The University of Texas at Austin2012/13 Focus on NLS 
2012/13 Thematic Program on nonlinear Schrodinger equations and Bose gases from a multidisciplinary, integrative perspective. With focus on research, and on the training of graduate and advanced undergraduate students. 
Schedule of Events 
Minicourses: Survey and Research Talks Advanced minicourses consisting of survey and research talks by experts in their respective fields.
* Joint invitations with Natasa Pavlovic. Introductory and survey talks, held by graduate students.

Multidisciplinary Perspective 
The study of interacting Bose gases has been extraordinarily successful in recent years, both in physics (BoseEinstein condensation, superfluidity) and mathematics. In mathematics, this topic bridges some of the most active research areas in mathematical physics and nonlinear PDE's. Due to the large number of degrees of freedom, the dynamics of a Bose gas is exceedingly complicated. Mean field limits provide a mathematically rigorous way to describe average dynamical properties of the bulk system. The nonlinear Schrodinger equation (NLS) emerges as a mean field limit for dilute Bose gases in the socalled GrossPitaevskii (GP) scaling limit. The study of NLS is a central and extremely successful area in the field of dispersive nonlinear PDE's. We mainly emphasize aspects of the following disciplines: Nonlinear PDE theory Key concepts and results in the wellposedness theory of the Cauchy problem for NLS. Survey of recent advances. Mathematical Physics Derivation of NLS and GrossPitaevskii hierarchies from quantum manyparticle systems and Quantum Field Theory. Wellposedness theory of GrossPitaevskii hierarchies. Computational Simulations Numerical study of properties of solutions of NLS beyond current grasp in PDE theory. Predictions from numerical simulations, and key problems in numerical analysis. Applications in Physics and Engineering Experimental observations in BoseEinstein condensates, phenomena and questions. 
Program Information

This is the first in a series of five thematic years held at the Department of Mathematics, centered around a single equation or method, viewed from an integrative, multidisciplinary perspective encompassing nonlinear PDE's, mathematical physics, computational simulations, as well as applications in physics and engineering. Focus topics addressed in these thematic years tentatively include nonlinear Schrodinger equations, wave propagation in random media, Vlasov and Boltzmann equations, Euler equations, and multiscale and renormalization group methods. The mathematical physics component will address the derivation of these equations from quantum dynamics. Some of the main educational goals are:
This program is supported by the NSF CAREER grant DMS1151414. Organizer: Thomas Chen. 
Recommended Reading 
T. Cazenave, Semilinear Schrodinger equations, Courant lecture notes 10, Amer. Math. Soc. (2003). T. Chen, N. Pavlovic, On the Cauchy problem for focusing and defocusing GrossPitaevskii hierarchies, Discr. Contin. Dyn. Syst. A, 27 (2), 715  739, 2010. L. Erdos, B. Schlein, H.T. Yau, Derivation of the cubic nonlinear Schrodinger equation from quantum dynamics of manybody systems, Invent. Math. 167, 515  614, 2007. S. Klainerman, M. Machedon, On the uniqueness of solutions to the GrossPitaevskii hierarchy, Commun. Math. Phys. 279 (1), 169  185, 2008. E.H. Lieb, R. Seiringer, J.P. Solovej, J. Yngvason, The mathematics of the Bose gas and its condensation, Birkhauser, 2005. B. Schlein, Derivation of Effective Evolution Equations from Microscopic Quantum Dynamics, Lecture notes, CMI 2008 Summer School on Evolution Equations. G. Staffilani, The theory of nonlinear Schrodinger equations I + II, Lecture notes, CMI 2008 Summer School on Evolution Equations. C. Sulem, P.L. Sulem, The Nonlinear Schrödinger Equation: SelfFocusing and Wave Collapse, Springer, 1999. T. Tao, Nonlinear dispersive equations. Local and global analysis, CBMS 106, eds: AMS, 2006.
