Seminars, for informal dissemination of research results, exploratory work by research teams, outreach activities, etc., constitute the simplest form of meetings at a Mathematics research centre.
CAMGSD has recorded the calendar of its seminars for a long time, this page serving both as a means of public announcement of forthcoming activities but also as a historic record.
The classical Stein-Tomas theorem extends from the theory of linear Fourier restriction estimates for smooth manifolds to the one of fractal measures exhibiting Fourier decay. In the multilinear “smooth” setting, transversality allows for estimates beyond those implied by the linear theory. The goal of this talk is to investigate the question “how does transversality manifest itself in the fractal world?” We will show, for instance, that it could be through integrability properties of the multiple convolution of the measures involved, but that is just the beginning of the story. In the special case of Cantor-type fractals, we will construct multilinear Knapp examples through certain co-Sidon sets which, in some cases, will give more restrictive necessary conditions for a multilinear theorem to hold than those currently available in the literature. This is work in progress with Ana de Orellana (University of St. Andrews, Scotland).
Dimension 4 is the next horizon for applications of Ricci flow to topology, where the main goal is to understand the topological operations that Ricci flow generically performs at singular times. Shrinking Ricci solitons model these topological operations, and only the stable ones should arise generically.
I will present recent joint works with Olivier Biquard and Keaton Naff that determine the stability of all of the currently known shrinking Ricci solitons in dimension 4. The arguments use structural features unique to dimension four, in particular self-duality.
Decomposable plane curves of degree up to 5 were shown to be quantum homogeneous spaces by Brown and Tabiri. It was conjectured that all decomposable plane curves of any degree are quantum homogeneous spaces. In this talk, we will discuss recent results which show that decomposable surfaces and plane curves of any degree are quantum homogeneous spaces. Other algebras such as the reduced algebra will be constructed and its properties discussed.
I will construct an example of a bounded planar domain with one single hole for which the nodal line of a second Dirichlet eigenfunction is closed and does not touch the boundary. This shows that Payne's nodal line conjecture can at most hold for simply-connected domains in the plane.
