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Complete List of IMA PI Graduate Students Programs
CoFunded by the Rocky Mountain Mathematics Consortium (RMMC)
University of Wyoming, Laramie, Wyoming
During June 13  July 1, 2005 the University of Wyoming, Laramie will be the host of the Institute for Mathematics and its Applications (IMA) summer graduate program in mathematics. The course will concentrate on Stochastic Partial Differential Equations and Environmental and Geophysical Modeling.
This program is open to graduate students from IMA Participating Institutions. Students are nominated by their department head. Participating institution department heads nominate graduate students from their institution by an email to visit@ima.umn.edu with the students' names and email addresses.
Those students may then register by filling out the registration form. Places are guaranteed for two graduate students from each participating institution, with additional students accommodated as space allows.
Please contact Jeanette Marie Reisenburg (Jeanette@uwyo.edu, 3077664222) or Terry Shearin (ashearin@uwyo.edu, 3077664222) with questions on your travel arrangement.
Stochastic Navier
Stokes Equations on Riemannian Manifolds and Stochastic Partial Differential Equations with Nonlinear Constraints By Zdzislaw Brzezniak Department of Mathematics University of Hull England Z.Brzezniak@hull.ac.uk 

Length Three Weeks 
June 13  July 1 

Course Description In this lecture series the speaker will discuss stochastic partial differential equations where the solution is subjected to certain additional constraints. Examples will include fluid dynamics on spherical surfaces modeling ocean and atmospheric dynamics. Suitable stochastic integration theory will also be developed along with study of dynamical systems aspects such as random attractors and invariant measures. Topics:


White Noise Theory
and Malliavin Calculus for Lévy Processes and Applications to SPDEs
and Finance By Bernt Øksendal Department of Mathematics University of Oslo Norway oksendal@math.uio.no 

Length Two Weeks  June 20 – July 1 
Course Description White noise theory was originally developed by T.Hida for the case of Brownian motion. It may be regarded as a stochastic distribution theory which, combined with the Wick product, extends the classical Itô calculus, both to the anticipating case (Skorohod integrals) and to the multiparameter case (random fields). Like the classical distribution theory of Laurent Schwartz, which is useful in the study of deterministic PDEs, the white noise theory is useful in the study of SPDEs. Recently there has been an increased interest in stochastic models driven by Lévy processes (i.e., processes with stationary independent increments), One reason for this is that in applications such models can be made more realistic than the classical Brownian motion based models. This makes it natural to request a white noise theory for such processes as well. Topics:


Stochastic Hyperbolic
Equations and Random Wave Propagation By PaoLiu Chow Department of Mathematics Wayne State University Detroit plchow@math.wayne.edu 

Length Two Weeks  June 13  June 24 
Course Description The course consists of ten hourlectures on the analysis of stochastic hyperbolic equations and their applications to wave propagation through random or turbulent media. The topics to be covered may include the following subjects:


Statistical Theory
of Turbulence and Modeling of Vortex Dynamics By Franco Flandoli University of Dini Italy flandoli@dma.unipi.it 

Length Two Weeks  June 20  July 1 
Course Description An important problem of fluid dynamics, almost open, is concerned with the foundations of the Statistical Theory of Turbulence, not to say the knowledge of the exact, not only approximate, laws of it. The role of vortex dynamics in turbulence is well established in fluid mechanics. This course will introduce modern statistical/stochastic analysis of vortex dynamics and vortex filaments. Topics:


Stochastic Partial
Differential Equations: Theory & Applications By Jerzy Zabczyk Polish Academy of Sciences Poland zabczyk@impan.gov.pl 

Length Two Weeks  June 13  June 24 
Course Description This course will deal with the foundations of stochastic partial differential equations. Linear and nonlinear partial differential equations subjected to Gaussian and Poisson type noise will be studied. Applications and motivating examples will come from control and filtering theory. Topics:
