Our colloquium takes place on the first Tuesday of each month from 15:30 to 16:30, usually in room A709.
A renowned expert (being an excellent speaker as well) visits us for an afternoon and gives a panorama of one of her research areas. The talk is meant to be accessible to all members of the lab, including PhD students in analysis, game theory, probability and statistics. Ideally, it should start gently with an historical background on the problem and an overview of the main questions and applications, keeping a non technical style during at least the first half of the talk. Of course it is also nice to have a part with more mathematical details: the most appreciated colloquia were those in which the speaker succeeded to develop a nice technical idea or an elegant argument that everyone should know.
Food and drinks are served after the event, usually in Espace 7!
Date: Tuesday, November 5th 2024 (15:30-16:30, room A709)
Speaker: (Sorbonne Université)
Title: Geometry of excursion sets: Computing the surface area from discretized points
Abstract: The excursion sets of a smooth random field carry information on the field that can be recovered using various geometric measures, such as the area or surface area of the excursion sets. After an introduction on these geometrical quantities, showing how they can be related to some parameters of the field, we focus on the problem of discretization. One never has access to the continuous observation of the excursion sets, but rather to observations at discrete points in space. In dimensions 2 and 3 and for specific regular grids, it has been reported that the usual estimate of the surface area of the excursion sets remains biased even when the grid becomes dense in the domain of observation. We study this limiting bias in any dimension and for polytopic tessellations. (Based on joint work with R. Cotsakis and E. Di Bernardino).