The seminar of the team Labo is under the responsibility of Michel Raibaut.
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Year 2016

Thursday 24th November 2016 at 15h Alicia Dickenstein (Universidad de Buenos Aires),
From chemical reaction networks to Descartes' rule of signs

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In the context of chemical reaction networks with mass-action and other rational kinetics, a major question is to preclude or to guarantee multiple positive steady states. I will explain this motivation and I will present necessary and sufficient conditions in terms of sign vectors for the injectivity of families of polynomials maps with arbitrary real exponents defined on the positive orthant. These conditions extend existing injectivity conditions expressed in terms of Jacobian matrices and determinants, obtained by several authors. In the context of real algebraic geometry, this approach can be seen as the first partial multivariate generalization of the classical Descartes' rule, which bounds the number of positive real roots of a univariate real polynomial in terms of the number of sign variations of its coefficients. This is joint work with Stefan Müller, Elisenda Feliu, Georg Regensburger, Anne Shiu and Carsten Conradi. I will also present some further advances in this multivariate generalization obtained in collaboration with Frédéric Bihan, together with applications to biochemical MESSI systems obtained in collaboration with Mercedes Pérez Millán.

Wednesday 21st September 2016 at 14h Boulos El-Hilany (LAMA / université de Tübingen),
Soutenance de thèse, Géométrie tropicale et systèmes polynomiaux

Abstract available as a PDF file.

Thursday 31st March 2016 at 14h Yann Brenier (Centre de mathématiques Laurent Schwartz, Ecole Polytechnique),
Nuages browniens, transport optimal, gravitation et hydrodynamique

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L'observation à un instant T du mouvement brownien d'un nuage de points indistinguables dont on connaît la position initiale conduit naturellement au problème de transport optimal de Monge, comme on le comprend dorénavant bien à la suite d'un article de Schroedinger datant des années 30. En poussant un peu plus loin l'analyse, à l'aide du principe de grandes déviations et de techniques de calcul des variations, on arrive à un système dynamique de particules liée au groupe symétrique, dont on peut ensuite dériver par analyse asymptotique des modèles classiques de mécanique, tels que la gravitation de Newton et l'hydrodynamique d'Euler.

The seminar of the team Labo is under the responsibility of Michel Raibaut.
Settings: See with increasing date . Hide abstracts
Other years: 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2017, 2018, all years together.