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Summer Graduate School

Nonlinear dispersive PDE, quantum many particle systems and the world between July 17, 2017 - July 28, 2017
Parent Program: --
Location: Istituto Nazionale di Alta Matematica, Cortona, Italy
Organizers Natasa Pavlovic (University of Texas), Gigliola Staffilani (Massachusetts Institute of Technology), Nikolaos Tzirakis (University of Illinois at Urbana-Champaign)
Description

The purpose of the summer school is to introduce graduate students to the recent developments in the area of dispersive partial differential equations (PDE), which have received a great deal of attention from mathematicians, in part due to ubiquitous applications to nonlinear optics, water wave theory and plasma physics.

Recently remarkable progress has been made in understanding existence and uniqueness of solutions to nonlinear Schrodinger (NLS) and KdV equations, and properties of those solutions. We will outline the basic tools that were developed to address these questions. Also we will present some of recent results on derivation of NLS equations from quantum many particle systems and will discuss how methods developed to study the NLS can be relevant in the context of the derivation of this nonlinear equation.

Suggested prerequisites:

Real Analysis: Modern Techniques and Their Applications by Gerald B. Folland

For eligibility and how to apply, see the Summer Graduate Workshop homepage

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Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
  • nonlinear dispersive equations

  • well-posedness

  • derivation of nonlinear Schrodinger equations from quantum systems

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC