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Organizers:
Edward
C. Waymire (chair)
Mathematics Department
Oregon State University
waymire@math.orst.edu
Jinqiao Duan
Department of Applied Mathematics
Illinois Institute of Technology
duan@iit.edu
This summer program is devoted to the role of probabilistic methods in modern applied mathematics from perspectives of both a tool for analysis and in modeling. Researchers involved in contemporary problems involving dispersion and flow, e.g. fluid flow, cash flow, genetic migration, flow of internet data packets, etc., were selected as speakers and to lead discussion groups. There is a growing recognition in the applied mathematics research community that stochastic methods are playing an increasingly prominent role in the formulation and analysis of diverse problems of contemporary interest in the sciences and engineering. In organizing this workshop an explicit effort is being made to bring together researchers with a common interest in the problems, but with diverse mathematical expertise and perspective. In particular, many are researchers who might not ordinarily interact with one another.
The NavierStokes equations, Euler equations, Burgers equation etc. arise naturally in the context of the basic physics of fluid motions. As such these equations play a fundamental role in the science and engineering of all varieties of fluid flow, from oceanic circulation to the flow of water beneath the earth's surface. The nonlinearity of the equations makes explicit solutions possible only for the simplest of flows. The development of a more complete understanding of these equations from the laminar to the turbulent regime ranks among the most important outstanding problems of modern mathematical physics.
A probabilistic representation of solutions allows one to exploit the power of stochastic calculus and probabilistic limit theory in the analysis of deterministic problems, as well as to offer new perspectives on the phenomena for modeling purposes. In addition such approaches can be effective in sorting out multiple scale structure and in the development of Monte Carlo type numerical methods. Among the relevant probability topics are multitype branching random walks, Brownian motion and stochastic calculus, Kolmogorov cascade theory, the vortex method and multiscale methods. In addition to NavierStokes equations, other deterministic linear and nonlinear partial differential equations amenable to probabilistic methods of analysis will be of interest in this workshop, e.g. variations on BlackScholes options equations, contaminant transport, reactiondiffusion, Schrodinger equation, etc.
There is a growing recognition of a role for the inclusion of stochastic terms in the modeling of complex flows. The addition of such terms has led to interesting new mathematical problems at the interface of probability, numerical analysis, and partial differential equaitons. During the last decade, significant progress has been made towards building a comprehensive theory of random dynamical systems, statistical cascades, stochastic flows, stochastic pde's, etc. Some core questions in the modeling, analysis and simulation of complex flows under uncertainty are: exploring appropriate ways to take stochastic effects into account; understanding the impact of randomness on the evolution of complex systems; and designing efficient numerical algorithms to simulate random phenomena.
There is also a need for new ways in which to incorporate the impact of probability, statistics, pde's and numerical analysis in the training of present and future PhD students in the mathematical sciences. The engagement of graduate students is an important feature of this summer program. A poster session will be included in each workshop.
The first workshop will be devoted to the role of probability as an analysis tool as described above. The second workshop will emphasize stochastic methods in connection with modeling of various dispersion and flow scenarios. Thus the combined focus of the two workshops is broadly on probabilistic methods in the modeling and analysis of dispersion and flow, but from two different perspectives.
Workshop 1: July 21July 25, 2003: Probabilistic Methods
in Analysis of PDE's.
Organizers: Edward C. Waymire,
Mina E. Ossiander, Enrique A. Thomann, Ronald B. Guenther, Larry
Chen (Mathematics, Oregon State University), Rabi N. Bhattacharya
(Mathematics, Indiana University)
Workshop 2: July 28August 1, 2003: Stochastic Models and
their Analysis
Organizers: Jinqiao Duan (Illinois
Institute of Technology), Bjorn Schmalfuss (Merseburg), Peter
E. Kloeden (Frankfurt), Salah Mohammed (Southern Illinois University),
Sri Namachchivaya (UIUC)




WEEK 1: JULY 2125, 2003 (Probabilistic Methods in Analysis of PDE's)  

MONDAY,
JULY 21 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:30 am  Coffee and Registration  Reception Room EE/CS 3176 

8:459:00  Douglas N. Arnold, Scot Adams, and Organizers  Welcome and Introduction  
9:0010:00  Rabi
N. Bhattacharya University of Arizona 
Multiscale Diffusions and a Transport Problem in Composite Media Slides: html 

10:0010:30  

10:3011:00  Coffee Break  Reception Room EE/CS 3176  
11:0012:00  Vassili
N. Kolokoltsov Nottingham Trent University 
Preprints: 

12:0012:30  

12:302:00  Lunch
Break 

2:003:00  Zhenqing
Chen University of Washington 
Discontinuous Markov Processes and PseudoDifferential Operators Slides: pdf 

