The HADES seminar on Tuesday, February 13th, will be at 3:30pm in Room 939.

Speaker: Dongxiao Yu

Abstract: I will discuss the long time dynamics of a scalar quasilinear wave equation in three space dimensions. This equation satisfies the weak null condition and has global existence for sufficiently small $C_c^{\mathrm{\infty }}$ initial data. In the talk, I will first present an asymptotic completeness result which describes the asymptotic behavior of global solutions to the scalar quasilinear wave equation near the light cone ($|x|\approx t$). Then, I will discuss a work in progress on the asymptotic behavior inside the light cone  ($|x|\ll t$).

The HADES seminar on Tuesday, February 6th, will be at 3:30pm in Room 939.

Speaker: Izak Oltman

Abstract: I will apply exact WKB theory of analytic finite difference equations to estimate the spectrum of the Scottish flag matrix.

This is based on joint work with Frédéric Klopp and Shengtong Zhang.

The HADES seminar on Tuesday, January 30th, will be at 3:30pm in Room 939 (not in 740 this semester!).

Speaker: Joonhyun La

Abstract: In this talk, we will prove local well-posedness of kinetic wave equation arising from MMT equation, which is introduced by Majda, Mclaughlin, and Tabak and is one of the standard toy models to study wave turbulence. Surprisingly, our result reveals a regularization effect of the collision operator, which resembles the situation of non-cutoff Boltzmann. This talk is based on a joint work with Pierre Germain (Imperial College London) and Katherine Zhiyuan Zhang (Northeastern).