Wednesday, Sep 17, 15:00-16:00, Zoom: Link

Speaker: Titouan Vayer, Inria
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, Sep 24, 15:00-16:00, SAS 4201

Speaker: Arunima Bhattacharya, UNC
Title: Lagrangian mean curvature equations and flows
Abstract: In this talk, we will introduce the special Lagrangian equation and the Lagrangian mean curvature flow. We will discuss interior Hessian estimates for shrinkers and expanders of the Lagrangian mean curvature flow, and further extend this result to a broader class of Lagrangian mean curvature type equations. We assume the Lagrangian phase to be hypercritical, which results in the convexity of the potential of the initial Lagrangian submanifold. Convex solutions of the second boundary value problem for certain such equations were constructed by Brendle-Warren 2010, Huang 2015, and Wang-Huang-Bao 2023. We will also briefly introduce the fourth-order Hamiltonian stationary equation and mention some recent results on the regularity of solutions of certain fourth-order PDEs, which are critical points of variational integrals of the Hessian of a scalar function. Examples include volume functionals on Lagrangian submanifolds. This is partially based on joint work with Jeremy Wall.
———————————————————————————————————–

Wednesday, Oct 01, 15:00-16:00, SAS 4201

Speaker: Toan Nguyen, Penn State University
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, Oct 08, 15:00-16:00, SAS 4201

Speaker: TBA
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, Oct 15, 15:00-16:00, Zoom: Link

Speaker: Marius Tucsnak, University of Bordeaux
Title: Relaxation enhancement by controlled incompressible fluid flows
Abstract: We propose a PDE-controllability based approach to the enhancement of diffusive mixing for passive scalar fields. Unlike in the existing literature, our relaxation enhancing fields are not prescribed ab initio at every time and at every point of the spatial domain. Instead, we prove that time-dependent relaxation enhancing vector fields can be obtained as state trajectories of control systems described by the  incompressible Euler equations either driven by finite-dimensional controls or by controls localized in space. The main ingredient of our proof is a new approximate controllability theorem for the incompressible Euler equations on the two dimensional torus, ensuring the approximate tracking of the full state all over the considered time interval. Combining this with a continuous dependence result  yields enhanced relaxation for the passive scalar field. Another essential tool in our analysis is the exact controllability of the incompressible Euler system driven by spatially localized forces.
———————————————————————————————————–

Wednesday, Oct 22, 15:00-16:00, SAS 4201

Speaker: PLCom
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, Oct 29, 15:00-16:00, SAS 4201

Speaker: PLCom
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, Nov 05, 15:00-16:00, SAS 4201

Speaker: PLCom
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, Nov 12, 15:00-16:00, SAS 4201

Speaker: Mateo Diaz Diaz, Johns Hopkins University
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, Nov 19, 15:00-16:00, SAS 4201

Speaker: TBA
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, Jan 14, 15:00-16:00, SAS 4201

Speaker: TBA
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, Jan 21, 15:00-16:00, SAS 4201

Speaker: TBA
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, Jan 28, 15:00-16:00, SAS 4201

Speaker: TBA
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, Feb 04, 15:00-16:00, SAS 4201

Speaker: TBA
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, Feb 11, 15:00-16:00, SAS 4201

Speaker: TBA
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, Feb 18, 15:00-16:00, SAS 4201

Speaker: TBA
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, Feb 25, 15:00-16:00, SAS 4201

Speaker: TBA
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, Mar 04, 15:00-16:00, SAS 4201

Speaker: TBA
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, Mar 11, 15:00-16:00, SAS 4201

Speaker: TBA
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, Mar 25, 15:00-16:00, SAS 4201

Speaker: TBA
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, April 01, 15:00-16:00, SAS 4201

Speaker: TBA
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, April 08, 15:00-16:00, SAS 4201

Speaker: TBA
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, April 15, 15:00-16:00, SAS 4201

Speaker: TBA
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, April 22, 15:00-16:00, SAS 4201

Speaker: TBA
Title: TBA
Abstract: TBA
———————————————————————————————————–

Wednesday, April 29, 15:00-16:00, SAS 4201

Speaker: TBA
Title: TBA
Abstract: TBA
———————————————————————————————————–