The mathematics colloquium is a monthly scientific activity organised by the IRMP. It consists of a one-hour talk in which the speaker presents a theme related to research in mathematics. The target audience is general and includes all IRMP members: doctoral students, post-docs and professors from all research fields. Masters students are also welcome.

Colloquium coordinator : Prof. Tom CLAEYS

### Upcoming events

**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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### 2023 Colloquium

**Thursday december 14, 16h15 (CYCL01)**

Prof. **Johan Segers** (ISBA - Iof Statistics, Biostatistics and Actuarial Sciences - 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.

**Thursday May 25, 4.15 pm– 5.15pm (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.

**Thursday April 13, 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