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Mathematics in the Geosciences, September 2001  June 2002
Michael Ghil
Department of Atmospheric Sciences and
IGPP
University of CaliforniaLos Angeles
ghil@atmos.ucla.edu
http://webster.atmos.ucla.edu/~ghil/
William I. Newman
Departments of Earth and Space Sciences,
Physics and Astronomy, and Mathematics
University of CaliforniaLos Angeles
win@ucla.edu
Ferenc Varadi
Institute of Geophysics and Planetary Physics
University of CaliforniaLos Angeles
varadi@ucla.edu
Dynamical systems theory provides fundamental ideas and tools for the modeling, analysis, and prediction of the climate system. The successive bifurcation approach, in particular, has provided a systematic way to help understand increasingly complex climate behavior, in space and time. The ideas and tools of nonlinear dynamics are most easily grasped and applied in the context of lowdimensional models, but have been applied more recently to large and detailed models, such as the general circulation models used in atmospheric, oceanic, and climatesystem dynamics. The workshop will be dedicated to the systematic application of this approach to the full hierarchy of climate models. For didactic and methodological purposes, we shall emphasize relatively simple models with a clear mathematical description, such as paleoclimate models and their astronomical forcing.
Conservative Hamiltonian systems will be illustrated by models of planetary motion, while forceddissipative systems will be illustrated primarily by models of the Quaternary ice ages and other paleoclimate models. The study of the Solar System's stability has motivated many advances in dynamical systems theory. The workshop will emphasize the applications of these advances to the largely unsolved problems of the actual system's evolution on various time scales. Paleoclimate models will be formulated, based on physicochemical principles and the available empirical evidence, as closed mathematical systems. These systems will be analyzed and the results compared with the most recent information on past climate change.
Keywords: bifurcations, celestial mechanics, climate dynamics, transitions
Monday  Tuesday 
MONDAY,
OCTOBER 29
All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 


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

9:15 am  Douglas N. Arnold, Robert Gulliver, and Ferenc Varadi  Welcome and Introduction  
9:30 am  Joseph
A. Burns Cornell University 

10:30 am  Coffee Break  Reception Room EE/CS 3176  
11:00 am  William
I. Newman UCLA 
Numerical Integration, Lyapunov Exponents, and the Outer Solar System Slides: pdf (5MB) 

12:00 pm 
Lunch
Break


2:00 pm  Richard
Rand Cornell University 
A Nonlinear Quasiperiodic Mathieu Equation pdf (568KB) 

3:00 pm  Coffee Break  Reception Room EE/CS 3176  
3:30 pm  Wang
Sang Koon California Institute of Technology 
Invariant Manifolds, the ThreeBody Problem and a Petit Grand Tour of Jovian Moons 

4:40 pm  IMA
Tea/Reception
A variety of appetizers and beverages will be served. 
IMA East, 400 Lind Hall  
TUESDAY,
OCTOBER 30 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:30 am  Coffee  Reception Room EE/CS 3176  
9:30 am  James
F. Kasting Pennsylvania State University 

10:30 am  Coffee Break  Reception Room EE/CS 3176  
11:00 am  Michael
Ghil University of CaliforniaLos Angeles 

12:00 pm 
Lunch
Break


2:00 pm  Glen
R. Stewart University of Colorado 

3:00 pm  Coffee Break  Reception Room EE/CS 3176  
3:30 pm  Ferenc
Varadi University of CaliforniaLos Angeles 

4:45 pm  Illustrations:
Ferenc Varadi University of CaliforniaLos Angeles 
Simulation and time series analysis (software demonstration)  
WEDNESDAY,
OCTOBER
31
All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:30 am  Coffee  Reception Room EE/CS 3176  
9:30 am  Roger
Temam Indiana University 
Some recent developments on the Primitive Equations  
10:30 am  Coffee Break  Reception Room EE/CS 3176  
11:00 am  Andrew
Majda New York University 
Mathematical Strategies for Stochastic Climate Modelling  
12:00 pm 
Lunch
Break


