All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.
|wed dec 1||Peter Markowich (Cambridge and Vienna)||On Wigner and Bohmian Measures||Shi (Wasow Lecture)|
|dec 3||Saverio Spagnolie (UCSD)||Locomotion at low and intermediate Reynolds numbers||Jean-Luc (job talk)|
|mon dec 6||Brian Street (Madison)||A quantitative Frobenius Theorem, with applications to analysis||local (job talk)|
|dec 10||Benson Farb (Chicago)||TBA||Jean-Luc|
|mon dec 13 3 pm||Jun Yin (Harvard)||Random Matrix Theory: A short survey and recent results on universality||Timo (job talk)|
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.
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.