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TBA
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TBA
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Orateurs et oratrice
Enguerrand Brun (UMPA) Tristan Bullion-Gauthier (ICJ) Théo Fradin (LAMA) Théotime Girardot (IF) Ward Haegeman (LAMA) Maxime Ingremeau (IF) Carlo Marcati (ICJ) Arnaud Munch (LMBP) Charlotte Perrin (LJK) Gabriele Todeschi (LJK) Francesco Vecil (LMBP) Julien Vovelle (UMPA)
PROGRAMME: https://jeara2026.sciencesconf.org/program?lang=fr
Nous obtenons une règle de Descartes permettant de borner le nombre de solutions positives de n'importe quel système polynomial généralisé (les monômes ont des exposant réels) carré. C'est une règle de Descartes au sens où elle est déterminée par des signes attachés aux matrices des coefficients et des exposants (les signes des mineurs). Notre règle de Descartes généralise celle obtenue par Bihan-Dickenstein-Forsgard dans le cas des circuits. La preuve s'obtient en raffinant la preuve des bornes fewnomiales obtenues par Bihan-Sottile en 2007 en considérant le système de Gale correspondant dans le complémentaire d'un arrangement d'hyperplans. Les signes ont plusieurs sources: notamment, la combinatoire de l'arrangement d'hyperplans et du système de Gale, une minoration du degré topologique d'une application donnée par des jacobiens successifs au dessus d'une chambre.
Orateurs et oratrice
Enguerrand Brun (UMPA) Tristan Bullion-Gauthier (ICJ) Théo Fradin (LAMA) Théotime Girardot (IF) Ward Haegeman (LAMA) Maxime Ingremeau (IF) Carlo Marcati (ICJ) Arnaud Munch (LMBP) Charlotte Perrin (LJK) Gabriele Todeschi (LJK) Francesco Vecil (LMBP) Julien Vovelle (UMPA)
PROGRAMME: https://jeara2026.sciencesconf.org/program?lang=fr
TBA
Les diagrammes de Blaschke–Santaló permettent de visualiser les inégalités optimales reliant des fonctionnelles données. Cet exposé en présentera le principe et les principales techniques d’analyse à travers une étude théorique détaillée du diagramme associé au périmètre, au volume et à la première valeur propre du laplacien Dirichlet. Nous aborderons ensuite des méthodes numériques permettant d’approcher ces diagrammes. L’exposé s’appuiera sur des travaux en collaboration avec Jimmy Lamboley et Eloi Martinet.
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We consider the low-Mach-number limit of a compressible two-phase flow model with algebraic pressure closure. We first derive formally the corresponding incompressible non-homogeneous two-phase system: the phase densities become constant, while the volume fractions remain variable and are transported by the flow. We then discuss the rigorous convergence towards this limit. The main difficulty lies in obtaining strong convergence of the partial masses, which is not directly controlled by the standard relative entropy. A logarithmic relative entropy provides the additional control required to close the argument.
On considère un corps $K$ muni d'une mesure et d'une distance. La densité locale d'un ensemble $X$ dans $K^n$ en un point est définie comme la limite, si elle existe, de volumes locaux normalisés. On peut généraliser cette notion à des corps valués pour lesquels il n'existe pas de théorie de la mesure classique, comme $\mathbb{C}(!(t)!)$, en utilisant l'intégration motivique. Le but de cet exposé est de présenter une formule permettant le calcul de la densité locale motivique de singularités isolées de surfaces, en utilisant une donnée supplémentaire : les taux internes reliés à la géométrie bilipschitz de la singularité, introduits par Birbair, Neumann et Pichon.
Humans are pretty good at coming up with heuristics that solve hard problems almost optimally. In the 1980s and 1990s, researchers began asking whether it was possible to design efficient algorithms that approximately solve hard problems, such as NP-hard problems. For some problems, there was success, for others, not so much. This led to a fundamental question: Can we rule out the existence of good approximation algorithms?
There were some lower bounds, but a general methodology for proving such results was lacking. Then came the PCP theorem, which provided a powerful new way to prove hardness of approximation and has since become a go-to hammer for establishing limits on approximation algorithms.
In this mini course, we will start with the definition of a NP, see why it naturally leads to inapproximability results, and then prove the PCP theorem (or at least a weaker version of it). The course will consist of 2 talks, with the following rough outline.
Talk 2: A strategy towards proving the PCP theorem, abstracting out the steps, testing zeroeness of a polynomial is enough, zero-on-variety test. This talk will be based on parts from https://eccc.weizmann.ac.il/report/2025/165/ and https://eccc.weizmann.ac.il/report/2026/134/. These are joint works with Prashanth Amireddy, Srikanth Srinivasan, Madhu Sudan, and Sophus Valentin Willumsgaard.
Humans are pretty good at coming up with heuristics that solve hard problems almost optimally. In the 1980s and 1990s, researchers began asking whether it was possible to design efficient algorithms that approximately solve hard problems, such as NP-hard problems. For some problems, there was success, for others, not so much. This led to a fundamental question: Can we rule out the existence of good approximation algorithms?
There were some lower bounds, but a general methodology for proving such results was lacking. Then came the PCP theorem, which provided a powerful new way to prove hardness of approximation and has since become a go-to hammer for establishing limits on approximation algorithms.
In this mini course, we will start with the definition of a NP, see why it naturally leads to inapproximability results, and then prove the PCP theorem (or at least a weaker version of it). The course will consist of 2 talks, with the following rough outline.
Talk 1: Introduction to PCP, Gap Problems, Hardness of approximation for Gap problems, Intuition behind why even the PCP theorem is true. Finally, if time permits, then a strategy towards the proof of PCP theorem.
The goal of this talk is to introduce skeletal semantics, a software framework for specifying and analysing programming languages, and provide a mathematical foundation for it. To this end, we will first introduce SKI calculus as an example of a target programming language and we will show how skeletal semantics can be used to specify it. In a second part, we will motivate our mathematical setting by introducing initial algebra semantics and Lawvere theories, before studying virtual double theories. They are a virtual-double-categorical extension of the latter, allowing for the interpretation of some morphisms as relations. Finally, we show that a skeletal specification (in particular the one of the SKI calculus) may be interpreted as a presentation of a virtual double theory, so that its category of models provides the intended language.