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Résumé : Consider closed holomorphic curves in symplectic $G$-manifolds, with respect to a $G$-invariant almost complex structure. We should not expect the moduli space of such curves to be a manifold (after all, transversality and symmetry are famously incompatible). However, we can hope for a clean intersection condition: the moduli space decomposes into countably many disjoint strata which are smooth manifolds, whose dimensions are explicitly computable.

I present this decomposition for simple curves, and indicate how to extend this to multiple covers. These are the first steps towards a well-behaved theory of equivariant holomorphic curves. This has applications to the 3-body problem and real Gromov-Witten theory.

Résumé :  Any closed, flat Riemannian manifold is finitely covered by the torus, by Bieberbach's classical theorem. Similar classifications have been pursued for closed, Riemannian conformally flat manifolds, as well as for closed, flat Lorentzian manifolds. I will present the classification of closed, Lorentzian conformally flat manifolds with unipotent holonomy. This is joint work with Rachel Lee.

Résumé : It is well known that cluster structures and Poisson structures in the algebra of regular functions on a quasi-affine variety are closely related. In this talk, I will discuss this connection for Poisson structures on a simple simply connected complex Lie group G defined by a pair of classical R-matrices. The key element of the construction is a rational Poisson map from the group with a bracket defined by a pair of suitably chosen standard R-matrices to the same group with an arbitrary pair of R-matrices. In the case of G=SL_n one can build explicitly the corresponding cluster structure and prove its regularity and completeness.

Résumé : In this talk, we discuss the construction cluster structures on the symplectic groupoid of upper-triangular structures and related structures on the Teichmuller spaces. This is a joint project with L. Chekhov.

Résumé : After providing a short overview of the interdisciplinary research we are carrying on in the field of Structural Music Information Research (SMIR), we focus on two very active axes: the application of mathematical morphology to music analysis and the algebraic combinatorics of a special family of rhythmic structures. Although mathematical morphology was originally developed for image processing, it has been successfully applied to pattern discovery in the case of symbolic music representations (i.e. representations such as MIDI that are not based on the audio signal). We will present some recent approaches aiming to extend the classical morphological operators (erosion, dilation and opening) to the case of pattern discovery up to variations. These constructions can also be applied to the study of musical meters and rhythms, together with some other approaches that are more algebraically oriented. We will focus in particular to the family of so-called "perfectly balanced rhythms", i.e. rhythms that are obtained as sums or differences of regular rhythms seen as regular polygons within a cyclic group of a given order. Surprisingly, the classification of these algebraic structures remains an open problem in mathematics.

Moreno Andreatta holds diplomas in mathematics from the University of Pavia, piano performance from the Novara Conservatory and computational musicology from the EHESS in Paris. Senior researcher in maths & music at CNRS/IRMA he is also associate researcher at IRCAM. He is at the present the coordinator of the SMIR (Structural Music Information Research) and LaMaMu (LaboMathéMusique) projects at IRMA.

Paul Lascabettes is a postdoctoral researcher at IRMA at the University of Strasbourg, working on the discovery of musical patterns and the generation of musical rhythms. He holds a PhD in mathematics applied to music, obtained at IRCAM and Sorbonne University under the supervision of Isabelle Bloch and Elaine Chew.

Résumé : Dans un article méconnu de 1844, G. Eisenstein suggère une piste pour étendre la théorie des fonctions elliptiques au cas de "réseaux de rang 3". Il indique également que la nouvelle classe de produits infinis méromorphes qu’il considère possède de riches applications arithmétiques. Je présenterai des résultats de nature expérimentale et théorique qui donnent à penser qu’il avait effectivement mis à jour un analogue pour les corps cubiques complexes de la théorie de la multiplication complexe pour les unités elliptiques. Il s’agit d’un travail en commun avec Nicolas Bergeron et Luis Garcia.

