Agenda depuis 2026

Seminaire : TOPOCS - séminaire Steve Oudot

02/02/2026 à 11h00

Title: "Preventing dimensional collapse in self-supervised learning" Subtitle: "A tale of sphere packings, minimum spanning trees, and topological data analysis" Abstract: "This talk is about recent work by my PhD student Julie Mordacq, who proposed a new regularizer based on minimum spanning tree length to prevent dimensional collapse in self-supervised learning. Focusing specifically on the joint-embedding problem, her work draws connections to dimension estimation, sphere packings, and topological data analysis. In the talk I will describe these connections and explain how they help address the problem via a remarkably simple method.

Seminaire : Séminaire ACRO : Lucas Picasarri-Arrieta (02/02, 10h00, REU 4.05)

02/02/2026 à 10h00

Lucas Picasarri-Arrieta (National Institute of Informatics, Tokyo) Title: Edge-colouring and orientations: applications to degree-boundedness and χ-boundedness 02/02/2026 10h00, salle REU 04.05 (LIS Luminy) Hide abstract We prove that every $2$-edge-coloured graph with sufficiently large minimum degree contains a monochromatic induced subgraph whose minimum degree remains large. As a consequence, we deduce that some classes of graphs are degree-bounded. A class $\mathcal{G}$ is degree-bounded if, for every integer $s$, there exists $d=d(s)$ such that every graph $G\in \mathcal{G}$ either contains $K_{s,s}$ or has minimum degree at most $d$. We obtain that the following classes are degree-bounded: (i) for every $k$, the graphs $G$ whose edge-set can be $k$-coloured such that no even hole of $G$ is monochromatic; (ii) for every fixed antidirected forest $F$, the graphs admitting an orientation without any induced copy of $F$; (iii) for every $\ell\geq 4$, the graphs admitting an orientation without any induced antidirected cycle of length at least $\ell$. For $k=2$, class (i) contains odd-signable graphs. Class (ii) characterises the oriented graphs $H$ such that the class of graphs admitting an orientation without any induced copy of $H$ is degree-bounded. For $\ell=5$, class (iii) contains Burling graphs. In case (i) and case (iii) for $\ell=4$, we further obtain that the classes are polynomially $\chi$-bounded.

Seminaire : Séminaire ACRO : Clément Legrand-Duschesne (12/01, 10h00, REU 4.05)

12/01/2026 à 10h00

Le séminaire de l'équipe ACRO aura lieu lundi 12 janvier à 10h en salle REU 04.05 du TPR2. On aura le plaisir d’écouter Clément Legrand-Duschesne (Jagiellonian University, Kraków) qui nous parlera de théorème de Dirac et de géométrie de couplages parfaits. Title: Dirac’s theorem and the geometry of perfect matchings Abstract: Dirac's theorem states that all $n$-vertex graphs with minimum degree $n/2$ contain a perfect matching. This is tight and graphs with minimum degree $cn$ are more generally called $c$-Dirac graphs. In fact, a phase transition occurs at $c=1/2$: $c$-Dirac graphs with $c \ge 1/2$ contain $(\frac{cn}{e+o(1)})^{n/2}$ perfect matchings [Cuckler, Kahn 2009]. Moreover, for any fixed $c$-Dirac graph $G$ with $c\ge 1/2$, there exist nice probability distributions on the perfect matchings of $G$ called spread distributions [Pham, Sah, Sawhney, Simkin 2024]; as a result, if the edges of $G$ are sampled with probability $O(\log(n)/n)$, the resulting graph still contains a perfect matching with good probability, thereby witnessing that these matchings are "everywhere" in $G$. With Ross Kang, we give a new understanding of this phase transition by describing how the perfect matchings of a Dirac graph cluster. More precisely, we analyse the geometrical properties of the space of perfect matchings of $G$, endowed with the graph metric such that perfect matchings differing on at most $k$ edges are at distance one. For any fixed $k$, we pinpoint sharp thresholds at which this space is shattered into exponentially many components, has isolated perfect matchings, becomes connected, or becomes an expander. https://acro.lis-lab.fr/seminars