Journée de l'équipe Combinatoire et Optimisation

vendredi 27 juin 2025, 11:00 → 16:30 Europe/Paris

Salle 15-16 101 (Jussieu)

La journée 2025 de l'équipe Combinatoire et Optimisation de l'IMJ-PRG a eu lieu le vendredi 27 juin. Les exposés ont été donnés en salle 15-16 101, avec un buffet-déjeuner en salle 15-16 417. Voici une photo des convives.

 

11:00 → 11:15 Jean-Paul Allouche : A tribute to Tom Johnson, or music composition from mathematical objects¶

Tom Johnson passed away on December 31, 2024. An American composer living in Paris, he was a ``minimalist'', composing his music from mathematical objects. We will give a short survey of some of his work and ask about links (if any) between math. and music.

11:15 → 11:30 Ennio Grammatica : Computing the genus of an algebraic curve¶

11:30 → 11:45 Thomas Lejeune : Enumeration of planar hypermaps with general boundary conditions¶

A way of studying bidimensional physics on random Riemann surfaces is by discretizing them, hence an embedding of a graph in on of these surfaces is called a map, which is called planar if the graph is drawn on a sphere.

In this talk I will present some beautiful results on bicolored maps, which we call hypermaps, and show a general method that enables us to decompose any hypermap into simpler ones, using the method of slice decomposition.

11:45 → 12:00 Mingzhi Zhang : Unimodality in characteristic polytopes¶

12:00 → 14:00 Pause déjeuner

14:00 → 15:00 Elsa Marchini : Optimally Controlled Moving Sets with Geographical Constraints¶

(exposé donné dans le cadre du séminaire Combinatoire, Optimisation, et Interactions)

The talk is concerned with a family of geometric evolution problems, modeling the spatial control of an invasive population within a plane region bounded by geographical barriers.

The ``contaminated region'' is a set moving in the plane, which we would like to shrink as much as possible. To control the evolution of this
set, we assign the velocity in the inward normal direction at every boundary point.

Three main problems are studied: existence of an admissible strategy which eradicates the contamination in finite time, optimal strategies
that achieve eradication in minimum time, strategies that minimize the average area of the contaminated set on a given time interval.

For these optimization problems, a sufficient condition for optimality is proved, together with several necessary conditions. Based on these
conditions, optimal set-valued motions are explicitly constructed in a number of cases.

15:00 → 15:30 Pause

15:30 → 15:50 Vasiliki Petrotou : Combinatorics meets Commutative Algebra: The degenerate Kustin-Miller unprojection method¶

Unprojection is a method in commutative algebra that allows to construct and analyze commutative rings in terms of simpler ones. In addition, it sometimes reveals hidden geometric or combinatorial patterns. In 1983, A. Kustin and M. Miller introduced the simplest and most classical form of this method, known as Kustin–Miller unprojection. Over a decade later, in 1995, M. Reid independently rediscovered a similar procedure while pursuing applications in algebraic geometry. Since then, Kustin–Miller unprojection has found wide-ranging applications in both algebraic geometry and algebraic combinatorics. Recently, in joint work with K.A. Adiprasito and S.A. Papadakis, we introduced a variation of this method, which we call degenerate Kustin–Miller unprojection. In this talk, I will introduce the key ideas behind the classical Kustin–Miller unprojection, explain how the degenerate version extends the method, and discuss its connections and applications in combinatorics.

15:50 → 16:10 Geunho Lim : Bounds on Cheeger-Gromov invariants and simplicial complexity of triangulated manifolds¶

Using L^2 cohomology, Cheeger and Gromov define the L^2 rho-invariant on manifolds with arbitrary fundamental groups, as a generalization of the Atiyah-Singer rho-invariant. There are many interesting applications in geometry, topology, and combinatorics. In this talk, we show linear bounds on the rho-invariants in terms of simplicial complexity of manifolds by using hyperbolization methods. As applications, we give new concrete examples in the complexity theory of high-dimensional (homotopy) lens spaces. This is a joint work with Shmuel Weinberger.

16:10 → 16:30 Jesse Elliott : Sampling One Point per Connected Component of a Smooth Real Complete Intersection¶