We are in the process of hiring another postdoc to join our team (see current members). We are looking for someone with research interests in analysis, and, more precisely, someone who is interested in how to approximate infinite dimensional objects in finite dimensions. A typical example is approximating operators in Hilbert space. If you think this sounds interesting please apply. Of course, you will also be free to continue your own research.

This will involve joint work with our colleagues Marco Marletta (Cardiff) and Anders Hansen (Cambridge).

# Marie Skłodowska-Curie Fellowship Success

Jonathan Ben-Artzi and Junyong Zhang have been awarded a Marie Skłodowska-Curie Fellowship which will commence on 1 July 2018 for a period of two years. Their project, entitled “Geometric Analysis of Dilute Plasmas” (GRANDPA), will focus on studying regularity theory and long-time behavior of plasmas governed by the Vlasov-Maxwell system. The abstract reads:

“The ultimate goal of this Fellowship is to understand the long time behaviour of plasmas governed by the relativistic Vlasov- Maxwell system (RVM). The main difficulty is the hyperbolic nature of Maxwell’s equations (the electromagnetic fields propagate at the speed of light): particles that travel close to the speed of light nearly interact with their own fields. It is not currently known whether particles can be accelerated to such speeds, and, if so, whether this necessarily leads to development of singularities. This is a major open problem.”

The combined expertise of Jonathan and Junyong in kinetic theory and in dispersive equations played a central role in the success of this application. The total value of the award is €195,455.

# New team member: Junyong Zhang

This month we welcomed Dr Junyong Zhang as a research associate. He joins us from the Beijing Institute of Technology, where he maintains his affiliation. Junyong is interested in harmonic analysis, spectral analysis and PDEs. Specifically, he studies problems related to the long-time behaviour of nonlinear dispersive equations, as well as Strichartz and restriction estimates. An added complication is that he considers such problems on nontrivial underlying manifolds.

He obtained his PhD in 2011 at the Institute of Applied Physics and Computational Mathematics in Beijing and has since then also spent a year at both the Australian National University and Stanford University.

Welcome Junyong!

# New paper: Arbitrarily Large Solutions of the Vlasov-Poisson System

Jonathan Ben-Artzi recently uploaded a new paper entitled Arbitrarily large solutions of the Vlasov-Poisson system, co-authored with Stephen Pankavich and Simone Calogero.

The Vlasov-Poisson system, which models the statistical behavior of many-particle systems, is known to have global-in-time classical solutions (in three dimensions). However, the underlying particle systems (of attractive or repulsive particles) may have singularities appearing in finite time. For instance, attractive particles (stars) can collapse to a single point in finite time. It is therefore interesting to ask how close to a singularity can the Vlasov-Poisson system get?

This has recently been done by Rein & Taegert in the attractive case, however the repulsive case remained open. The main result states that for any constants $C_1,C_2>0$ there exists initial data with density whose $L^\infty$ norm is initially bounded by $C_1$ but that at some later time $T>0$ is greater than $C_2$. The main tool is obtaining a priori estimates for particle trajectories and choosing initial data carefully. This data is chosen to be supported on a spherical shell about the origin, with initial velocities pointing inwards.

# New team member: Baptiste Morisse

Baptiste Morisse, who recently graduated from Université Paris Diderot (Paris 7), joined the project on 1 September 2017. Baptiste, who was a student of Benjamin Texier, brings expertise in well-posedness theory for first-order quasilinear operators, in particular in the context of Gevrey spaces. Baptiste will be in Cardiff for the next three years.

Welcome Baptiste!

# Talks in Princeton and Montréal

Last month Jonathan Ben-Artzi gave talks in the analysis seminar at Princeton University and at the Montréal Analysis Seminar hosted at McGill University. Following these successful talks, we expect a busy time traveling elsewhere and hosting colleagues in Cardiff.

# Postdoc applications being reviewed

Thank you to all those who applied to the postdoc position! The system is now no longer open to applications, and all submitted applications are under evaluation. You will hear back shortly, and interviews will be conducted towards the end of February, most likely via Skype.

# Second postdoc position

A second postdoc position is now advertised here. The deadline is 5 February 2017.

# Thanks to all applicants!

The deadline for applications for the first of two postdoc positions was last week (11 November 2016) and the applications are now being evaluated. Thank you to all those who applied; you will hear back shortly.

# Welcome!

The project QUEST: Quantitative Estimates in Spectral Theory and Their Complexity is finally being launched at Cardiff University. We have plenty to do over the next 5 years, and we will strive to keep you updated on our progress and work through this blog.

Comments, suggestions, requests to join us (as a student, postdoc or fellow) and collaboration proposals are all welcome.