Surfaces isogenous to a product of curves, moduli spaces and finite groups
Catégorie d'évènement : Séminaire de géométrie complexe Date/heure : 24 mars 2014 14:00-15:00 Lieu : Oratrice ou orateur : Matteo Penegini Résumé :In this talk we shall present a group theoretical method to calculate the number of connected components of the moduli space of surfaces of general type isogenous to a product of curves. Then, we give then asymptotic growth of the number of these components for certain families of surfaces isogenous to a product with group either an alternating group, or a symmetric group or an abelian group or finally 2-groups. With our methods we get a better lower bound than the one obtained by Manetti. (jww. S.Garion/M.Loenne).
Min-Max theory for the area functional and applications
Catégorie d'évènement : Colloquium Date/heure : 24 mars 2014 16:30-17:30 Lieu : Oratrice ou orateur : Résumé :Fernando Codá Marques
Motivated by a foundational question of Poincaré, Birkhoff used min-max methods to prove the existence of a closed geodesic in any Riemannian two-sphere. This has inspired great developments in the field, like the Three Geodesics Theorem of Lusternik-Schnirelmann and the Almgren-Pitts min-max theory of minimal surfaces.
In this talk I will give an overview of these ideas and of applications to geometry, including recent results in collaboration with Andre Neves that lead to the existence of infinitely many minimal hypersurfaces in positive Ricci curvature.