K. L. Kirkpatrick
Associate Professor of
Mathematics and Physics
My American Mathematical Society invited address slides
and my AMS Notices article Dark matter may be a Bose-Einstein condensate of axions.
Math 564 in Fall 2021 has a public webpage
here, and there is more content in
It will be similar to the Fall 2016 version, linked here.
Research Interests: quantum and statistical mechanics,
condensed and dark matter, and foundations of neuroscience and
Here's a description of my dark matter interests for a broad
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
- Relaxation times for Bose-Einstein condensation in
axion miniclusters, with Anthony E. Mirasola and Chanda Prescod-Weinstein: arxiv.org/abs/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 new paper, Biological
2018 Beckman talk slides, BIO-LOGIC, and IMCT talk slides, Bose-Einstein
Condensation and Biological Machines.
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
Blog: How to
Grad School While Poor.
Brannan, now at Texas A&M
Nawaz, now at Illinois NetMath
Leslie A. Ross
Jing Wang, now
- 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
- 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
- 2020-2021 LAS Study in a Second Discipline Fellowship
- 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
- 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,
- 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
- 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