Colloquia 2012-2013: Difference between revisions

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== Abstracts ==
== Abstracts ==
'''Peter Markowich''' ''On Wigner and Bohmian Measures''
We present the most important approaches to the semiclassical analysis of the Schrödinger equation, based on Wigner measures and WKB techniques.
These approaches are then compared to the Bohmian approach to semiclassical analysis, based on a highly singular system pf phase space ODEs, or equivalently on a highly nonlinear and singular self-consistent Vlasov equation.
'''Saverio Spagnolie''' ''Locomotion at low and intermediate Reynolds numbers''
Many microorganisms propel themselves through fluids by passing either helical waves (typically prokaryotes) or planar waves (typically eukaryotes) along a filamentous flagellum. Both from a biological and an engineering perspective, it is of great interest to understand the role of the waveform shape in determining an organism's locomotive kinematics, as well as its hydrodynamic efficiency. We will begin by discussing polymorphism in bacterial flagella, and will compare experimentally measured biological data on swimming bacteria to optimization results from accurate numerical simulations. For eukaryotic flagella, it will be shown how the optimal sawtoothed solution due to Lighthill is regularized when energetic costs of internal bending and axonemal sliding are included in a classical efficiency measure. Finally, the locomotive dynamics of bodies at intermediate Reynolds numbers will be discussed, where a number of surprising and counter-intuitive behaviors can be seen even in very simple systems.
'''Brian Street''' ''A quantitative Frobenius Theorem, with applications to analysis''
This talk concerns the classical Frobenius theorem from differential
geometry, about involutive distributions.  For many problems in harmonic
analysis, one needs a quantitative version of the Frobenius theorem.  In
this talk, we state such a quantitative version, and discuss various
applications.  Topics we will touch on include singular integrals,
regularity of some linear PDEs, sub-Riemannian geometry, and singular
Radon transforms.
'''Benson Farb''' ''Isometries, rigidity and universal covers''
Abstract: Which contractible Riemannian manifolds (e.g. R^n with any metric) cover
both compact and noncompact finite volume manifolds? Which Riemannian
products XxY cover compact nonproducts? Do complex manifolds
M with c_1(M) < 0 holomorphically split as a product of a locally symmetric
manifold and a “rigid” manifold? What are the isometries of Teichmuller
space? These seemingly unrelated questions turn out to be instances of a single
underlying phenomenon, allowing for complete answers to each question.
The goal of this talk is to explain, to a general audience, some of the ideas behind this.
This is joint work with Shmuel Weinberger.
'''Jun Yin''' ''Random Matrix Theory: A short survey and recent results on universality''
We give a short review of the main historical developments of random
matrix theory. We emphasize both the theoretical aspects, and the
application of the theory to a number of fields, including the recent
works on the universality of random matrices.

Revision as of 18:00, 30 December 2010

Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.

Spring 2011

date speaker title host(s)
jan 28 Marcus Roper (Berkeley) TBA Paul Milewski
feb 25 Omri Sarig (Penn State) TBA Shamgar
mar 4 Jeff Weiss (Colorado) TBA Jean-Luc
mar 11 Roger Howe (Yale) TBA Shamgar
apr 1 Amy Ellis (Madison) TBA Steffen
apr 8 Alan Weinstein (Berkeley) TBA Yong-Geun
apr 15 Max Gunzburger (Florida State) TBA James Rossm.
apr 22 Jane Hawkins (U. North Carolina) TBA WIMAW (Diane Holcomb)
apr 29 Jaroslaw Wlodarczyk (Purdue) TBA Laurentiu