Summer Graduate School
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| Location: | Istituto Nazionale di Alta Matematica, Cortona, Italy |
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- Erin Compaan (University of Illinois at Urbana-Champaign)
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
Hosted in cooperation with:
nonlinear dispersive equations
well-posedness
derivation of nonlinear Schrodinger equations from quantum systems