Kay Kirkpatrick

Assistant Professor of Mathematics,

University of Illinois at Urbana-Champaign

E-mail: kkirkpat (at) illinois (dot) edu

I'm organizing the Urbana-Champaign probability seminar.

Teaching

Math 461 C13, Spring 2012

Math 286 X1, Fall 2011

Research

Interests: statistical mechanics, nonlinear PDEs, and dynamical systems, using a variety of methods from probability, functional analysis, harmonic analysis, and number theory--with applications to physics and computational biology.

Fundamental to my research is the idea of scaling limits. Specifically, I'm interested in:

Bose-Einstein 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 long-range 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: Hard-sphere models of dilute gases, and the Boltzmann equation in the Boltzmann-Grad limit. Soft-sphere models of plasmas, and the Landau equation in the weak coupling limit.
Curie-Weiss and Ising models of ferromagnetism. The classical Heisenberg model.
Computational PDEs and large deviations: discretization schemes for PDEs that are nonlocal in time or space, and algorithms for quantum many-body systems.

Brief Vita

Academic Positions:
Assistant Professor of Mathematics, University of Illinois at Urbana-Champaign, since 2011
Courant Instructor/PIRE Fellow, NYU, 2009-2011
NSF Postdoctoral Fellow, MIT, 2007-2009

Education:
Ph.D. in Mathematics, U.C. Berkeley, 2007
B.S. in Mathematics, Montana State University-Bozeman, 2002

Awards:
NSF Division of Mathematical Sciences grant DMS-1106770, Aug. 2011 - present
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, 2002-2005
Phi Kappa Phi, Kathleen Greey Graduate Fellowship, 2002-2003
Schafer Prize, 2002
Goldwater Scholarship, 2001-2002

Articles:
Blanchet, J. and Kirkpatrick, K. Rare event analysis of a dynamic quantum Curie-Weiss-type model. In preparation.
Kirkpatrick, K. and Meckes, E. Asymptotics of the empirical spin distribution in the mean-field Heisenberg model.
Kirkpatrick, B. and Kirkpatrick, K. Optimal State-Space Reduction for Pedigree Hidden Markov Models.
Ben Arous, G., Kirkpatrick, K., and Schlein, B. A Central Limit Theorem in many-body quantum dynamics.
Kirkpatrick, K. Solitons and Gibbs measures for nonlinear Schrodinger equations, invited article for a special issue of MMNP.
Kirkpatrick, K., Lenzmann, E., and Staffilani, G. On the continuum limit for discrete NLS with long-range lattice interactions. To appear in CMP.
Chatterjee, S. and Kirkpatrick, K. Probabilistic methods for discrete nonlinear Schrodinger equations. To appear in CPAM.
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.
Kirkpatrick, K. Rigorous derivation of the Landau equation in the weak coupling limit (updated April, 2009) Communications in Pure and Applied Analysis, 2009.
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.
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.

Teaching:
Courant instructor, Analysis I (V63.0325), spring 2010.
Courant instructor, Calculus II (V63.0122-8), 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.

Recent Talks:
Northwestern University analysis seminar, Mar. 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
UIUC Harmonic Analysis/Differential equations seminar, Nov. 2011
University of Wisconsin-Madison Probability seminar, Oct. 2011
UIUC Probability seminar, Sept. 2011
University of Bonn PDE seminar, July 14, 2011
University of Edinburgh analysis seminar, May 9, 2011
Brown University International Conference on Stochastics and Dynamics, April 30, 2011
Universities of Copenhagen and Lund joint seminar, Mar. 25, 2011
Institut Henri Poincaré, Probability Groupe de Travail series of seminars, March 2011
Missouri S&T colloquium, Jan. 10, 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.
SIAM Meeting on Nonlinear Waves, session on Bose-Einstein condensation, Aug. 16, 2010.
Canadian Mathematical Society Summer Meeting, Fredericton, June 4, 2010.

Kay Kirkpatrick

Assistant Professor of Mathematics,

University of Illinois at Urbana-Champaign

Teaching

Research

Brief Vita