Attractors for equations of mathematical physics

Speaker: 

Prof, Mark Vishik

Time: 

Thursday, February 5, 2004 - 4:00pm

Location: 

MSTB 254

The lecture will cover the following topics:
1. Global attractor for an autonomous evolution equation. Examples. between the attractor and the family of complete solutions.
2. Fractal dimension of a global attractor. Examples.
3. Nonautonomous evolution equations and corresponding processes. Uniform global attractor of a process.
4. Global attractor of the nonautonomous 2D Navier Stokes system. Translation-compact forcing term. Relation between the uniform attractor and the family of complete solutions. Nonautonomous 2D Navier-Stokes system with a simple attractor.
5. Kolmogorov epsilon-entropy of the global attractor of a nonautonomous equation. Estimates of the epsilon-entropy. Examples.
6. Some open problems.

Geometric Motion in Plasmas

Speaker: 

Prof. Marshall Slemrod

Institution: 

University of Wisconsin

Time: 

Thursday, January 29, 2004 - 4:00pm

Location: 

MSTB 254

This talk outlines recent work by Feldman, Ha, and Slemrod on the dynamics of the sheath boundary layer which occurs in a plasma consisting of ions and electrons. The equations for the motion are derived from the classical Euler- Poisson equations. Of particular interest is that the boundary layer interface moves via motion by mean curvature where the acceleration of the front (not the velocity) is proportional to the mean curvature of the front.

Twisted K-theory and moduli spaces

Speaker: 

Prof. C. Teleman

Institution: 

Cambridge University

Time: 

Thursday, December 11, 2003 - 11:00am

Location: 

MSTB 254

The notion of topological field theory has stymied topologists partly because it assigns to spaces quantities that are multiplicative under disjoint union; traditional homological or homotopical constructions are additive. In this talk I will survey how the use of an old "multiplicative" object in topology ("the spectrum of
units" in the class of vector spaces) leads to a successful formulation of a simple (but non-trivial) 2-dimensional field theory (the "Verlinde ring" and its deformations) and to new topological results about the moduli space of vector bundles on a Riemann surface. This is based on joint work with Freed-Hopkins and with Woodward.

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