Gene Golub SIAM Summer School 2016
July 25 - August 5, 2016




 
                                
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Main courses will be taught by

Nawaf Bou-Rabee
Rutgers University - Camden

Nestor Guillen
University of Massachusetts-Amherst

Jonathan Mattingly
Duke University

Andrea Nahmod
University of Massachusetts-Amherst

David Nualart
University of Kansas

Hendrik Weber
University of Warwick


Other speakers for tutorials
and lectures are


Liliana Borcea
University of Michigan

Georgi Mevedev
Drexel University

Kui Ren
University of Texas
at Austin

Gideon Simpson
Drexel University

Xiaoming Song
Drexel University

Vlad Vicol

Princeton University

J. Douglas Wright
Drexel University
          

  
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All the lectures and tutorial sections will take place in Randell Hall, Room 326.
 
Six short courses will be taught as traditional classroom-style lectures. There will also be a number of tutorial sessions in which students, together with an instructor, work out detailed example problems.

     (1) Introduction to stochastic differential equations I
               -- Brownian motion, martingales and stopping times, Markovian properties of Brownian motion
          -- Ito and other versions of stochastic calculus
          -- Stochastic differential equations (SDEs), O-U processs, Malliavin calculus


     (2) Introduction to stochastic computation
          -- Convergence and structural properties of integrators: Euler-Maruyama and Milstein methods
          -- Metropolis algorithms for unbiased sampling and their application to SDEs


     (3) Introduction to stochastic differential equations II
          -- Randomly forced partial differential equations
          -- Probability measures in infinite dimensions, rough path theory and regularity structures


     (4) Stochastically forced Fluid equations
          -- the effect of random forcing on partial differential equations from fluid dynamics
          -- Navier-Stokes, Euler and other fluid models, ergodicity of solutions


     (5) Invariant measures for dispersive equations
          -- invariant measures for dynamical systems, Gibbs and Wiener measures
          -- Schrodinger equations

 
     (6) Introduction to stochastic homogenization
          -- Methods for computing effective deterministic equations for PDEs with random coefficients
          -- Multiscale expansion and cell problems, elliptic boundary value problems

All lecture notes or related files can be found below:

Nawaf Bow-Rabee
David Nualart (Lecture 1, Lecture 2, Lecture 3)
Gideon Simpson
Xiaoming Song
(Tutorial 1, Tutorial 2, Talk and the related paper)