Résumé : Finding the solutions to a system of polynomial equations is hard, but counting the number of solutions is a surprisingly doable computational problem. This is because of Bernshtein's theorem, which relates the number of solutions to the volume of certain polyhedra in affine euclidean space. We will explain this result and maybe show how effective it is for computations.

Résumé : Résumé : Le groupe pro-unipotent DMR0, qui sous-tend le schéma des relations de double mélange satisfaites par les nombres zêtas multiples (Racinet 2002), est un sous-groupe de celui des automorphismes de l'algèbre de Lie libre en deux générateurs e0 et e1, envoyant e1 sur lui-même et e0 sur un conjugué. Nous montrons que DMR0 est en fait contenu dans le sous-groupe des automorphismes spéciaux, c'est-à-dire envoyant également einfty:=-e0-e1 sur un conjugué, et est globalement invariant sous l'involution du groupe des automorphismes spéciaux induit par l'échange de e0 et einfty (travail commun avec H. Furusho).

Résumé :

Dans ce sem’in, nous présenterons OPLA, un générateur de pages personnelles à destination du personnel de recherche. OPLA transforme simplement un fichier Markdown en une page web personnelle. L’outil intègre automatiquement vos publications scientifiques depuis des fichiers BibTeX ou directement depuis HAL.

Au programme :

• Démonstration de la création et de l’édition d’une page OPLA

• Présentation de deux méthodes de publication :

  1. Via gitlab.math.unistra.fr avec GitLab Pages
  2. En ligne de commande vers le répertoire public_html sur file.math.unistra.fr

Que vous souhaitiez créer votre première page web ou moderniser une page existante, ce sem’in est fait pour vous !

Résumé : In this work, we are interested in the mathematical modeling of the impact of apoptosis on the dynamics of cellular tissues, and in particular on cell tissue fluidity. Indeed, cell apoptosis corresponds to the programmed cell death: when they leave the tissue, they induce local contractions but also enable cells rearrangements.

We first propose an individual-based model that provides the dynamics of the positions, velocities and polarities of the cells, idealized as hard spheres. Cells interact with each other through contact forces, smooth attraction, and polarity alignment. The model also involves a microscopic description of apoptotic and proliferation events. The present work is an extension of the model proposed in [3] and validated by experiments on cellular rings. Numerical simulations are performed and several indicators of fluidity are analyzed.

Next, we derive a macroscopic description, following the methodology proposed in [1], [2]. We start from a mean-field dynamics of the kinetic distribution function in phase-space (position, polarity, radius), where contact forces have been replaced with repulsion forces. We then introduce a specific time and space rescaling and identify the equilibria distribution functions, which are parameterized by two macroscopic quantities: the density and the mean polarity. Based on the Generalized Collision Invariant (GCI) method [2], we are then able to identify their dynamics: the resulting description can be seen as a modified Self-Organized Hydrodynamics (SOH) model. We finally discuss the obtained model and highlight the effect of the apoptotic events on the dynamics.

This is a joint work with Laurent Navoret (Université de Strasbourg) and Marcela Szopos (Université Paris Cité). It has also been carried out in collaboration with Romain Levayer (Institut Pasteur) and Daniel Riveline (IGBMC, Université de Strasbourg) in the context of the ANR project MAPEFLU.

References

[1] Degond, P., Dimarco, G., Mac, T. B. N., and Wang, N. Macroscopic models of collective motion with repulsion. Communications in Mathematical Sciences, 13(6), 1615–1638 (2015).

[2] Degond, P., and Motsch, S. Continuum limit of self-driven particles with orientation interaction. Mathematical Models and Methods in Applied Sciences, 18(supp01), 1193–1215 (2008).

[3] Vecchio, S. L., Pertz, O., Szopos, M., Navoret, L., and Riveline, D. Spontaneous rotations in epithelia as an interplay between cell polarity and boundaries. Nature Physics (2024).

Résumé : TBA

Résumé : Online