Kay Kirkpatrick

Research

An idea fundamental to my research is that 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. Chaos in spin glasses.
• Computational PDEs and large deviations: discretization schemes for PDEs that are nonlocal in time or space, and algorithms for quantum many-body systems.

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Other Interests

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Brief Vita

Academic Positions:

Courant Instructor/PIRE Fellow, NYU, current

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-PIRE Fellowship, 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:

Chatterjee, S. and Kirkpatrick, K. Probabilistic methods for discrete nonlinear Schrodinger equations.

Blanchet, J. and Kirkpatrick, K. Rare event analysis of a dynamic quantum Curie-Weiss-type model. Forthcoming.

Kirkpatrick, K.; Lenzmann, E.; and Staffilani, G. Quantum lattice systems and fractional nonlinear Schrodinger equations. Forthcoming.

Kirkpatrick, K., Schlein, B., and Staffilani, G. Derivation of the two dimensional nonlinear Schrodinger equation from many body quantum dynamics. Accepted, American Journal of Mathematics, 2009.

Kirkpatrick, K. Rigorous derivation of the Landau equation in the weak coupling limit (updated April, 2009) Accepted, 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.

Talks:

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.

University of Kentucky colloquium, Mar. 11, 2010.

Columbia Probability seminar, Feb. 19, 2010.

University of Maryland PDE seminar, Feb. 16, 2010.

Case Western colloquium, Feb. 12, 2010.

University of Nebraska - Lincoln colloquium, Feb. 8, 2010.

University of Michigan Applied and Interdisciplinary Math seminar, Feb. 5, 2010.

University of Michigan AIM student seminar lecture, Feb. 5, 2010.

Courant Institute Analysis seminar, Jan. 28, 2010.

University of Illinois at Urbana-Champaign colloquium, Jan. 22, 2010.

CUNY Probability Seminar, Dec. 8, 2009.

Pacific Institute for the Mathematical Sciences, Workshop on nonlinear dispersive and geometric evolution problems, Aug. 21, 2009.

Centre de Recherches Mathematiques, Workshop on Spin Glasses, June 12, 2009. The slides.

Centre de Recherches Mathematiques, Workshop on Interacting Stochastic Particle Systems, May 21, 2009.

Montana State University special colloquium, Apr. 16, 2009. The slides.

Courant Institute, NYU, Probability seminar, Mar. 27, 2009. The slides.

Case Western Reserve University Applied Math seminar, Mar. 16, 2009.

MIT PDE/analysis seminar, Feb. 25, 2009.

Boston University Dynamical Systems seminar, Jan. 29, 2009.

University of Rochester colloquium, Jan. 27, 2009.

UC Berkeley Analysis and Partial Differential Equations seminar, Sept. 22, 2008.

Clay Math Summer School on Evolution Equations (Zurich), July 16, 2008.

Case Western Reserve University math department colloquium, Oct. 19, 2007. The slides.

Stanford University Mathematics Camp guest lecture: ''A random walk through statistical mechanics,'' July 27, 2007.

MIT PDE/analysis seminar, Dec. 6, 2006.

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Full Vita: CV

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