Geometry and Dynamics Seminar

Schedule for the geometry and dynamics seminar

Fall 2016 :

The seminar takes place on Wednesday,  16:15 - 17:30, room MA-10.

 

November 16 Adrien Marcone
title : On the total curvature of immersed manifolds.
abstract :

We will present an article by S.-S. Chern and R. Lashof published in 1957. This paper contains four theorems about the total curvature of compact manifolds immersed in a Euclidean space. More precisely, they are interested in the case where the total curvature is "small". The main theorem "can be interpreted as a characterization of convex hypersurfaces among all immersed submanifolds of a given dimension in a Euclidean space of arbitrary dimension".​

In order to explain the ideas of the proof of the latter theorem, we will begin by recalling some basics about moving frames and total curvature.

 

 

 

 

 

 

 

 

 

 

 

November 23 16:15 Federica Fanoni
title: Basmajian-type inequalities for maximal representations.
abstract: Basmajian's celebrated identity gives a way to compute the length of the boundary of a hyperbolic surface in terms of the lengths of the so-called orthogeodesics (geodesics orthogonal to the boundary at both endpoints). In collaboration with Beatrice Pozzetti, we generalized this result to special representations of the fundamental group of a surface into the symplectic group, called maximal representations.
In this talk I will describe the classical identity, show how maximal representations can be seen as a generalization of Teichmüller space and discuss Basmajian's identity in this context.

 

 

 

 

 

November 23 15:00

Bram Petri
title : Constructions of hyperbolic surfaces with long systoles.
abstract : The length of the shortest non-contractible curve - the systole - of a closed hyperbolic surface is at most logarithmic in the genus of the surface. In this talk I will speak about constructions of hyperbolic surfaces with systoles of logarithmic length and discuss their properties. Part of this is joint work with Alex Walker.

 

 

 

 

 

November 30 Matthieu Gendulphe
title: On moduli spaces of non-orientable surfaces.
abstract: Teichmüller spaces and moduli spaces have been widely studied in the case of compact orientable surfaces.
The aim of the talk is to point out some particular phenomena that occur in the case of non-orientable surfaces.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

November 30 Pier Domenico Lamberti (Università degli Studi di Padova)
title :

Spectral stability for higher order elliptic operators subject to homogeneous boundary conditions on varying domains
abstract : We consider elliptic partial differential operators of second and higher order, subject to homogeneous boundary conditions on bounded domains of the N-dimensional Euclidean space. We discuss a general theorem ensuring their spectral stability upon perturbation of the underlying domain, in the frame of  so-called E-compact convergence. We discuss some applications to the case of the bi-harmonic operator with Dirichlet, Neumann and Intermediate boundary conditions. In particular, in the case of Intermediate boundary conditions, we analyze the limiting behavior of the problem when the boundary of the domain is described by a periodic oscillatory profile depending on a parameter. We show that there is a critical parameter such that the limiting problem depends on whether we are above, below or just sitting on such critical value. The critical case leads to the study of a somewhat typical homogenization problem and provides a limiting strange term which plays the role of a “strange curvature”. Time permitting, boundary homogenization for the triharmonic operator will also be considered.
       
Based on joint works with José M. Arrieta and Francesco Ferraresso.

 

 

 

 

 

 

December 14 Ivan Izmestiev
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December 21 Enrico Le Donne
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