Séminaire de Mathématiques et Colloquium
En Salle 201 Bâtiment K, FST, 18 rue des Frères Lumière, Mulhouse
Conférence à venir :
Jeudi 16 avril à 14h
Maria Martin Vega
(Univ. de Paris-Cité)
The Bruno ideal for logarithmic vector fields.
Given a germ of analytic vector field ∂, let ∂= ∂_ss + ∂_nilp be its unique formal Jordan decomposition, where ∂_ss is its semi-simple component and ∂_nilp is its nilpotent component. When ∂ is logarithmic, we define the Bruno ideal B(∂) as the formal locus where the semi-simple and the nilpotent components are collinear, that is, the vanishing locus of ∂_ss ∧ ∂_nilp.
We prove the following result originally stated by A. D. Bruno: If the eigenvalues of ∂_ss satisfy an arithmetic condition, then B(∂) is analytic and the restriction of ∂ to its zero set V is analytically normalizable.
This is a joint work with Daniel Panazzolo.
Jeudi 16 avril à 15h30 en visioconférence
Polyxeni Spilioti
(Univ. of Patras, Grèce)
Determinants of twisted Laplacians and the twisted Selberg zeta function.
In this talk, we consider a compact hyperbolic surface with finite order singularities and its unit tangent bundle.
We consider also the twisted Selberg zeta function associated with an arbitrary, finite-dimensional representation of the fundamental group of the unit tangent bundle.
We will present recent results concerning a relation between the twisted Selberg zeta function and the regularized determinant of the twisted Laplacian. The main tool we use is the Selberg trace formula. If the surface has no finite order singularities, we obtain as a corollary a corresponding relation. These results can be viewed as an extension to the non-unitary twists case of the results by Sarnak and Naud. This is joint work with Jay Jorgenson and Lejla Smajlovic.
Prochains exposés :
Une triangulation d’un ensemble de points dans le plan euclidien est dite de Delaunay si chaque cercle circonscrit à un triangle ne contient aucun autre sommet de la triangulation. Son extension à des surfaces, ainsi que certains algorithmes permettant de la calculer, se heurte à des difficultés topologiques (genre de la surface) et géométriques (systole de la surface).
Cet exposé introduira la notion de triangulation de Delaunay, et présentera des méthodes de calcul permettant de la calculer comme l’algorithme de flip ou de Bowyer-Watson. Nous nous focaliserons ensuite sur ce-dernier, en l’étendant d’abord au tore, puis aux surfaces hyperboliques, en passant par la surface de Bolza. Aucun prérequis en géométrie hyperbolique, topologie ou algorithmique n’est nécessaire pour suivre l’exposé.
Given a germ of analytic vector field ∂, let ∂= ∂_ss + ∂_nilp be its unique formal Jordan decomposition, where ∂_ss is its semi-simple component and ∂_nilp is its nilpotent component. When ∂ is logarithmic, we define the Bruno ideal B(∂) as the formal locus where the semi-simple and the nilpotent components are collinear, that is, the vanishing locus of ∂_ss ∧ ∂_nilp.
We prove the following result originally stated by A. D. Bruno: If the eigenvalues of ∂_ss satisfy an arithmetic condition, then B(∂) is analytic and the restriction of ∂ to its zero set V is analytically normalizable.
This is a joint work with Daniel Panazzolo.
In this talk, we consider a compact hyperbolic surface with finite order singularities and its unit tangent bundle.
We consider also the twisted Selberg zeta function associated with an arbitrary, finite-dimensional representation of the fundamental group of the unit tangent bundle.
We will present recent results concerning a relation between the twisted Selberg zeta function and the regularized determinant of the twisted Laplacian. The main tool we use is the Selberg trace formula. If the surface has no finite order singularities, we obtain as a corollary a corresponding relation. These results can be viewed as an extension to the non-unitary twists case of the results by Sarnak and Naud. This is joint work with Jay Jorgenson and Lejla Smajlovic.