Institut de recherche mathématique avancée

Résumé : Since its inception in 2008 as the underlying technology behind Bitcoin, blockchain has evolved far beyond its cryptocurrency origins. Over the past decade, various blockchain systems have emerged, demonstrating diverse applications across industries. This talk provides a quick dive into blockchain analysis. I will cover the essentials of blockchain technology with a focus on consensus protocols like proof-of-work and proof-of-stake before discussing some applications in Finance and Insurance.

The seminar will take place in the Amphithéâtre du Bâtiment de la Grande Coupole, opposite the entrance at 11 rue de l'Université.

Pierre-Olivier Goffard is an Associate Professor at the University of Strasbourg, France. He conducts research at the intersection of applied probability, statistics, and their applications in finance and insurance. His areas of expertise encompass blockchain technology and Bayesian statistics. Pierre-Olivier actively participates in the actuarial science program at the University of Strasbourg, where he teaches courses on stochastic calculus and survival analysis.

Résumé : In this talk, we explore the Serre–Green–Naghdi equations, which describe shallow-water waves while considering the influence of surface tension. These equations are locally (in time) well-posed. We identify a class of smooth initial data, leading to the development of singularities in finite time for the corresponding strong solutions. Additionally, we demonstrate the existence of global weak solutions for small-energy initial data.

Résumé : Given a reasonable topological space or algebraic variety, its covering spaces are classified by the fundamental group, via the monodromy correspondence. Recently, this was upgraded to an exodromy correspondence, classifying constructible sheaves as representations of a 'stratified fundamental category'. I will show how to prove this for toric varieties over an arbitrary field, including an explicit determination of the fundamental category. Over the complex numbers, this is a slight simplification of a result of Braden and Lunts from 2006.

Résumé : Before the development of modern algebraic geometry with tools such as sheaves and schemes, geometers tried to classify two-dimensional varieties defined by polynomial equations over the field of complex numbers. This zoology use mainly minimal models and blow-up, this tools are the basis of birational geometry which can be generalized to larger dimension. The presentation will focus mainly on the geometrical meaning of these concepts applied to algebraic complex surfaces.