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Schedule, Notes/Handouts & Videos

Dispersive Partial Differential Equations June 16, 2014 - June 27, 2014

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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
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