Events for 04/09/2024 from all calendars

Number Theory Seminar

Time: 09:45AM - 10:45AM

Location: BLOC 302

Speaker: Zhining Wei, Brown University

Title: Effective Open Image Theorem for pairs of elliptic curves

Abstract: In 1972, Serre proved the celebrated Open Image Theorem, claiming that for a non-CM elliptic curve E over Q, the residue modulo $\ell$ Galois representation associated with E is surjective for sufficiently large prime $\ell$. An effective version of this theorem seeks to bound such least non-surjective prime $\ell$. In the talk, I will review some results concerning the effective version of Serre's Open Image Theorem. Then, I will present a work in progress on the effective open image theorem for pairs of elliptic curves, especially the semistable elliptic curves. This is joint with Tian Wang.

Nonlinear Partial Differential Equations

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Yeyu Zhang, Shanghai University of Finance and Economics

Title: Coupled Nonlinear Evolution and Inverse Energy Transfer in Moist Boussinesq Dynamics

Abstract: The interaction between slow and fast components in geophysical fluid dynamics, especially under the influence of phase changes, poses significant analytical challenges. Our study develops a fast-wave averaging framework for the moist Boussinesq system, expanding past dry dynamics to include phase changes between water vapor and liquid water. We examine whether these phase transitions induce coupling between slow and fast waves or if the slow component evolves independently. Numerical simulations with a range of Froude and Rossby numbers reveal that phase changes may disrupt the proportionality of wave influence on the slow component, evidenced by a nonzero time-averaged wave component due to phase transitions. Furthermore, inverse energy transfer to larger scales is investigated in rotating and stratified flows, including water effects and rapid cloud microphysics. The findings could imply that potential vorticity, phase boundaries, and vertical velocity contribute to the formation of coherent structures in strongly rotated and stratified flows, appearing to indicate a revision to the traditional view of energy cascades in geophysical fluids.

Nonlinear Partial Differential Equations

Time: 4:00PM - 5:00PM

Location: BLOC 302

Speaker: Ricardo Alonso, Texas A&M University - Qatar

Title: An energy method for the Boltzmann equation: Higher integrability and boundedness of solutions

Abstract: We cover in detail an argument for proving higher integrability and uniform boundedness for solutions of the homogeneous Boltzmann equation. Techniques are reminiscent of the level set De Giorgi's method for classical elliptic/parabolic PDE. A rough idea of the method's implementation for the spatially inhomogenous problem is discussed at the end.