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Résumé : As more and more mathematical content is published, having an efficient way to check its correctness is of vital importance. One helpful tool to this end is given by computer proof assistants. These are programming languages which understand definitions, theorems and proofs, and if a file compiles, then it means that everything that's written inside is correct!
Lean is among the most popular proof assistants at the moment. In this talk I will explain what it is, how it works and what kind of mathematics is contained in its library. I will then talk about my contributions and some of the hot projects the community is working on.

Résumé : Abstract: Consider the compact orbits of diagonal action on SL(3,R)/SL(3,Z). Each such compact orbit can be assigned a two dimensional lattice of periods in R^2 and thus a point in SL(2,R)/SL(2,Z). This is called the "shape" of the compact orbit. We show that the set of these shapes is dense in SL(2,R)/SL(2,Z). Joint work with Nguyen-Thi Dang and Jialun Li.

Résumé : The moduli space is the set of hyperbolic surfaces of a given topological type, up to isometries. It is naturally equipped with a finite measure which makes it a probability space. The geometric quantities that can be measured on hyperbolic surfaces then become random variables, so we can try to compute their expectation. This idea leads to the development of the theory of random hyperbolic surfaces: we compute the average geometric behavior of hyperbolic surfaces through the introduction of probabilistic tools. This presentation will introduce some of the main tools and results of this theory through the study of a typical example of random surfaces problem: the average counting of curves.

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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 be also broadcasted via BBB: https://bbb.unistra.fr/b/hum-51d-suf-mzq

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.

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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.

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