Math Department
https://wp0.vanderbilt.edu/math
College of Arts and Science | Vanderbilt UniversityFri, 19 Apr 2019 22:10:08 +0000en-UShourly1https://wordpress.org/?v=4.9.8146940276On the Linear Forced Euler and Navier-Stokes Equations: Damping and Modified Scattering
https://wp0.vanderbilt.edu/math/2019/04/talk-title-tba-279/
Fri, 19 Apr 2019 22:10:08 +0000https://wp0.vanderbilt.edu/math/?p=8685We study the long-time asymptotic behavior of the linearized Euler and nonlinear Navier-Stokes equations close to Couette flow. As a main result we show that suitable forcing breaks asymptotic stability results at the level of the vorticity, but that solutions never the less exhibit convergence of the velocity field. Thus, here linear inviscid damping persists despite instability of the vorticity equations.
]]>8685Talk Title TBA
https://wp0.vanderbilt.edu/math/2019/04/talk-title-tba-297/
Fri, 19 Apr 2019 21:10:07 +0000https://wp0.vanderbilt.edu/math/?p=87708770On PDE Aspects of the Navier-Stokes Equations and Some Simpler Model Equations
https://wp0.vanderbilt.edu/math/2019/04/talk-title-tba-241/
Thu, 18 Apr 2019 22:10:52 +0000https://wp0.vanderbilt.edu/math/?p=8034Although the Navier-Stokes equations are widely used, it is not known rigorously whether the mathematical model they represent satisfies one of the basic tenets of the Newtonian mechanics that a complete information about the system at a given time together with the equations of motion should uniquely determine the state of the system at all future times. I will recall what is known about these questions for the Navier-Stokes equations, and will also present examples of relevant model problems for which one can obtain a fairly good understanding of these issues, at least if we are willing to rely on numerical simulations. Tea at 3:33 pm in Stevenson 1425. (Contact Person: Gieri Simonett)
]]>80342019 Mathematics Departmental Awards Ceremony
https://wp0.vanderbilt.edu/math/2019/04/2019-mathematics-departmental-awards-ceremony/
Wed, 17 Apr 2019 21:30:58 +0000https://wp0.vanderbilt.edu/math/?p=8965The annual awards ceremony will honor the recipients of the following awards: The B.F. Bryant Prize, The Bjarni Jónsson Prize, and The Richard J. Larsen Prize. The gathering will also be an occasion to celebrate the end of the academic year and the achievements of our departmental community. A reception will follow the ceremony.
]]>8965Deriving New Runge-Kutta Methods Using Unstructured Numerical Search
https://wp0.vanderbilt.edu/math/2019/04/deriving-new-runge-kutta-methods-using-unstructured-numerical-search/
Tue, 16 Apr 2019 21:10:48 +0000https://wp0.vanderbilt.edu/math/?p=8948Runge-Kutta methods are a popular class of numerical methods for solving ordinary differential equations. Every Runge-Kutta method is characterized by two basic parameters: its order, which measures the accuracy of the solution it produces, and its number of stages, which measures the amount of computational work it requires. The primary goal in constructing Runge-Kutta methods is to maximize order using a minimum number of stages. However, high-order Runge-Kutta methods are difficult to construct because their parameters must satisfy an exponentially large system of polynomial equations. In this talk, I will present the first known 10th-order Runge-Kutta method with only 16 stages, breaking a 40-year standing record for the number of stages required to achieve 10th-order accuracy. I will also discuss the tools and techniques that enabled the discovery of this method using a straightforward numerical search.
]]>8948SSP ?= RC
https://wp0.vanderbilt.edu/math/2019/04/ssp-rc/
Tue, 16 Apr 2019 21:10:26 +0000https://wp0.vanderbilt.edu/math/?p=8970Sauer-Shelah-Perles lemma says that a set family shatters at least as many sets as it has. From a lattice standpoint, this lemma implicitly considers a boolean lattice of all subsets of a base set. It does not in general hold for arbitrary lattice. We denote the class of those lattices for which SSP lemma does hold by, well, SSP and try to characterize this class somehow. At the moment, a standing conjecture (probably wrong) is that SSP = RC, and we will keep a little intrigue about what RC stands for. This talk stems from a preprint “A Sauer–Shelah–Perles Lemma for Lattices” by Zeev Dvir, Yuval Filmus and Shay Moran, and from a brief collaboration of the speaker with these authors.
]]>8970Shanks Workshop on Homotopy Theory 2019, April 13-14
https://wp0.vanderbilt.edu/math/2019/04/shanks-workshop-on-homotopy-theory-2019-april-13-14/
Sat, 13 Apr 2019 15:00:24 +0000https://wp0.vanderbilt.edu/math/?p=8708For more information, visit the workshop website.
]]>8708The Fractional Porous Medium Equation on Manifolds with Conic Singularities
https://wp0.vanderbilt.edu/math/2019/04/talk-title-tba-278/
Fri, 12 Apr 2019 21:10:57 +0000https://wp0.vanderbilt.edu/math/?p=8683Due to the need to model long range diffusive interaction, during the last decade there has been a growing interest in considering diffusion equations involving non-local operators, e.g. the fractional powers of differential operators. In this talk, I will report some recent work with Nikolaos Roidos on the fractional porous medium equation on manifolds with cone-like singularities. I will show that most of the properties of the usual (local) porous medium equation, like existence, uniqueness of weak solution, comparison principle, conservation of mass, are inherited by the non-local version.
]]>8683A Covariant Stone-von Neumann Theorem
https://wp0.vanderbilt.edu/math/2019/04/talk-title-tba-290/
Fri, 12 Apr 2019 22:10:56 +0000https://wp0.vanderbilt.edu/math/?p=8742In this talk, we formulate and prove a version of the Stone-von Neumann Theorem for every C*-dynamical system of the form (G, K(H), a) where G is a locally compact Hausdorff abelian group and H is a Hilbert space. The novelty of our work stems from our covariant representation of the Weyl Commutation Relation on Hilbert K(H)-modules instead of just Hilbert spaces. This is joint work with Leonard Huang (University of Nevada, Reno).
]]>8742Functional Barcoding for Lineage-Resolved Analysis of Cancer Cells
https://wp0.vanderbilt.edu/math/2019/04/functional-barcoding-for-lineage-resolved-analysis-of-cancer-cells/
Fri, 12 Apr 2019 20:00:24 +0000https://wp0.vanderbilt.edu/math/?p=89578957