3:003:30  

3:305:30 
POSTER SESSION IMA Tea/Reception 

TUESDAY,
JULY 22 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:459:00  Coffee  Reception Room EE/CS 3176  
9:0010:00  Mark
Freidlin University of Maryland 
Multiparameter Asymptotic Problems for Stochastic Differential Equations and PDE's  
10:0010:30  

10:3011:00  Coffee Break  Reception Room EE/CS 3176  
11:0012:00  Charles
Newman Courant Institute 
The
Brownian Web and Scaling Limits Reprint/Preprint: 0203184.pdf 0304119.pdf 

12:0012:30  

12:302:00  Lunch
Break 

2:003:00  William
G. Faris University of Arizona 

3:003:30  

WEDNESDAY,
JULY 23 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:459:00  Coffee  Reception Room EE/CS 3176  
9:0010:00  Marco
Cannone Université de MarnelaVallée 
Smooth and Singular solutions for the NavierStokes Equations Reprints/Preprints: 

10:0010:30  

10:3011:00  Coffee Break  Reception Room EE/CS 3176  
11:0012:00  Enrique
Thomann Oregon State University 
Partial Differential Equations and Multiplicative Processes 

12:0012:30  

12:302:00  Lunch
Break 

2:003:00  Sylvie
Meleard MODALX, Université Paris 10Nanterre 
Probabilistic Interpretation and Stochastic Particle Method for Vortex Equations pdf ps  
3:003:30  

3:304:00  Coffee Break  Reception Room EE/CS 3176  
4:005:00  Robert
Krasny University of Michigan 
Particle Simulations of Vortex Sheet RollUp in Fluid Dynamics Slides: pdf 

5:005:30  
THURSDAY,
JULY
24
All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:459:00  Coffee  Reception Room EE/CS 3176  
9:0010:00  Siva
Athreya Indian Statistical Institute 
Hölder
Norm Estimates for Elliptic Operators on Finite and
Infinite Dimensional Spaces Slides: html 

10:0010:30  

10:3011:00  Coffee Break  Reception Room EE/CS 3176  
11:0012:00  Priscilla
E. Greenwood (Cindy) Arizona State University 

12:0012:30  
12:302:00  
2:002:30  M.
Aslam Chaudhry King Fahd University of Petroleum & Minerals, Saudi Arabia 
Extended Beta Distribution  
2:303:00  Rolf
Moritz Kassman University of Connecticut 
Stochastic Methods for Regularity of Nonlocal Operators of Variable Order 

3:003:30  Edward
C. Waymire Oregon State University 
Remarks on Steady State Limits for NS in Majorizing Spaces: A Probabilistic View  
3:304:00 


4:005:30 


FRIDAY,
JULY
25 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:459:00  Coffee  Reception Room EE/CS 3176  
9:0010:00  Boris
L. Rozovskii University of Southern California 
Stochastic NavierStokes Equations for Turbulent Flows: Propagation of Chaos and Moments Problem Preprints: 

10:0010:30  

10:3011:00  Coffee Break  Reception Room EE/CS 3176  
11:0012:00  Wojbor
A. Woyczinski Case Western Reserve University 
Nonlinear Partial Differential Equations Driven by Levy Diffusions and Related Statistical Issues  
12:0012:30  

12:302:00  Lunch
Break 

2:003:00  Martin
Greiner Siemens AG, CT IC 4 
DataDriven Stochastic Processes in Fully Developed Turbulence Reprints:
greiner_EPL61_2003_756.pdf


3:003:30  

3:304:00  Coffee Break  Reception Room EE/CS 3176  
4:005:00  Cecile
Penland NOAACIRES/Climate Diagnostics Center 

5:005:30  

WEEK 2: JULY 28AUGUST 1, 2003 (Stochastic Models and their Analysis)  
MONDAY,
JULY 28 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:459:00  Coffee  Reception Room EE/CS 3176  
9:0010:00  SalahEldin
A. Mohammed Southern Illinois University, Carbondale 
The Stable Manifold Theorem for SemiLinear Stochastic Partial Differential Equations  
10:0010:30  

10:3011:00  Coffee Break  Reception Room EE/CS 3176  
11:0012:00  Kening
Lu Michigan State University 
Invariant Manifolds for Stochastic PDE's  
12:0012:30  

12:302:00  Lunch
Break 

2:003:00  Björn
Schmalfuss University of Applied Sciences Merseburg 
Stochastic Partial Differential Equations and Random Dynamical Systems Slides: html 

3:003:30  

3:304:00  Coffee Break  Reception Room EE/CS 3176  
4:005:00  Hao
Wang University of Oregon 
Papers: 

