Kay Kirkpatrick
Helen Corley Petit Scholar
Associate Professor of Mathematics
University of Illinois at UrbanaChampaign
 Email: kkirkpat (at) illinois (dot) edu
Jing Wang and
Partha Dey
are now
organizing the probability
seminar.
I organized an MSRI semester in fall 2015:
PDE, dynamics, and
randomness in high dimensions
Teaching
Math 564
Applied Stochastic Processes, Fall 2016
Math 461
Probability Theory, Spring 2015
Math 564
Applied Stochastic Processes, Fall 2014
Resources for improving
writing
skills and presenting skills.
Research
Interests: statistical mechanics, nonlinear differential equations, and dynamical systems, using a variety of methods from probability, functional analysis, harmonic analysis, and number theorywith applications to physics and biology.

Scaling
limits are fundamental to my research. Specifically, I'm interested in:
 Spin
models of ferromagnets and superconductors: the Heisenberg
model, the XY model, coupled XY models, and connections with the
macroscopic equations for magnets and superconductors, especially
critical behavior. Here's a
notverytechnical description of some of my research goals.
 BoseEinstein condensation and nonlinear Schrödinger equations (NLS). Various scaling limits, invariant measures for the NLS, probabilistic approaches to the NLS. Terry Tao's blog entry on this topic.
 Discrete NLS and other lattice systems with noise or longrange interactions to model condensates or polymers, and fractional nonlinear Schrodinger equation models of energy transport in biopolymers like DNA.
 Dilute gases, plasmas, and kinetic equations: Hardsphere models of dilute gases, and the Boltzmann equation in the BoltzmannGrad limit. Softsphere models of plasmas, and the Landau equation in the weak coupling limit.
 Computational probability: algorithms for quantum manybody
systems, Monte Carlo simulations of spin systems, and family genetic data analysis.
 Noncommutative probability: quantum groups as models of freely independent random
variables, especially in nontracial von Neumann algebras.
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 UIUC's
Sonia Kovalevsky Math Days for girls.
Mentees:
Michael
Brannan, now at Texas A&M
Haojian Li
Janna Lierl,
now at U Conn
Tayyab Nawaz
Leslie A. Ross
Danni Sun
Jack Weinstein
Jing Wang
Samantha Xu
Brief Vita
 Academic Positions:
 Assistant Professor of Mathematics, University of Illinois at
UrbanaChampaign, since 2011
 Visiting Professor, Université de Paris IX Dauphine, June 2012
 Courant Instructor/PIRE Fellow, NYU, 20092011
 NSF Postdoctoral Fellow, MIT, 20072009
 Education:
 Ph.D. in Mathematics, U.C. Berkeley, 2007
 Honors:
 20162017 Petit Scholar
 2016 Tenney Peck Teaching Award
 UIUC List of Teachers Ranked as Excellent, Springs 2014 and 2015
 NSF CAREER Award DMS1254791, May 2013  April 2018 (est.)
 NSF REU supplement DMS1242731, July 2012  July 2014 (est.)
 NSF grant DMS1106770,
Aug. 2011  July 2014 (est.)
 Courant/NSF PIRE Fellowship at Université de Paris IX, NSF OISE0730136, 2010  2011
 NSF Mathematical Sciences Postdoctoral Fellowship, 20072009
 AAUW American Dissertation Fellowship, 20062007
 NSF Graduate Research Fellowship
 Phi Kappa Phi, Kathleen 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. P Vol. 282 (2016), No. 1, 35–61
 Ben Arous, G., Kirkpatrick, K., and Schlein, B. A Central Limit Theorem in
manybody quantum dynamics. Comm. Math. Phys., 321:2, 2013, 371417.
 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. Asymptotics of meanfield
O(N) models.
 Kirkpatrick, K. and Meckes, E. Asymptotics of the meanfield
Heisenberg model. J. Stat. Phys., 152:1, 2013, 5492.
 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. 727757.
 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, 97102.
 Kirkpatrick, K. and Zhang, Y.
Fractional
Schrodinger dynamics and decoherence.
 Kirkpatrick, B. and Kirkpatrick, K. Optimal StateSpace Reduction for Pedigree Hidden Markov Models.
 Kirkpatrick, K., Lenzmann, E., and Staffilani, G. On the continuum limit for discrete
NLS with longrange lattice interactions. Comm. Math. Phys.,
317:3, 2013, 563591.
 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.) CRSCTR0024, October 2000.
 Also:
 Blecher, D., Kirkpatrick, K., Neal, M., and Werner, W. Ordered involutive operator spaces. Positivity, vol. 11, 2007, 497509.
 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 (V63.01228), fall 2009.
 Stanford University Educational Program for Gifted Youth instructor, math, summer 2007.
 Stanford University instructor, Ordinary Differential Equations, summer 2006.
 Stanford University Mathematics Camp counselor, summers 2003  2006.
 Montana State University instructor, Language of Mathematics, 2001  2002.
 Talks:
 SIAM Conference on Nonlinear Waves and Coherent Structures minisymposium
"Quantum ManyBody Dynamics: Analysis, Modeling
And Computation" in Philadelphia, PA, August 811, 2016
 Plenary speaker at the first Great Lakes Mathematical Physics Meeting, June 1719, 2016
 Plenary talk at Frontier Probability Days, May 911, 2016
 Colloquium at Bradley University, Feb. 11, 2016
 Plenary talk at the Texas Analysis and Mathematical Physics
Symposium (TexAMP 2015), Nov. 68, 2015
 Colloquium at UC Berkeley, Sept. 10, 2015, blogged
about here.
 Workshop for Women in Analysis and PDE at IMA, May 2831, 2015
 Conference in Stochastic Analysis and Related Topics in honor
of Rodrigo Banuelos at Purdue, May 2022, 2015
 Colloquium at UWMadison, 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 nonlocal and nonlinear analysis: theory
and applications," at ETH Zurich, June 2014.
 KiNet workshop "Mathematical and Numerical Methods for
Complex Quantum Systems" at UIC, March 2014
 University of Minnesota Probability seminar, Oct. 2013
 UIUC Probability seminar, Sept. 2013
 UIUC IMSE (Initiative for Mathematical Sciences and
Engineering) Summer School on MultiAgent 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
 UIUC 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
 UIUC Math 499 Introductory talk for the new math graduate students,
Nov. 2012
 ICERM Conference on Monte Carlo Methods in Physics and Biology,
Nov. 2012
 Duke University Workshop for Women in Probability, Oct. 2012
 UIUC undergraduate WIMSE (women in math, science, and engineering) dinner series
speaker, Oct. 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 Schaferprize 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 AnalyseProbabilités,
Sept. 28, 2010
 CIME Summer School on Quantum ManyBody Systems, Sept. 2, 2010
 Invitations:
 IMA conference Mathematical and Physical Models of Nonlinear
Optics in Minneapolis, MN, Oct. 31  Nov. 4, 2016
I organized the
Conference on New Developments in Probability at
Northwestern University, May 68, 2016
 Full 2013 CV: CV