Skip to content

Events for October 31, 2017 from General and Seminar calendars

Working Seminar in Orbit Equivalence and Measured Group Theory

Time: 10:00AM - 11:00AM

Location: BLOC 624

Speaker: Konrad Wrobel

Title: Stable Actions and Asymptotically Central Sequences IV

Abstract: I'll finish proving a characterization of stable actions in the sense of Jones-Schmidt using Kida's language of groupoids.

Nonlinear Partial Differential Equations

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Alex Mahalov, Arizona State University

Title: Nonlinear PDE's seminar

Title:Stochastic Three-Dimensional Navier-Stokes Equations + Waves: Averaging, Convergence, Regularity and Nonlinear Dynamics

We consider stochastic three-dimensional Navier-Stokes equations + Waves on long time intervals. Regularity results are established by bootstrapping from global regularity of the averaged stochastic resonant equations and convergence theorems. The averaged covariance operator couples stochastic and wave effects. The energy injected in the system by the noise is large, the initial condition has large energy, and the regularization time horizon is long. Regularization is the consequence of precise mechanisms of relevant three-dimensional nonlinear interactions. We establish multi-scale stochastic averaging, convergence and regularity theorems in a general framework. We also present theoretical and computational results for three-dimensional nonlinear dynamics.

Analysis/PDE Reading Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 624

Speaker: Dean Baskin, TAMU

Title: A brief introduction to resonances

Abstract: Spectral theory for the Laplacian on compact manifolds gives you a discrete set of eigenvalues and an orthonormal basis of eigenfunctions. For non-compact problems, there is typically continuous spectrum and only finitely many eigenvalues. Is there anything resembling a discrete family of eigenvalues in this context? In some sense, the answer is yes: these are the resonances. In this talk I will provide a brief introduction to the theory of resonances. I will provide some motivation for their study by working through the case of the one-dimensional wave equation. I will then talk about resonances on Euclidean and hyperbolic spaces, where they can be calculated explicitly. Finally I will provide some discussion of how to define them in the case of potential scattering (and maybe some geometric scattering) via the analytic Fredholm theorem. In a future talk I will use the explicit calculation of the resonances on hyperbolic space to calculate the asymptotic behavior of the wave equation on Minkowski space.