Marie Albenque is a CNRS researcher at the department of computer science at École Polytechnique in Paris, working at the interplay of combinatorics and probability. In 2017 she co-organizes the thematic trimester “Combinatorics and interactions” at the Institute Henri Poincaré in Paris.
She’s one of the Blackboard Whisperers, see her complete interview here.
Marie’s diverse research interests have all in common that they involve a combined use of combinatorics and probability. This is the case, for example, of her work in random planar maps, where one considers a discretization (polygonization) of a smooth surface embedded in a sphere. Here, the goal is to study a sequence of these polygonizations (like quadrangulations or triangulations) when the number of polygons increases (or, what is the same, when the size of the polygons shrink). It turns out that although there are many different ways to consider a sequence of polygonizations, many of them converge in the limit to one universal object, called a Brownian map. Much like a random walk converges to a Brownian motion. The mathematical theory behind random maps takes care that these mathematical objects are well defined, can be considered as metric spaces, and that it makes sense to compute with them, that is, that one can define sequences of such objects and take limits in a certain sense. The subject of random maps has gathered a lot of attention in the recent years and is leading to new discoveries in probability theory, because of its interactions with other modern fields, discrete mathematics, geometry and physics.