London PDE Seminar

\( R_{ a b } - \frac{1}{2} R \cdot g_{ a b } + \Lambda \cdot g_{ a b } = T_{ a b } \text{.} \)

The London PDE Seminar is a London-based seminar featuring speakers at the forefront of mathematical research in partial differential equations.

Upcoming Seminars

The seminar convenes fortnightly, on approximately every other Friday. Some talks will be held in-person, while others will be held on Zoom.

Date/Time: 11:00 (UK time), Friday, 9 June 2023

Location: University College London (in-person)
Room: 505, 25 Gordon Street

Speaker: Toan Nguyen (Penn State)

Title: Landau damping and the survival threshold

Abstract: The talk is to precise the classical notion of Landau damping and to provide the survival threshold of spatial frequencies that dictates the transition from purely oscillatory modes, known as Langmuir waves, to the free dynamics of electrons near spatially homogeneous backgrounds, classically modeled by the Vlasov-Poisson system in plasma physics or the Hartree-Coulomb equations in quantum mechanics. The transition occurs due to the exact resonant interaction between excited electrons and the oscillatory waves, namely the classical Landau damping.

Date/Time: 11:00 (UK time), Friday, 16 June 2023

Location: University College London (in-person)
Room: 505, 25 Gordon Street

Speaker: Irfan Glogić (Vienna)

Title: Global-in-space stability of self-similar blowup for the wave maps equation

Abstract: We consider wave maps from the \((1+d)\)-dimensional Minkowski space into the \(d\)-sphere. Numerical simulations of this model indicate that in the energy supercritical case, \(d \geq 3\), generic large data lead to finite time blowup via an explicitly known self-similar solution. In the effort of rigorously proving these observations, many works have been produced over the last decade, starting with the pioneering work of Aichelburg-Donninger-Schörkhuber. In this talk, we outline a novel general framework for the analysis of spatially global stability of self-similar solutions to semilinear wave equations. We then implement this scheme in the aforementioned context of wave maps, thereby obtaining the first nonlinear stability result that is global-in-space. At the and, we discuss further open problems as well as the new mathematical challenges that our approach generates.

Date/Time: 11:00 (UK time), Monday, 19 June 2023 (special date)

Location: University College London (in-person)
Room: 707, 25 Gordon Street

Speaker: Wilhelm Schlag (Yale)

Title: On continuous time bubbling for the harmonic map heat flow in two dimensions

Abstract: I will describe recent work with Jacek Jendrej (CNRS, Paris Nord) and Andrew Lawrie (MIT) on harmonic maps of finite energy from the plane to the two sphere, without making any symmetry assumptions. While it has been known since the 1990s that bubbling occurs along a carefully chosen sequence of times via an elliptic Palais-Smale mechanism, we show that this continues to hold continuously in time. The key notion is that of the "minimal collision energy" which appears in the soliton resolution result by Jendrej and Lawrie on critical equivariant wave maps.

Date/Time: 11:00 (UK time), Friday, 23 June 2023

Location: University College London (in-person)
Room: 505, 25 Gordon Street

Speaker: Warren Li (Princeton)