Math Department
https://wp0.vanderbilt.edu/math
College of Arts and Science | Vanderbilt UniversityFri, 27 Mar 2020 22:10:20 +0000en-UShourly1https://wordpress.org/?v=4.9.8146940276CANCELLED
https://wp0.vanderbilt.edu/math/2020/03/talk-title-tba-360/
Fri, 27 Mar 2020 22:10:20 +0000https://wp0.vanderbilt.edu/math/?p=98519851CANCELLED- The Navier-Stokes, Euler and Other Related Equations
https://wp0.vanderbilt.edu/math/2020/03/the-navier-stokes-euler-and-other-related-equations/
Thu, 26 Mar 2020 22:10:01 +0000https://wp0.vanderbilt.edu/math/?p=9895In this talk I will present the most recent advances concerning the questions of global regularity of solutions to the three-dimensional Navier–Stokes and Euler equations of incompressible fluids. Furthermore, I will also present recent global regularity (and finite time blow-up) results concerning certain three-dimensional geophysical flows, including the three-dimensional viscous (non-viscous) “primitive equations” of oceanic and atmospheric dynamics.
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https://wp0.vanderbilt.edu/math/2020/03/talk-title-tba-333/
Wed, 25 Mar 2020 21:10:28 +0000https://wp0.vanderbilt.edu/math/?p=9437

]]>9437Axioms for Impartial Division
https://wp0.vanderbilt.edu/math/2020/03/axioms-for-impartial-division/
Mon, 23 Mar 2020 21:10:30 +0000https://wp0.vanderbilt.edu/math/?p=9949Click Zoom Link Here or copy & paste URL into browser: https://vanderbilt.zoom.us/j/604287660]]>I will discuss axioms for impartial division which lead to an interesting question about functions on a certain collection of directed graphs.
]]>9949CANCELLED- Nonlocal Modeling for Diffusion and Mechanics
https://wp0.vanderbilt.edu/math/2020/03/nonlocal-modeling-for-diffusion-and-mechanics/
Thu, 19 Mar 2020 22:10:00 +0000https://wp0.vanderbilt.edu/math/?p=9880Nonlocal continuum models allow for interactions between a point and other points separated by a nonzero distance, in contrast with PDE models for which interactions occur only in infinitesimal neighborhoods surrounding the point. If the extent of interactions are limited to be no greater than a finite distance, then a length scale is introduced into the models that renders them as being multiscale mono-models, by which we mean that depending on the size of the viewing window used relative to the extent of nonlocal interactions, a single model can display very different behaviors. Some nonlocal models that are spatial-derivative free also allow for discontinuous solutions which make them well suited for simulations of fracture and other settings. We discuss theories for the analysis and numerical analysis of the nonlocal models considered, relying on a nonlocal vector calculus to define weak formulations in function space settings. Brief forays into examples and extensions are made, including obstacle problems and wave problems.
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https://wp0.vanderbilt.edu/math/2020/03/talk-title-tba-362/
Wed, 18 Mar 2020 00:00:57 +0000https://wp0.vanderbilt.edu/math/?p=98589858CANCELLED
https://wp0.vanderbilt.edu/math/2020/03/talk-title-tba-358/
Tue, 17 Mar 2020 16:00:27 +0000https://wp0.vanderbilt.edu/math/?p=98459845CANCELLED- Shanks Workshop: Mathematical Aspects of Fluid Dynamics
https://wp0.vanderbilt.edu/math/2020/03/shanks-workshop-mathematical-aspects-of-fluid-dynamics/
Sat, 14 Mar 2020 16:00:12 +0000https://wp0.vanderbilt.edu/math/?p=9904March 14-15, 2020
]]>9904Computational Approach to Property (T)
https://wp0.vanderbilt.edu/math/2020/03/talk-title-tba-353/
Wed, 11 Mar 2020 22:10:19 +0000https://wp0.vanderbilt.edu/math/?p=9799Property (T) is a property of compactly generated group which has been introduced by Kazhdan in 1967. The property, expressed in the language of functional analysis is a very strong rigidity property and has far reaching consequences for the actions and the geometry of a group. During the talk I will briefly discuss the the theoretical results of Ozawa which make the computational approach to the Kazhdan property (T) possible. It is known that property (T) is equivalent to positivity of certain operator in the full group ∗-algebra. Surprisingly, this positivity is witnessed by the existence of a sum of (hermitian) squares decomposition of the operator in the real *group ring**. This in turn is equivalent to the feasibility of a certain semi-definite optimisation problem, which amounts to a finite computation. I will describe the algorithm encoding the optimisation problem, and how an (imprecise) numerical solution can be turned into a mathematical proof by using the order structure and the topology of cones in group rings. Since (due to its size) the optimisation problem is out of reach of the state-of-the-art solvers we will show how to use the representation theory of finite groups to exploit the symmetry of the optimisation problem to minimize its size. This leads to constructive computer-assisted proof that Aut(F5) has Kazhdan’s property (T).
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https://wp0.vanderbilt.edu/math/2020/03/9901/
Wed, 11 Mar 2020 21:30:21 +0000https://wp0.vanderbilt.edu/math/?p=99019901