Séminaires doctorant en 2020

Sperm whales have the loudest sonar in the animal kingdom. However, they are too large and heavy to have their head scanned. In order to validate a model made from vague organ geometry and rough estimation of mechanical parameters, I used recorded clicks to evaluate the synthetic clicks created by this model. I will first present the techniques used to locate sperm whales using a multi hydrophone antenna, and linked recorded clicks to their emitter using segmented video. I will then recall the techniques use to simulate wave propagation. Finally I will present the results of a wave propagation in the head of a sperm whale , and how to improve it, using the recorded clicks.

Je vous présenterai en avant-première l’exposé de ma soutenance de thèse. On s’intéresse à certaines suites infinies de caractères, que l’on engendre à l’aide d’itérations des morphismes particuliers appelés substitutions. Pour de telles suites, on cherchera s’il existe une lettre qui se répète périodiquement. On distinguera deux cas, selon que la substitution considérée soit de longueur constante ou non. Dans ce but, on utilisera des procédés provenant de l’étude des systèmes dynamiques topologiques, en particulier les valeurs propres associées à de tels systèmes. Une autre partie de l’exposé portera sur l’étude de la substitution permettant d’engendrer une sous-suite extraite d’une suite substitutive, et notamment du lien entre les valeurs propres des matrices qui y sont associées. This talk is the presentation of my PhD’s defense. It will be in french. The topic is a class of infinite sequence of symbols generated by the iteration of certain type of morphisms called substitutions. For such sequences, we want to check if a letter appears periodically. We will consider two cases : whether the substitution is of constant length or not. We will use some tool that comes from dynamical systems, especially the eigenvalues associated to such systems. An other part of the talk is devoted to the study of the substitution that generate a sequence extracted periodically from a substitutive one, and in particular the link between the eigenvalues of the underlying matrices.

Gentle algebras are algebras arising as certain quotients of path algebras of quivers. One of the interesting features of gentle algebras is that there is a combinatorial classification of their indecomposable modules. Another deep fact about gentle algebras is that they are stable under derived equivalences ; recent advances have led to a classification of gentle algebras up to derived equivalence. After recalling the relevant notions, the main goal of the presentation will be to introduce a mutation operation on gentle algebras and their modules, inspired by the reflection functors that exist for hereditary algebras, which give a very explicit and concrete way to pass from modules for one gentle algebra to modules for (some) derived equivalent gentle algebras.

Le but de cet exposé est de présenter "l’hypothèse du cobordisme". Ce théorème établit une correspondance entre les théories des champs quantiques et topologiques (TCQT) et les objets dualisants d’une certaine catégorie. Les TCQT, issues de la physique, nous intéressent car elles nous renseignent sur la structure des variétés et permettent d’en extraire des invariants. Les notions intervenant dans ce théorème seront progressivement définies dans cette présentation. On terminera par une application de ce résultat.

The voting system that is most commonly used in political elections (the first-past-the-post system FPTP) has major defects : for example, it yields compromising dilemmas and tactical voting. Does there exist voting systems that do not share these defects ? Is there even an optimal system, say with respect to robustness to manipulability ? Mathematics provide certain pieces of answer to these questions. My talk will present some of these results and describe certain voting systems that are considered more relevant and more democratic that the usual FPTP. The presentation should be very accessible, as it only relies on rather elementary mathematics.

We are trying to understand the variation of the sum of digits when we add a fixed integer written in base  : it gives informations on the number of carries created during such an addition. We are particularly interested in the asymptotic properties of this variation : for which density is the variation a particular integer ? To answer this question, we will place ourselves in a more general space than the natural numbers : the -adic integers and more precisely, in the context of the odometer. We will take the opportunity to introduce the very practical Rokhlin towers of this dynamical system. Finally, we will state a CLT related to the above question and which extends a result of Emme and Hubert. On cherche à comprendre la variation de la somme des chiffres quand on ajoute un entier écrit en base  : elle donne des informations sur le nombre de retenues créées pendant une telle addition. On s’intéresse en particulier aux propriétés asymptotiques de cette variation : pour quelle densité la variation vaut elle un certain entier relatif ? Pour y répondre, on se placera dans un cadre plus général que les entiers naturels : les entiers -adiques et plus précisément, dans le cadre de l’odomètre. On en profitera pour introduire les très pratiques tours de Rokhlin de ce système dynamique. Enfin, on énoncera un TCL en lien avec la question plus haut et qui étend un résultat de Emme et Hubert.