# LMS-MIGSAA-MI Mini Colloquium 4th November 2016

This Mini-Colloquium 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 followed by a dinner after the workshop on Friday, 4 November.

Full details can be found at http://www.maths.ed.ac.uk/~jazzam/LMS-Network-Meeting-2016

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: 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. 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$E$ are obtained from continuous deformations of E$E$ through mappings that preserve the boundary (sliding minimal sets), and on questions of boundary regularity of these objects of dimension 2 in 3$3$ -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 Singular perturbations of Dirac Hamiltonians Abstract:I shall present some recent work done in collaboration with N. Arrizabalaga and A. Mas about some singular perturbations of Dirac hamiltonians. In particular, we study the spectral properties of the coupling H+aV, where H is the massive free Dirac operator in 3d, and aV is an electrostatic shell potential (which depends on the coupling real parameter a) located on the boundary of a smooth domain. Our main result is an isoperimetric-type inequality for the admissible range of a's for which the coupling H+aV generates pure point spectrum. This optimization problem involves two classical operators. One is given by the Newtonian potential while the other one is the Clifford-Riesz transform. 17.30 - Wine Reception