# 13 mars 2018: 4 événements

## Séminaire

### Du 26 février au 15 mars - Alexander BUFETOV

Collaboration scientique avec A.DYMOV & P.NIKITIN

Résumé : Work on the infinite dimensional stochastic differential équations & work on Pfaffian processes

Lieu : Steklov Institute (Moscou&St.Pétersbourg)

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### Mardi 13 mars 11:00-12:00 - Mattia GALEOTTI - IMJ, Paris

Moduli of curves with principal and spin bundles : the singular locus via graph theory

Résumé : In a series of recent papers, Chiodo, Farkas and Ludwig carried out a
deep analysis of the singular locus of the moduli space of stable (twisted) curves
with an $\ell$-torsion line bundle. They showed that for $\ell\leq 6$ and $\ell\neq 5$
pluricanonical forms extend over any desingularization.
This opens the way to a computation of the Kodaira dimension without desingularizing,
as done by Farkas and Ludwig for $\ell=2$,
and by Chiodo, Eisenbud, Farkas and Schreyer
for $\ell=3$.
We can generalize this works in two directions.
At first we treat roots of line bundles on the universal curve systematically :
we consider the moduli space of curves
$C$ with a line bundle $L$ such that $L^\xx\ell\cong\omega_C^\xx k$.
New loci of canonical and non-canonical singularities appear
for any $k\not\in\ell\Z$ and $\ell>2$, we provide a set of combinatorial tools allowing us
to completely describe the singular locus in terms of dual graphs.
Furthermore, we treat moduli spaces of curves with a $G$-cover
where $G$ is any finite group. In particular for $G=S_3$ we approach
the evaluation of the Kodaira dimension of the moduli space, and list
the remaining obstacles to calculate it.

Lieu : CMI, salle C003 - I2M - Château-Gombert
39 rue Frédéric Joliot-Curie
13453 Marseille cedex 13

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En savoir plus : Séminaire Géométrie Complexe

### Mardi 13 mars 11:00-12:00 - Adrien RICHARD - I3S, Université de Sophia-Antipolis

Fixing monotone boolean networks asynchronously

Résumé : A monotone boolean network with n components is a directed graph on [n]≔1,…,n where each vertex is labeled by a binary variable and a local transition function, which is monotone, boolean and whose inputs are the binary variables of the in-neighbors. An asynchronous run consists in updating vertices, one at each step, by applying its local transition function. Thus a run can be described by the sequence of vertices to update, that is, a word on the alphabet [n]. We prove that there exists a word W on [n] of cubic length such that, for every monotone network with n components, and for every initial configuration, the run described by W leads to a fixed configuration. We also prove that any word with this property is at least of quadratic length. To construct W, we use the following basic result about n-complete words : there is a word of quadratic length containing, as subsequences, all the permutations of [n]. For the lower-bound, we prove the following : there exists a subexponential set of permutations of [n] such that every word containing all these permutations as subsequences is of quadratic length.
This is a joint work with Julio Aracena, Maximilien Gadouleau and Lilian Salinas. A preprint is available here : https://arxiv.org/abs/1802.02068.

Lieu : Salle des séminaires 304-306 (3ème étage) - Institut de Mathématiques de Marseille (UMR 7373)
Site Sud - Bâtiment TPR2
Campus de Luminy, Case 907
13288 MARSEILLE Cedex 9

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En savoir plus : Séminaire Dynamique, Arithmétique, Combinatoire (Ernest)

### Mardi 13 mars 11:00-12:00 - Weiwei DING - Meiji University

Dynamics of time-periodic reaction-diffusion equations with compact initial support on R

Résumé : This work is concerned with the asymptotic behavior of bounded solutions of the Cauchy problem

where $u_0$ is a nonnegative bounded function with compact support and $f$ is periodic in $t$ and satisfies $f(\cdot,0)=0$. We first prove that the $\omega$-limit set of any bounded solution either consists of a single time-periodic solution or it consists of time-periodic solutions as well as heteroclinic solutions connecting them. Furthermore, under a minor nondegenerate assumption on time-periodic solutions of the corresponding ODE, the convergence to a time-periodic solution is proved. Lastly, we apply these results to equations with bistable nonlinearity and combustion nonlinearity, and specify more precisely which time-periodic solutions can possibly be selected as the limit.
This is a joint work with Hiroshi Matano.

Weiwei DING

Lieu : CMI, salle de séminaire R164 (1er étage) - I2M - Château-Gombert
39 rue Frédéric Joliot-Curie
13453 Marseille cedex 13

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En savoir plus : Séminaire Analyse Appliquée (AA)

• # 13 mars 2018: 2 événements

## groupe de travail

### Du 12 au 16 mars - Pierre LAZAG

Collaboration scientifique avec Nizar DEMNI

Résumé : Collaboration portant sur l’étude des processus déterminantaux

Lieu : UFR Mathématiques Rennes

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### Mardi 13 mars 14:00-15:00 - Federico LO BIANCO - I2M, Aix-Marseille Université

Théorème de Torelli global

Résumé : TBA

Federico LO BIANCO

Lieu : CMI, salle C003 - I2M - Château-Gombert
39 rue Frédéric Joliot-Curie
13453 Marseille cedex 13

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En savoir plus : Groupe de Travail Espaces de modules de surfaces K3