
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
Blog: How to
Grad School While Poor.
- Shubhang Goswami
- Daniel Inafuku
- Kesav Krishnan
Brannan, now at Texas A&M
Nawaz, now at Illinois NetMath
- Leslie A. Ross
- Jing Wang, now
- 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
- Ph.D. in Mathematics, U.C. Berkeley
- B.S. in Mathematics, Montana State University
- 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
- 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
- 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.
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.
- 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,
- 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
562 Probability Theory II, Fall 2013
561 Probability Theory I, Spring 2013
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
skills and presenting skills.
- Banff Conference on Advances in Dispersive Equations, July 2019
- Keynote at the Seminar on Stochastic Processes (SSP), Utah,
- 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
- 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,
- "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,
- ICERM Conference on Monte Carlo Methods in Physics and Biology,
- 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,
- 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