22 avril 2020

Andras Szenes (Université de Genève)
Thom polynomials and multipoint formulas

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Lieu : Zoom - Demander le lien pour rejoindre l’exposé à
jean-michel.bismut chez math.u-psud.fr

Résumé : Global singularity theory deals with topological obstructions to the existence of various types of singularities of maps.
The subject has its beginnings in the works of Thom in the 50s, then Damon in 70s, who described the general form of the single point formulas.
Multipoint formulas are a classical subject which were the systematically studied by Kleiman and Katz in the 80’s. Finally, in the last 20 years, Kazarian and Rimanyi came up with a stunning set of conjectures linking the two problems. I will describe all this, as well as recent joint work with G. Berczi on a promising approach to these conjectures.

Thom polynomials and multipoint formulas  Version PDF

Mohamed-Slim Kammoun (Laboratoire Paul Painlevé, Université de Lille)
Plus longue sous-suite commune de permutations aléatoires (en ligne)

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Résumé : Bukh et Zhou ont conjecturé que pour deux permutations i.i.d, l’espérance de la longueur de la plus longue sous-suite commune est minorée par $\sqrtn$. Ce problème peut se ramener à la compréhension de la plus longue sous-suite croissante de permutations aléatoires. On détaillera le cas où la loi de la permutation est stable sous conjugaison qui peut être traité à l’aide de la compréhension de la structure en cycle de la composée de deux permutations indépendantes.

Plus longue sous-suite commune de permutations aléatoires (en ligne)  Version PDF

Maud DELATTRE (AgroParisTech/INRAE)
Inference for partially observed epidemic dynamics guided by Kalman filtering techniques

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Résumé : Estimating the parameters governing epidemic dynamics, such as the transmission rate, from available data is a major issue in order to provide reliable predictions of these dynamics and of the impact of control strategies. In this context, several difficulties occur : all the components of the system dynamics are not observed, and data are available at discrete times with measurement errors. Diffusion processes with small diffusion coefficient are a convenient set-up for modelling epidemics
the small diffusion coefficient being related to the population size. To estimate the key epidemic parameters, we therefore propose to consider time-dependent diffusion processes on R^p satisfying a stochastic differential equation.
In practical applications on epidemic dynamics, it often occurs that some coordinates of the process are not observed and, when observed, measurement errors are systematically present. We are then concerned with the estimation of the parameters when the diffusion process is discretely observed with noise and with sampling step on a finite time interval and when some components of the process cannot be observed. We propose a procedure derived from Kalman filtering approaches to compute estimates of the parameters based on approximate likelihoods. Our approach is original because
it combines the framework of diffusions with small diffusion coefficient with approximate likelihood methods and Kalman filtering, the latter being little exploited for the inference of epidemic dynamics partially observed and with errors.
We carry out simulation studies to assess the performances of the proposed methods. Applications to real epidemic data are still in progress.

Inference for partially observed epidemic dynamics guided by Kalman filtering techniques  Version PDF