5:005:30  

TUESDAY,
JULY 29 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:459:00  Coffee  Reception Room EE/CS 3176  
9:0010:00  Rene
Carmona Princeton University 
Malliavin Calculus for Stochastic Partial Differential Equations Slides: pdf 

10:0010:30  

10:3011:00  Coffee Break  Reception Room EE/CS 3176  
11:0012:00  Victor
W. Goodman Indiana University 

12:0012:30  
12:302:00  

2:002:30  Jinqiao
Duan Illinois Institute of Technology 
Ergodicity, Fluctuations and Stabilization in Fluid Flows  
2:303:00  Keith
Nordstrom University of Colorado at Boulder 
Critical Scaling in a Physical Model of Convective Rainfall  
WEDNESDAY,
JULY 30 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:459:00  Coffee  Reception Room EE/CS 3176  
9:0010:00  Yves
Le Jan Universite Paris Sud XI 
Flows, Coalescence, Noise and Glue Papers:
Bmatrix.pdf
Bmatrix.ps 

10:0010:30  

10:3011:00  Coffee Break  Reception Room EE/CS 3176  
11:0012:00  Erhan
Cinlar Princeton University 
Stochastic Flows with Jumps  
12:0012:30  
12:302:00  
2:003:00  Michael
Scheutzow Technische Universität Berlin 
On the Dispersion of Sets Under the Action of an Isotropic Brownian Flow  
3:003:30  

THURSDAY,
JULY
31
All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:459:00  Coffee  Reception Room EE/CS 3176  
9:0010:00  Hassan
Allouba Kent State University 
From BrownianTime Processes to Linearized KuramotoSivashinsky PDE 

10:0010:30  
10:3011:00  Coffee Break  Reception Room EE/CS 3176  
11:0012:00  Ian
M. Davies University of Swansea 
Stochastic Heat and Burgers Equations and their Singularities Slides: pdf 

12:0012:30  
12:302:00  
2:003:00  Michael
Cranston University of Rochester 
Some Recent Results on the Parabolic Anderson Model  
3:003:30  

3:304:00  Coffee Break  Reception Room EE/CS 3176  
4:005:00  Dirk
Blömker University of Warwick 
Structure of Invariant Measures Near Bifurcations Preprints: cubicsub.pdf cubicsub.ps quadratic03.pdf quadratic03.ps 

5:005:30  

FRIDAY,
AUGUST
1 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:459:00  Coffee  Reception Room EE/CS 3176  
9:0010:00  Mukul
Majumdar Cornell University 
Random Dynamical Systems with Monotone Laws of Motion: Examples from Economics Paper: pdf 

10:0010:30  
10:3011:00  Coffee Break  Reception Room EE/CS 3176  
11:0012:00  Krishna
B. Athreya Cornell University and Iowa State University 
Markov Chains Generated by Iteration of iid Maps on R+  
12:0012:30  


