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Summer Graduate School

Dispersive Partial Differential Equations June 16, 2014 - June 27, 2014
Parent Program: --
Location: SLMath: Eisenbud Auditorium
Organizers Natasa Pavlovic (University of Texas, Austin), Nikolaos Tzirakis (University of Illinois at Urbana-Champaign)
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Description

The purpose of the workshop is to introduce graduate students to the recent developments in the area of dispersive partial differential equations (PDE).

Dispersive equations have received a great deal of attention from mathematicians because of their applications to nonlinear optics, water wave theory and plasma physics. We will outline the basic tools of the theory that were developed with the help of multi-linear Harmonic Analysis techniques. The exposition will be as self-contained as possible.

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

Literature List for the Group Work

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Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Schedule, Notes/Handouts & Videos
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Jun 16, 2014
Monday
09:30 AM - 10:00 AM
  Intro to MSRI Intro to the summer school
10:00 AM - 10:45 AM
  What is a dispersive PDE. The fundamental solution to the linear Schrodinger equation. Dispersive estimates
Natasa Pavlovic (University of Texas, Austin)
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:00 PM
  Strichartz estimates
Natasa Pavlovic (University of Texas, Austin)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Intro to Group Work
Jun 17, 2014
Tuesday
10:00 AM - 10:45 AM
  Intro to NLS: what is a solution; symmetries of the NLS
Natasa Pavlovic (University of Texas, Austin)
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:00 PM
  Local well-posedness for smooth solutions
Natasa Pavlovic (University of Texas, Austin)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Group Work
Jun 18, 2014
Wednesday
10:00 AM - 11:30 AM
  Local well-posedness for the energy subcritical problem in the energy space
Natasa Pavlovic (University of Texas, Austin)
11:30 AM - 02:00 PM
  BBQ Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Group Work
Jun 19, 2014
Thursday
10:00 AM - 10:45 AM
  The defocusing NLS. Introduction to energy scattering. Virial Identities
Nikolaos Tzirakis (University of Illinois at Urbana-Champaign)
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:00 PM
  Interaction Morawetz estimates
Nikolaos Tzirakis (University of Illinois at Urbana-Champaign)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Group Work
Jun 20, 2014
Friday
10:00 AM - 10:45 AM
  The focusing NLS. Blow-up of solutions. A criteria for the existence of global-in-time solutions
Natasa Pavlovic (University of Texas, Austin)
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:00 PM
  Scattering in the energy space for the energy sub-critical problem. Scattering in other spaces.
Nikolaos Tzirakis (University of Illinois at Urbana-Champaign)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Group Work
Jun 23, 2014
Monday
10:00 AM - 10:45 AM
  The initial value problem for the KdV equation. The energy method
Nikolaos Tzirakis (University of Illinois at Urbana-Champaign)
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:00 PM
  The Keing-Ponce-Vega method on R.
Nikolaos Tzirakis (University of Illinois at Urbana-Champaign)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:00 PM
  Group Work
Jun 24, 2014
Tuesday
10:00 AM - 10:45 AM
  The restricted norm method of Bourgain.
Nikolaos Tzirakis (University of Illinois at Urbana-Champaign)
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:00 PM
  The restricted norm method of Bourgain continued. Local and global well posedness in L2(R).
Nikolaos Tzirakis (University of Illinois at Urbana-Champaign)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Group Work
Jun 25, 2014
Wednesday
10:00 AM - 10:45 AM
  The periodic KdV. Periodic Strichartz estimates.
Nikolaos Tzirakis (University of Illinois at Urbana-Champaign)
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:00 PM
  Local Well-Posedness for rough data. The Xs;b function space.
Nikolaos Tzirakis (University of Illinois at Urbana-Champaign)
12:00 PM - 02:00 PM
  Lunch break
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Group Work
Jun 26, 2014
Thursday
10:00 AM - 10:45 AM
  Normal form methods and nonlinear smoothing on T.
Nikolaos Tzirakis (University of Illinois at Urbana-Champaign)
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:00 PM
  Dispersive Quantization and the Talbot e ect.
Nikolaos Tzirakis (University of Illinois at Urbana-Champaign)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Group Work
Jun 27, 2014
Friday
10:00 AM - 10:45 AM
  Derivation of the NLS from quantum many body systems
Natasa Pavlovic (University of Texas, Austin)
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:00 PM
  On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
Natasa Pavlovic (University of Texas, Austin)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:30 PM
  Poster Session
03:30 PM - 04:00 PM
  Tea Break