Events for 04/30/2024 from all calendars

Number Theory Seminar

Time: 09:45AM - 10:45AM

Location: BLOC 302

Speaker: Junxian Li, University of California, Davis

Title: Joint value distribution of L-functions

Abstract: I will discuss the joint value distribution of L- functions in the critical strip. The values of distinct primitive L-functions behave like independently distributed random variables on the critical line, but some dependence shows up away from the critical line. Nevertheless, we can show distinct L-functions can obtain large/small values simultaneously infinitely often. Based on joint work with S. Inoue and W. Heap.

Nonlinear Partial Differential Equations

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Slim Ibrahim, Univeristy of Victoria

Title: Stable Singularity Formation for the Inviscid Primitive Equations

Abstract: The primitive equations (PEs) model large-scale dynamics of the oceans and the atmosphere. While it is by now well known that the three-dimensional viscous PEs are globally well posed in Sobolev spaces, and that there are solutions to the inviscid PEs (also called the hydrostatic Euler equations) that develop singularities in finite time, the qualitative description of the blowup still remains undiscovered. In this talk, we provide a full description of two blow-up mechanisms, for a reduced PDE that is satisfied by a class of particular solutions to the PEs. In the first one a shock forms, and pressure effects are subleading, but in a critical way: they localize the singularity closer and closer to the boundary near the blow-up time (with a logarithmic-in-time law). This first mechanism involves a smooth blow-up profile and is stable among smooth enough solutions. In the second one the pressure effects are fully negligible; this dynamics involves a two-parameter family of non-smooth profiles, and is stable only by smoother perturbations. This is a joint work with C. Collot and Q. Lin.

Department Retirement Reception

Time: 3:30PM - 5:00PM

Location: BLOC 140 (black

Nonlinear Partial Differential Equations

Time: 4:00PM - 5:00PM

Location: BLOC 302

Speaker: Quyuan Lin, Clemson University

Title: On the three-dimensional Nernst-Planck-Boussinesq system

Abstract: Electrodiffusion of ions is a phenomenon that takes place in electrolyte solutions when charged ions are transported in a fluid under the influence of an electric field. It has various real-world applications in neuroscience, semiconductor theory, water purification, desalination, ion separation, etc. In this talk, I will introduce the Nernst-Planck-Boussinesq (NPB) system, a new ionic electrodiffusion model that incorporates variational temperature and is forced by buoyancy force stemming from temperature and salinity fluctuations. The electromigration term in the NPB system displays a complex nonlinear structure influenced by the reciprocal of the temperature, which distinguishes its mathematical aspects from other electrodiffusion models studied in the literature, such as the Nernst-Planck-Navier-Stokes and the Nernst-Planck-Euler systems. I will discuss the global existence of weak solutions to the 3D NPB system as well as the long-time dynamics of these weak solutions and their exponential decay in time to steady states.