Thu, 27 Oct 2022

12:00 - 13:00
L1

Swimming in complex fluids

Prof. Saverio Spagnolie
(University of Wisconsin - Madison)
Further Information
Saverio Spagnolie is a professor of mathematics at the University of Wisconsin-Madison, with a courtesy appointment in chemical and biological engineering. His research focuses on problems in biological propulsion and soft matter, complex fluids, and numerical methods, and he is the director of the AMEP Lab (Applied Math, Engineering and Physics Lab). Prior to his post in Madison, Saverio received a Ph.D. in mathematics at the Courant Institute then held postdoctoral positions in engineering at UCSD and at Brown.
Abstract

Many microorganisms must navigate strange biological environments whose physics are unique and counter-intuitive, with wide-ranging consequences for evolutionary biology and human health. Mucus, for instance, behaves like both a fluid and an elastic solid. This can affect locomotion dramatically, which can be highly beneficial (e.g. for mammalian spermatozoa swimming through cervical fluid) or extremely problematic (e.g. the Lyme disease spirochete B. burgdorferi swimming through the extracellular matrix of human skin). Mathematical modeling and numerical simulations continue to provide new fundamental insights about the biological world in and around us and point toward new possibilities in biomedical engineering. These complex fluid phenomena can either enhance or retard a microorganism's swimming speed, and can even change the direction of swimming, depending on the body geometry and the properties of the fluid. We will discuss analytical and numerical insights into swimming through model viscoelastic (Oldroyd-B) and liquid-crystalline (Ericksen-Leslie) fluids, with a special focus on the important and in some cases dominant roles played by the presence of nearby boundaries.

Thu, 23 Oct 2014

12:00 - 13:00
L4

J.C. Maxwell's 1879 Paper on Thermal Transpiration and Its Relevance to Contemporary PDE

Marshall Slemrod
(University of Wisconsin - Madison)
Abstract
In his 1879 PRSL paper on thermal transpiration J.C.MAXWELL addressed the problem of steady flow of a dilute gas over a flat boundary. The experiments of KUNDT and WARBURG had demonstrated that if the boundary is heated with a temperature gradient , say increasing from left to right, the gas will flow from left to right. On the other hand MAXWELL using the continuum mechanics of his (and indeed our) day solved the ( compressible) NAVIER- STOKES- FOURIER equations for balance of mass, momentum, and energy and found a solution: the gas has velocity equal zero. The Japanese fluid mechanist Y. SONE has termed this the incompleteness of fluid mechanics. In this talk I will sketch MAXWELL's program and how it suggests KORTEWEG's 1904 theory of capillarity to be a reasonable “ completion” of fluid mechanics. Then to push matters in the analytical direction I will suggest that these results show that HILBERT's 1900 goal expressed in his 6th problem of passage from the BOLTZMANN equation to the EULER equations as the KNUDSEN number tends to zero in unattainable.
Tue, 10 Jun 2014

15:45 - 16:45
L4

What is the [Categorical] Weil Representation?

Shamgar Gurevich
(University of Wisconsin - Madison)
Abstract
The Weil representation is a central object in mathematics responsible for many important results. Given a symplectic vector space V over a finite field (of odd characteristic) one can construct a "quantum" Hilbert space H(L) attached to a Lagrangian subspace L in V. In addition, one can construct a Fourier Transform F(M,L): H(L)→H(M), for every pair of Lagrangians (L,M), such that F(N,M)F(M,L)=F(N,L), for every triples (L,M,N) of Lagrangians. This can be used to obtain a natural “quantum" space H(V) acted by the symplectic group Sp(V), obtaining the Weil representation. In the lecture I will give elementary introduction to the above constructions, and discuss the categorification of these Fourier transforms, what is the related sign problem, and what is its solution. The outcome is a natural category acted by the algebraic group G=Sp, obtaining the categorical Weil representation. The sign problem was worked together with Ofer Gabber (IHES).
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