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Summer Graduate School

Stochastic Partial Differential Equations July 07, 2014 - July 18, 2014
Location: MSRI: Simons Auditorium
Organizers Yuri Bakhtin (New York University, Courant Institute), LEAD Ivan Corwin (Columbia University), James Nolen (Duke University)
Lecturer(s)

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Speaker(s)

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Description

Stochastic Partial Differential Equations (SPDEs) serve as fundamental models of physical systems subject to random inputs, interactions or environments. It is a particular challenge to develop tools to construct solutions, prove robustness of approximation schemes, and study properties like ergodicity and fluctuation statistics for a wide variety of SPDEs. 

The purpose of this two week workshop is to educate graduate students on the state-of-the-art methods and results in SPDEs. The three courses which will be run simultaneously will highlight different (though related) aspects of this area including (1) Fluctuation theory of PDEs with random coefficients (2) Ergodic theory of SPDEs and (3) Exact solvability of SPDEs.

Reading List:

1. http://arxiv.org/abs/1106.1596
2. http://arxiv.org/abs/1212.3351
3. http://link.springer.com/chapter/10.1007%2FBFb0074920
4. http://www.math.utah.edu/~davar/ps-pdf-files/SPDE.pdf
5. http://www.math.toronto.edu/quastel/survey.pdf
6. http://www.cims.nyu.edu/~bakhtin/notes.pdf

Bibliography (pdf)

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


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Schedule
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Jul 07, 2014
Monday
09:15 AM - 09:30 AM
  Welcome
09:30 AM - 10:30 AM
  Corwin - Lecture 1
Ivan Corwin (Columbia University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Bakhtin - Lecture 1
Yuri Bakhtin (New York University, Courant Institute)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:30 PM
  Nolan - Lecture 1
James Nolen (Duke University)
02:30 PM - 03:30 PM
  TA Tutorial
03:30 PM - 04:00 PM
  Tea break
04:00 PM - 05:00 PM
  Problem Session
Jul 08, 2014
Tuesday
09:30 AM - 10:30 AM
  Bakhtin - Lecture 2
Yuri Bakhtin (New York University, Courant Institute)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Nolen - Lecture 2
James Nolen (Duke University)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:30 PM
  Corwin - Lecture 2
Ivan Corwin (Columbia University)
02:30 PM - 03:30 PM
  TA tutorial
03:30 PM - 04:00 PM
  Tea Break
04:00 PM - 05:00 PM
  Problem Session
Jul 09, 2014
Wednesday
09:30 AM - 10:30 AM
  Nolen - Lecture 3
James Nolen (Duke University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Corwin - Lecture 3
Ivan Corwin (Columbia University)
12:00 PM - 02:30 PM
  BBQ Lunch
02:30 PM - 03:30 PM
  TA tutorial
03:30 PM - 04:00 PM
  Tea Break
04:00 PM - 05:00 PM
  Problem Session
Jul 10, 2014
Thursday
09:30 AM - 10:30 AM
  Corwin - Lecture 4
Ivan Corwin (Columbia University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Bakhtin - Lecture 3
Yuri Bakhtin (New York University, Courant Institute)
12:00 PM - 01:30 PM
  Lunch
Jul 11, 2014
Friday
09:30 AM - 10:30 AM
  Corwin - Lecture 5
Ivan Corwin (Columbia University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Nolen - Lecture 4
James Nolen (Duke University)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:30 PM
  Bakhtin - Lecture 4
Yuri Bakhtin (New York University, Courant Institute)
02:30 PM - 03:30 PM
  TA tutorial
03:30 PM - 04:00 PM
  Tea Break
04:00 PM - 05:00 PM
  Problem Session
Jul 14, 2014
Monday
09:30 AM - 10:30 AM
  Nolen - Lecture 5
James Nolen (Duke University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Bakhtin - Lecture 5
Yuri Bakhtin (New York University, Courant Institute)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:30 PM
  Corwin - Lecture 6
Ivan Corwin (Columbia University)
02:30 PM - 03:30 PM
  TA tutorial
03:30 PM - 04:00 PM
  Tea Break
04:00 PM - 05:00 PM
  Problem Session
Jul 15, 2014
Tuesday
09:30 AM - 10:30 AM
  Corwin - Lecture 7
Ivan Corwin (Columbia University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Bakhtin - Lecture 6
Yuri Bakhtin (New York University, Courant Institute)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:30 PM
  Nolen - Lecture 6
James Nolen (Duke University)
02:30 PM - 03:30 PM
  TA tutorial
03:30 PM - 04:00 PM
  Tea Break
04:00 PM - 05:00 PM
  Problem Session
Jul 16, 2014
Wednesday
09:30 AM - 10:30 AM
  Bakhtin - Lecture 7
Yuri Bakhtin (New York University, Courant Institute)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Nolen - Lecture 7
James Nolen (Duke University)
12:00 PM - 01:30 PM
  Lunch
Jul 17, 2014
Thursday
09:30 AM - 10:30 AM
  Nolen - Lecture 8
James Nolen (Duke University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Corwin - Lecture 8
Ivan Corwin (Columbia University)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:30 PM
  Bakhtin - Lecture 8
Yuri Bakhtin (New York University, Courant Institute)
02:30 PM - 03:30 PM
  TA tutorial
03:30 PM - 04:00 PM
  Tea Break
04:00 PM - 05:00 PM
  Problem Session
Jul 18, 2014
Friday
09:30 AM - 10:30 AM
  Corwin - Lecture 9
Ivan Corwin (Columbia University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Bakhtin - Lecture 9
Yuri Bakhtin (New York University, Courant Institute)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:30 PM
  Nolen - Lecture 9
James Nolen (Duke University)
02:30 PM - 03:30 PM
  TA tutorial
03:30 PM - 04:00 PM
  Tea Break
04:00 PM - 05:00 PM
  Problem Session