Week 1  Monday  Tuesday  
Week 2  Monday  Tuesday 
Name  Department  Affiliation 

Scot Adams  IMA  University of Minnesota 
Hassan Allouba  Mathematical Sciences  Kent State University 
Anna Amirdjanova  Statistics  University of Michigan 
Douglas N. Arnold  IMA  University of Minnesota 
Krishna Athreya  Cornell University  
Siva Athreya  Indian Statistical Institute, New Delhi  
Paul Atzberger  Mathematics (Stochastic Processes)  New York University  Courant Institute 
Gerard Awanou  Mathematics  University of Georgia 
Michele Baldini  Physics  New York University 
Rabi Bhattacharya  Mathematics  Indiana University 
Dirk Bloemker  Mathematics Research Center  University of Warwick 
Maury Bramson  University of Minnesota  
Susanne C. Brenner  University of South Carolina  
Maria Carme Calderer  Mathematics  University of Minnesota 
Marco Cannone  Laboratoire d'Analyse et de Mathématiques Appliqué  Université de MarnelaVallée 
Rene Carmona  Princeton University  
Fernando Carreon  Mathematics  University of Texas  Austin 
Panagiotis Chatzipantelidis  Mathematics  Texas A&M University 
M. Aslam Chaudhry  Mathematical Sciences  King Fahd University of Petroleum & Minerals 
Larry Chen  Mathematics  Oregon State University 
Long Chen  Mathematics  Pennsylvania State University 
Zhenqing Chen  University of Washington  
Lan Cheng  Mathematics  University of Pittsburgh 
Erhan Cinlar  Operations Research & Financial Eng  Princeton University 
Michael Cranston  Mathematics  University of Rochester 
Ian M. Davies  Mathematics  University of Wales Swansea 
Hongjie Dong  Mathematics  University of Minnesota 
Jinqiao Duan  Illinois Institute of Technology  
Valdo Durrleman  Bendheim Center for Finance  
Maria Emelianenko  Mathematics  Pennsylvania State University 
William Faris  Mathematics  University of Arizona 
Mark Freidlin  Mathematics  University of Maryland, College Park 
Peter Friz  Courant Institute  
Victor Goodman  Mathematics  Indiana University 
Priscilla E. Greenwood  Mathematics  Arizona State University 
Martin Greiner  Max Planck Institute for the Physics of Complex Sys  
Ernesto GutierrezMiravete  Engineering and Science  Rensselaer Polytechnic Institute 
Naresh Jain  Mathematics  University of Minnesota 
Siwei Jia  Statistics  Oregon State University 
YuJuan Jien  Mathematics  Purdue University 
Yoon Mo Jung  Mathematics  University of Minnesota 
G Kallianpur  Statistics  University of North Carolina 
Rolf Moritz Kassmann  Mathematics  University of Connecticut 
Markus Keel  University of Minnesota  
Djivede Kelome  Mathematics and Statistics  University of Massachusetts 
Eun Heui Kim  California State University  Long Beach  
Kyounghee Kim  Mathematics  Indiana University 
Panki Kim  Mathematics  University of Washington 
Vassili N. Kolokoltsov  Mathematics  Nottingham Trent University 
Yuriy Kolomiyets  Mathematics  Kent State University 
Robert Krasny  Mathematics  University of Michigan 
Yves LeJan  Département de Mathématiques  University Paris Sud 
Seung Lee  Mathematics  Ohio State University 
GuangTsai Lei  Mayo Clinic  
Runchang Lin  Mathematics  Wayne State University 
Yuping Liu  Mathematics  Purdue University 
Kening Lu  Mathematics  Michigan State University 
Mukul Majumdar  Economics  Cornell University 
Rogemar Mamon  Statistics and Actuarial Science  University of Waterloo 
Sylvie Meleard  UFR Segmi  Université Paris X 
Oana Mocioalca  Mathematics  Purdue University 
Salah Mohammed  Mathematics  Southern Illinois University 
Charles M. Newman  New York University  
Mahdi Nezafat  Electrical and Computer Engineering  University of Minnesota 
Keith Nordstrom  C4CIRES  University of Colorado at Boulder 
Chris Orum  Oregon State University  
Mina Ossiander  Mathematics  Oregon State University 
Chetan Pahlajani  Mathematics  University of Illinois  UrbanaChampaign 
Veena Paliwal  Mathematics  Southern Illinois University 
Jun Hyun Park  University of Illinois  UrbanaChampaign  
Cecile Penland  NOAACIRES  University of Colorado 
Lea Popovic  Statistics  University of California  Berkeley 
Jorge M. Ramirez  Mathematics  Oregon State University 
Vivek Ranjan  Mathematics  Indiana University 
Marco Romito  Dipartimento di Matematica  Universita' di Firenze 
Boris Rozovskii  University of California  Los Angeles  
Fadil Santosa  IMA  University of Minnesota 
David Saunders  Mathematics  University of Pittsburgh 
Michael Scheutzow  Fakultät II, Institut für Mathematik  Technische Universität Berlin 
Bjoern Schmalfuss  Science  University of Merseburg 
Rongfeng Sun  Courant Institute  New York University 
LiYeng Sung  University of South Carolina  
Michael Tehranchi  Mathematics  University of Texas  Austin 
Enrique Thomann  Mathematics  Oregon State University 
Ilya Timofeyev  Mathematics  University of Houston 
Daniell Toth  Mathematics  Juniata College 
Hao Wang  University of Oregon  
Jing Wang  Institute for Mathematics and its Application  University of Minnesota 
Li Wang  Probability and Statistics  Michigan State University 
Lixin Wang  Operations Research and Financial Engineering  Princeton University 
Ed Waymire  Mathematics  Oregon State University 
Hans Weinberger  Mathematics  University of Minnesota 
Andrew Westmeyer  Mathematics  University of Wyoming 
Wojbor A. Woyczynski  Statistics  Case Western Reserve University 
Jian Yang  Mathematics  University of Illinois  UrbanaChampaign 
Zhihui Yang  Mathematics  University of Maryland, College Park 
Aaron Nung kwan Yip  Mathematics  Purdue University 
Toshio Yoshikawa  University of Minnesota  Institute for Mathematics and its Applications 
Jianfeng Zhang  Mathematics  University of Minnesota 
Tao Zhang  Mathematics  Purdue University 
Yongcheng Zhou  Mathematics  Michigan State University 