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Summer Graduate School

From Symplectic Geometry to Chaos July 23, 2018 - August 03, 2018
Parent Program:
Location: MSRI: Simons Auditorium, Atrium
Organizers Marcel Guardia (Universitat Politecnica de Catalunya), Vadim Kaloshin (University of Maryland), Leonid Polterovich (Tel Aviv University)
Lecturer(s)

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Description

The purpose of the summer school is to introduce graduate students to state-of-the-art methods and results in Hamiltonian systems and symplectic geometry. We focus on recent developments on the study of chaotic motion in Hamiltonian systems and its applications to models in Celestial Mechanics.

Prerequisites:

Students will be expected to have had a basic course on ordinary differential equations at the level of Arnold's "Ordinary Differential Equations", as well as graduate-level courses in manifolds and differential forms. A typical first or second year graduate course at the level of Guillemin and Pollack "Differential Topology", for example, would be sufficient. Exposure to some basic dynamical systems and Hamiltonian dynamics (especially, acquaintance with Arnold's "Mathematical Methods of Classical Mechanics") would be desirable, but not assumed. The basic results from those areas needed to understand subsequent material in the summer school will be developed in the course.

Bibliography (PDF)

Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
  • Hamiltonian systems

  • Symplectic Geometry

  • Celestial Mechanics

  • Hamiltonian diffeomorphisms

  • Arnold diffusion

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Schedule, Notes/Handouts & Videos
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Jul 23, 2018
Monday
09:00 AM - 09:15 AM
  Introduction to MSRI
09:15 AM - 10:30 AM
  Course One: Lecture 1
Marcel Guardia (Universitat Politecnica de Catalunya)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Course Two: Lecture 1
Leonid Polterovich (Tel Aviv University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:15 PM
  Discussion Session 1
03:15 PM - 03:45 PM
  Tea
03:45 PM - 05:00 PM
  Discussion Session 2
Vukasin Stojisavljevic (Tel Aviv University)
Jul 24, 2018
Tuesday
09:00 AM - 10:30 AM
  Course One: Lecture 2
Marcel Guardia (Universitat Politecnica de Catalunya)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Course Two: Lecture 2
Leonid Polterovich (Tel Aviv University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:15 PM
  Discussion Session 1
03:15 PM - 03:45 PM
  Tea
03:45 PM - 05:00 PM
  Discussion Session 2
Vukasin Stojisavljevic (Tel Aviv University)
Jul 25, 2018
Wednesday
09:00 AM - 10:00 AM
  Course One: Lecture 3
Ke Zhang (University of Toronto)
10:00 AM - 10:30 AM
  Break
10:30 AM - 11:30 AM
  Course Two: Lecture 3
Leonid Polterovich (Tel Aviv University)
11:30 AM - 02:00 PM
  BBQ Lunch
Jul 26, 2018
Thursday
09:00 AM - 10:30 AM
  Course One: Lecture 4
Marcel Guardia (Universitat Politecnica de Catalunya)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Course Two: Lecture 4
Leonid Polterovich (Tel Aviv University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:15 PM
  Discussion Session 1
03:15 PM - 03:45 PM
  Tea
03:45 PM - 05:00 PM
  Discussion Session 2
Vukasin Stojisavljevic (Tel Aviv University)
Jul 27, 2018
Friday
09:00 AM - 10:30 AM
  Course One: Lecture 5
Vadim Kaloshin (University of Maryland)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Course Two: Lecture 5
Leonid Polterovich (Tel Aviv University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:15 PM
  Discussion Session 1
03:15 PM - 03:45 PM
  Tea
03:45 PM - 05:00 PM
  Discussion Session 2
Vukasin Stojisavljevic (Tel Aviv University)
Jul 30, 2018
Monday
09:00 AM - 10:30 AM
  Course One: Lecture 6
Vadim Kaloshin (University of Maryland)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Course One: Lecture 7
Vadim Kaloshin (University of Maryland)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:15 PM
  Discussion Session 1
03:15 PM - 03:45 PM
  Tea
03:45 PM - 05:00 PM
  Discussion Session 2
Jul 31, 2018
Tuesday
09:00 AM - 10:30 AM
  Course Two: Lecture 6
Michael Entov (Technion---Israel Institute of Technology)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Course Two: Lecture 7
Michael Entov (Technion---Israel Institute of Technology)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:15 PM
  Discussion Session 1
Yaniv Ganor (Tel Aviv University)
03:15 PM - 03:45 PM
  Tea
03:45 PM - 05:00 PM
  Discussion Session 2
Yaniv Ganor (Tel Aviv University)
Aug 01, 2018
Wednesday
09:00 AM - 10:30 AM
  Course One: Lecture 8
Ke Zhang (University of Toronto)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Course Two: Lecture 8
Michael Entov (Technion---Israel Institute of Technology)
12:00 PM - 02:00 PM
  Lunch
Aug 02, 2018
Thursday
09:00 AM - 10:30 AM
  Course One: Lecture 9
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Course Two: Lecture 9
Michael Entov (Technion---Israel Institute of Technology)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:15 PM
  Discussion Session 1
03:15 PM - 03:45 PM
  Tea
03:45 PM - 05:00 PM
  Discussion Session 2
Yaniv Ganor (Tel Aviv University)
Aug 03, 2018
Friday
09:00 AM - 10:30 AM
  Course One: Lecture 10
Ke Zhang (University of Toronto)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Course Two: Lecture 10
Michael Entov (Technion---Israel Institute of Technology)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:15 PM
  Discussion Session 1
03:15 PM - 03:45 PM
  Tea
03:45 PM - 05:00 PM
  Discussion Session 2
Yaniv Ganor (Tel Aviv University)