Séminaire de Géométrie Enumérative


Contacts :
Penka Georgieva, Elba Garcia-Failde
Ilia Itenberg, Alessandro Chiodo


Année 2023 - 2024

Temps : Vendredi à 14h
Lieu : Jussieu, 1516 - 413

Institut de Mathématiques de Jussieu - Paris Rive Gauche,
Sorbonne Université


Date Orateur Titre et résumé Lieu
22/09/2023 Kento Osuga,
University of Tokyo
Refined correspondence between Hurwitz numbers and topological recursion
It has been proven that one can construct generating functions of Hurwitz numbers from topological recursion on an appropriate spectral curve. In this talk, I will explore this correspondence in a refined setting. On one hand, we have enumerative invariants of maps onto possibly nonorientable surfaces, and on the other hand, we have refined topological recursion on a refined spectral curve. After reviewing both aspects, I will give a sketch of how to prove their correspondence. If time permits, I will mention how far we can extend, and also mention other applications of the refined topological recursion. This talk is partly based on work in progress with Nitin Chidambaram and Maciej Dolega.
Jussieu,
1516 - 413
20/10/2023

Michele Ancona,
Université Côte d'Azur
Aspects métriques et spectraux des courbes planes aléatoires
Toute courbe complexe plane est munie d’une métrique riemannienne induite par la métrique ambiante de Fubini- Study du plan projectif complexe. Nous donnons des bornes inférieures probabilistes sur certaines quantités métriques et spectrales (telles que la systole ou le trou spectral) des courbes planes lorsque celles-ci sont choisies aléatoirement. Il s’agit d’un travail commun avec Damien Gayet.
Jussieu,
1516 - 413
17/11/2023

Francesca Carocci,
Université de Genève
Smooth compactifications of moduli of low genus curves in projective spaces —via log geometry and Gorenstein singularities
Moduli spaces of stable maps in higher genus have many components of different dimensions meeting each other in complicated ways, and the closure of the smooth locus (the so called main component) does not have a modular interpretation. Constructing modular desingularisations of the main component is strictly related to understanding degenerations of canonical divisors and Gorenstein singularities. I will explain how logarithmic and tropical techniques can be used to solve the problem in genus one and two and say a few words on how the methods used can be adapted to construct modular birational models of pointed curves in low genus. This is based on a joint work with L.Battistella.
Jussieu,
1516 - 413
30/11/2023
15h

Grigory Mikhalkin,
Université de Genève
Tropical trigonometry and wave fronts
We'll take a look at geometry of angles in the tropical plane by means of the tropical wave front evolution. Resulting caustic produces a subdivision of the tropical angle to the elementary (right) angles. If both bounding rays of the angle are rational then the angle corresponds to a toric surface singularity, and the caustic subdivision corresponds to the minimal toric resolution. Otherwise, the subdivision is infinite. Joint work with Mikhail Shkolnikov.
Jussieu,
1516 - 413
08/12/2023

Gurvan Mével,
Nantes Université
Universal polynomials for coefficients of tropical refined invariant in genus 0
An important application of tropical geometry is Mikhalkin's correspondence theorem. It states that counting algebraic curves on toric surfaces is the same as counting tropical curves with multiplicities. Several multiplicities can be chosen. In particular, the count with the Block-Göttsche multiplicities leads to the tropical refined invariant, which is a polynomial. In this talk we will investigate the polynomial behavior of the coefficients of this invariant.
Jussieu,
1516 - 413
19/01/2024

Thomas Blomme,
Université de Neuchâtel
Asymptotique des invariants raffinés
Il y a une dizaine d’années, I. Itenberg et G. Mikhalkin ont montré que le compte des courbes tropicales solutions de certains problèmes énumératifs avec la multiplicité de Block-Göttsche mène à de mystérieux invariants polynomiaux qui ont été au cœur de nombreux travaux depuis. Ceux-ci ont partiellement été démystifiés en les reliant à des invariants réels ou complexes. Plus récemment, E. Brugallé et A. Jaramillo-Puentes ont montré que les coefficients de co-degré fixé de ces polynômes avaient également un comportement polynomial. Des calculs explicites exigeants laissent suggérer une remarquable régularité de ces derniers et envisager une subtile « conjecture de Göttsche duale ».
Jussieu,
1516 - 413
09/02/2024

Sergey Finashin,
Middle East Technical University
Root eigenlattices and lines on real rational elliptic surfaces
In a joint work with V.Kharlamov, out aim is to understand the topology of sections (aka lines) of real rational elliptic surfaces. The main tool is the Mordell-Weil group (formed by automorphisms acting as a group shift in each elliptic fiber). In the complex setting, it can be identified with the lattice E_8, which acts freely and transitively on the set of lines. In the real setting, the real Mordell-Weil groups is identified with the (-1)-eigenlattice of the complex conjugation acting on E_8. It acts similarly on the set of real lines, which becomes a key to understand their topology.
Jussieu,
1516 - 413

Archive Séminaire de Géométrie Enumérative 2022/2023

Archive Séminaire de Géométrie Tropicale