## LMS Harmonic Analysis Network Meeting

### Maxwell Institute

 Information Speakers Programme Registration (closed)

## Information

This Mini-Symposium is a one day event in various areas of Analysis and will take place at the International Centre for Mathematical Sciences
ICMS, 15 South College Street, Edinburgh. The event is sponsered by the LMS Harmonic Analysis and PDEs research network, MIGSAA (the Maxwell Institute Graduate School in Analysis and its Applications) as well as UoE's Analysis and its Application Research Theme.

For accommodation in Edinburgh, the following link may be useful: Accommodation.

There will be a wine reception after the workshop on Friday, 4 November.

There is no registration fee for this workshop. However if you are planning to attend, please register by clicking the link above.

## Speakers

Luis Vega (University of the Basque Country)

Guy David (Université Paris-Sud)

Veronique Fischer (University of Bath)

John Mackay (University of Bristol)

## Programme

 10.30 - 11.30 John Mackay p-Laplacians on random graphs and applications to group theory Abstract: The first eigenvalue of the graph Laplacian has been used byBallmann-Swiatkowski, Zuk and others to show that certain groups havefixed points whenever they act on Hilbert space. Recently thisframework has been extended to consider graph p-Laplacians and actionson L^p spaces. I will discuss some of this background, and recentwork with Cornelia Drutu where we considering "random" graphs andgroups. 11.30 - 12.00 Coffee and Tea 12.00 - 13.00 Veronique Fischer Multipliers on compact Lie groups Abstract: In this talk, I will present conditions on a Fourier multiplier of a compact Lie group which ensure that the corresponding operator is Lp bounded. They imply the well-known case of spectral multiplier in the Laplace-Beltrami operator, thereby showing that the conditions are sharp. Old and new questions on the subject will be discussed. 13.00 - 15.00 Lunch 15.00-16.00 Guy David Boundary regularity of soap films and the Plateau problem Abstract: There are many ways to state a Plateau problem for soap films with a given boundary, and many of them don't have a solution yet. We will concentrate on one version of the problem, where competitors of a set $E$ are obtained from continuous deformations of $E$ through mappings that preserve the boundary (sliding minimal sets), and on questions of boundary regularity of these objects of dimension 2 in $3$-space. This is probably connected to existence (still unknown in this case), and other problems (existence and regularity of size-minimizing currents, for instance). We will mostly get a chance to draw pictures. 16.00 - 16.30 Coffee and Tea 16.30 - 17.30 Luis Vega The Talbot effect and the evolution of vortex dynamicsAbstract: Firstly, I will introduce the binormal curvature flow as an approximation of the evolution of vortex filaments. Then, I will review the construction of solutions of this flow that, despite the fact that they develop a singularity in the form of a corner, can be continued after the singularity appears. As a consequence I will show how the complex dynamics of regular polygons can be explained as a non-linear Talbot effect. Finally, I will present recent results about the discontinuity of some appropriate norm at the singularity time and the lack of conservation of the linear momentum. Motivation comes from some recent numerical simulations about the evolution of regular polygons that strongly suggest the existence of a non-trivial transfer of energy and momentum. 17.30 - Wine Reception