Séminaires : Séminaire des Thésards

Le séminaire des thésards est l'occasion pour les doctorants de présenter des résultats et des problématiques dignes d'intérêt devant un public de non-spécialistes. L'ambiance y est informelle ; poser des questions naïves est encouragé, et les questions moins naïves sont bienvenues dans la mesure où elles n'entravent pas le bon déroulement de l'exposé.

Un jeudi sur deux à 18h00, en alternance entre Jussieu et Sophie Germain.

Tropical geometry has recently been proven extremely useful to study plane curve counting problems. In this context, tropical geometry describes certain "limits" of families of complex algebraic curves in a combinatorial way, providing an algebraic curve over a "dequantized" version of real numbers. After motivating these tools through Newton-Puiseux method, I will present tropical curves and describe different point of views on the degeneration process of a family of complex algebraic curves to a tropical curve. These include a non-Archimedean interpretation, an analytical description connected to Monge-Ampère equations as well as a degenerating process from toric geometry. I will end this talk by discussing some applications to enumerative geometry and topology of real algebraic curves.