Date: Friday, Feb 28.

• Speaker: Puskar Mondal, Harvard University.
• Title: Einstein Vlasov system in large data regime.
• Abstract: In this talk, our object of study is the Einstein-Vlasov system with a massless Vlasov matter field in topologically trivial spacetimes. Complementing various important works obtaining the stability of Minkowski spacetime as a solution to this system, we look at the large data regime, motivated in turn by the signature for decay rates of various Ricci coefficients, curvature and matter components, first introduced by X. An. Our work provides a semi-global existence result and a trapped surface formation result for the Einstein-Vlasov system in the absence of any symmetry and restriction on data size. Our proof is based on a double null gauge. Interestingly, we give a new way of obtaining estimates for the Vlasov matter, purely by commuting with various vector fields and without the need to use Jacobi fields. This is joint work with N. Athanasiou.
• Location: Sony Building, A1013.

Date: Friday, April 11, 8AM (notice different time).

• Speaker: Huali Zhang, Hunan University.
• Title: Strichartz estimates and low regularity solutions of 3D relativistic Euler equations.
  Abstract: Disconzi proposed an open Problem D, about establishing low regularity solutions for 3D relativistic Euler equations with the logarithmic enthalpy $h_0$, initial velocity $\bu_0$, and modified vorticity $\bw_0$ belonging to $H^s \times H^s \times H^{s_0} (2<s_0<s)$. Similar results have been obtained for compressible Euler equations by Wang (see also Andersson-Zhang). Compared with the non-relativistic case, the velocity varies from space-like to time-like in relativistic Euler, which brings us challenges for Problem D. In this talk, we will give a positive answer to this open Problem D for 3D relativistic Euler equations.
• Zoom link: https://vanderbilt.zoom.us/j/98625175307

Date: Friday, April 25.

• Speaker: Casey Rodriguez, UNC Chapel Hill.
• Title: Green-elastic solids with gradient elastic boundaries
• Abstract. In this talk, we explore recent developments in the field of gradient elasticity. We begin by providing an intuitive introduction to the theory, which extends classical elasticity by incorporating higher-order spatial derivatives that capture microstructural effects. These contributions become particularly important at small spatial scales, offering a more refined description of deformation that classical models cannot account for. We then present a novel theory of three-dimensional Green-elastic bodies with gradient elastic material boundary surfaces and highlight its application to modeling brittle fracture.
• Location: Sony Building, A1013.