The HADES seminar on Tuesday, April 22nd, will be at 3:30pm in Room 740.

Speaker: Robert Schippa

Abstract: We revisit the classical Córdoba-Fefferman square function estimate and give applications to moment inequalities for exponential sums. Next, we extend the CF estimate to higher dimensional manifolds with tangent spaces satisfying a transversality condition. Finally, we show square function estimates for the conical extension by the High-Low method, which in the scalar case is due to Guth-Wang-Zhang.

The HADES seminar on Tuesday, April 1st, will be at 3:30pm in Room 740.

Speaker: Ryan Martinez

Abstract: The method of normal forms was introduced to PDEs by Shatah, who used it to
study the long time behavior of semilinear Klein Gordon equations and the method
has been widely used in the context of semilinear problems. The modified energy
method of Hunter, Ifrim, Tataru, and Wong extends the idea of normal forms to
quasilinear problems.

In this talk, we will discuss the method of normal forms, the related method
of modified energy, and my recent work which extends these in a novel way. The aim is
to give a selection of nonlinear PDEs which demonstrate in detail how these methods
are used, why they work, and what gains they achieve.

The HADES seminar on Tuesday, March 11th, will be at 3:30pm in Room 740.

Speaker: Hanna Kim

Abstract: We study problems involving the optimization of eigenvalues in various boundary conditions. The Steiner symmetrization was the important key to solving the classical isoperimetric inequality, where the solution is the ball.  Based on this problem, analogous problems were introduced in spectral problems with Dirichlet, Neumann and Robin boundaries and so on. I will discuss recent results on showing maximization of third Robin eigenvalue for negative parameters. This work is based on joint work with R. Laugesen.

The HADES seminar on Tuesday, January 28th, will be at 3:30pm in Room 740.

Speaker: Ely Sandine

Abstract: This will be an expository talk on shock formation for quasilinear wave equations from small,  smooth, radially symmetric initial data. I will focus in particular on the case of two spatial dimensions. The primary reference for this talk is the survey article “Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations: An Overview” by Holzegel, Klainerman, Speck and Wong (2016).