2:00 pm  Special
Seminar: James A. Sethian University of California, Berkeley 
Ordered Upwind Methods: Computing Viscosity Solutions to Optimal Control and NonViscosity Solutions to Wave Propagation  
3:30 pm  Richard
Kleeman Courant Institute of Mathematical Sciences 
Predictability in dynamical systems relevant to climate and weather  
4:30 pm  Discussion (chaired by Michael Ghil)  Ask not what climate can do for you, but what you can do for understanding & predicting climate  
THURSDAY,
NOVEMBER 1
All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:30 am  Coffee  Reception Room EE/CS 3176  
9:30 am  Edriss
S. Titi University of California, Irvine 

10:30 am  Coffee Break  Reception Room EE/CS 3176  
11:00 am  Jinqiao
Duan Illinois Institute of Technology 

12:00 pm 
Lunch
Break


2:00 pm  Steve
Shkoller University of California, Davis 
A Variational LevelSet Approach for TwoPhase Incompressible Fluids  
3:00 pm  Coffee Break  Reception Room EE/CS 3176  
3:30 pm  Shouhong
Wang Indiana University 
Topology of 2D Incompressible Flows  
6:00 pm  Workshop Dinner  Gardens
of Salonica 19 Fifth Street N.E., Minneapolis 

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

8:30am  Coffee  Reception Room EE/CS 3176  
9:30 am  James
E. Howard University of Colorado, Boulder 

10:30 am  Coffee Break  Reception Room EE/CS 3176  
11:00 am  Daniel
Schertzer University of Paris VI 
Chaos, ergodic theory and multifractal singularities of stochastic differential equations Slides: html pdf powerpoint 

12:00 pm 
Conclusion
and Lunch

Monday  Tuesday 
Name

Department  Affiliation 

Doug Arnold  Institute for Mathematics & its Applications  
Joseph Burns  Theoretical & Applied Mechanics  Cornell University 
Colin Cotter  Mathematics  Imperial College, University of London 
Dacian Daescu  Mathematics  University of Iowa 
Doug Dokken  Mathematics  University of St. Thomas 
Jinqiao Duan  Applied Mathematics  Illinois Institute of Technology 
Gregory S. Duane  Institute for Mathematics & its Applications  
Fabien DuBuffet  Geology and Geophysics  University of Minnesota 
Michael Efroimsky  Physics  Harvard University 
Jason Frank  CWI  
Hongjun Gao  Mathematics  Nanjing Normal University 
Michael Ghil  Atmospheric Sciences  University of California, Los Angeles 
Robert Gulliver  Institute for Mathematics & its Applications  
James E. Howard  Laboratory for Atmospheric and Space Physics  University of Colorado 
James Kasting  Geosciences  Pennsylvania State University 
Daniel Kern  
Seongjai Kim  Mathematics  University of Kentucky 
Richard Kleeman  Center for Atmospheric Ocean Science  Courant Institute of Mathematical Sciences 
Wang Sang Koon  California Institute of Technology  
Hyeona Lim  Mathematics  Michigan State University 
Andrew Majda  Courant Institute of Mathematical Sciences  New York University 
William Newman  Earth & Space Sciences  University of California, Los Angeles 
Richard Rand  Theoretical & Applied Mechanics  Cornell University 
Fadil Santosa  Institute for Mathematics & its Applications  
Arnd Scheel  Mathematics  University of Minnesota 
Daniel Schertzer  Centre de Calcul Recherche  Reseau Jussieu 
George Sell  Mathematics  University of Minnesota 
Robert Shcherbakov  Earth & Atmospheric Sciences  Cornell University 
Jianhong Shen  Mathematics  University of Minnesota 
Steve Shkoller  Mathematics  University of California, Davis 
Glen R. Stewart  Lab Atmos/Space Physics  University of Colorado, Boulder 
Roger Temam  Institute for Scientific Computing & Appl. Math.  Indiana University 
Edriss Titi  Mathematics  University of California, Irvine 
Donald Turcotte  Geological Sciences  Cornell University 
Ferenc Varadi  Insitute of Geophysics and Planetary Physics  University of California, Los Angeles 
Shouhong Wang  Mathematics  Indiana University 
Xiaoming Wang  Courant Institute of Mathematical Science  New York Universtiy 
Toshio Yoshikawa  Institute for Mathematics & its Applications  
David A. Yuen  Geology & Geophysics  University of Minnesota 