Le colloquium de mathématiques est une activité scientifique mensuelle de l'IRMP. Il consiste en un exposé d'une heure au cours duquel l'orateur présente un thème lié à la recherche en mathématiques. Le public cible est généraliste, il inclut l'ensemble des membres de l'IRMP: doctorants, post-docs et professeurs de tous les domaines de recherche. Les étudiants de master sont également les bienvenus.
Responsable du Colloquium : Prof. Tom CLAEYS
A venir
Thursday February 22 16h15 (CYCL01)
Speaker: Prof. Jean-Charles Delvenne (ICTEAM - UCLouvain)
Markov chains, transport theory and statistical physics
Abstract: We look at the following motivating problem: how to move an electronic memory from a 'zero' state to a 'one' state, at minimal energy cost? Mathematically, this amounts to design a Markov chain that drives a certain probability measure (encoding a 'zero') towards another one (a 'one') through an 'optimal' path --- an avatar of Gaspard Monge's so-called 'earth mover problem', at the core of transport theory. We explore various recent results and conjectures around this theme at the interface of statistical physics and Markov chain theory. We support these by illustrations on realistic simulations on electronic memories.
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Colloquium 2023
Jeudi 14 décembre 16h15 (CYCL01)
Prof. Johan Segers (ISBA - Institut de statistique, biostatistique et sciences actuarielles UCLouvain)
Measuring dependence between random vectors via optimal transport
Abstract: Joint work with Gilles Mordant (Universität Göttingen, formerly UCLouvain).
The Wasserstein distance is a metric on the space of probability measures on a common Euclidean space. It relies on the notion of optimal couplings, which formalise the idea of minimizing the cost of transporting mass so as to transform one measure into another. For absolutely continuous measures, the optimal coupling takes the form of a deterministic transformation which satisfies a multivariate form of monotonicity called cyclic monotonicity and which can be loosely described as being the gradient of a convex function. Between centered Gaussian measures, the optimal transport map is linear and is the solution of an interesting matrix equation. We rely on the latter solution to propose a new coefficient of dependence between random vectors of possibly different dimensions. Maximum dependence occurs at the joint covariance matrix with minimal von Neumann entropy under certain constraints. The dependence coefficient can be estimated accurately from data using their component-wise ranks.
Jeudi 25 mai 16h15 – 17h15 (CYCL01)
Prof. Maria Manuel Clementino (Université de Coimbra) : Shuffling groups and topologies using categories
Abstract: Category theory plays a key role on the unification of results and clarification of their essence, on simplification of proofs, and on the conception of new ideas. This talk intends to present, to a general mathematical audience, instances of each of these facets, having as common ground the study of topological groups and continuous group homomorphisms.
Jeudi 13 avril 16h15 – 17h15 (CYCL01)
Mathematics Colloquium Special edition on The ecological footprint Of the IRMP researcher
Mini-talks
- Marc Servais, Chargé de mission développement durable, UCLouvain en Transition
- Pierre-Emmanuel Caprace, IRMP Green Team
Followed by discussion and poll
Math-Break : All attendees are welcome for drinks and snacks from 16h onwards