Session S02 - Diverse Aspects of Elliptic PDEs and Related Problems

Thursday, July 15, 17:00 ~ 17:30 UTC-3

Old and New Perspectives on Effective Equations

Matthew Rosenzweig

Massachusetts Institute of Technology, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this talk, we consider nonlinear-Schr\"odinger-type equations as partial differentiation equations (PDEs) arising as effective descriptions of systems of finitely many interacting bosons. We approach this topic from two perspectives. The \emph{old} perspective consists of proving quantitative convergence in an appropriate function space of solutions to the finite problem to a solution of an effective, limiting PDE, as the number of particles tends to infinity. The \emph{new} perspective consists of proving qualitative convergence of geometric structure, such as the properties of being an integrable and Hamiltonian system. Through these two complementary perspectives, focusing on both quantitative and qualitative convergence, we gain a deeper understanding of how field theories, both classical and quantum, may be deformed to a new field theory, and of how this deformation may be reversed.

Joint work with Dana Mendelson (University of Chicago), Andrea Nahmod (University of Massachusetts, Amherst), Natasa Pavlovic (University of Texas at Austin) and Gigliola Staffilani (Massachusetts Institute of Technology).

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