K. Kirkpatrick

Simons Fellow, Visiting Associate Professor of Mathematics at MIT

Blackwell Scholar in Mathematics, Associate Professor of Mathematics and Physics

University of Illinois at Urbana-Champaign

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

Jing Wang and Partha Dey are now organizing the probability seminar.

Research Interests: quantum and statistical mechanics, condensed matter, and machine learning.

Here's a general description of some of my results and aims. Specifically, I'm interested in:

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.
What's new: Turing, von Neumann, Shannon, and Hopper; foundations of computer science, cognitive science, and artificial intelligence.

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 Urbana's Kovalevsky Days.

People:

Michael Brannan, Texas A&M
Haojian Li
Tayyab Nawaz
Leslie A. Ross
Jing Wang

Teaching

Math 461 Probability Theory, Spring 2017

Math 595 Special Topics: Interacting Particle Systems, Spring 2017

Math 564 Applied Stochastic Processes, Fall 2016

Math 461 Probability Theory, Spring 2015

Math 564 Applied Stochastic Processes, Fall 2014

Brief Vita

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 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, 2007

Honors:: 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

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.

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 (V63.0122-8), fall 2009.

Resources for improving writing skills and presenting skills.

Talks:: 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'm organizing the 39th Midwest Probability Colloquium at Northwestern, Oct 14-16, 2017.

Spring 2016 CV: CV