Thursday - November 21

Time

Room

Speaker/Title/Abstract

13:30 - 15:30

BBL 308

Gael Meignez - The benefits of inflation

16:30 - 18:30

BBL 308

Marcos Alexandrino -  Isometry flows on orbit spaces and dynamical behavior of   singular Riemannian foliations

Abstract:  In this talk, we discuss the following result: Given a proper isometric  action K\times M\to M on a complete Riemannian manifold M then each continuous isometric flow on the orbit space M/K is smooth, i.e., it is the projection of an K-equivariant smooth flow  on the manifold M.

The first application of our result concerns with the dynamical behavior of singular Riemannian foliations and Molino's conjecture,  which states that  the  partition of a Riemannian manifold into the closures of  the leaves of a singular Riemannian foliation is still a singular Riemannian foliation. We prove Molino's conjecture for the main class of foliations considered in his book, namely orbit-like foliations.

As another direct application of  our  result we remark that,  if  G is a connected closed group of isometries of the leaf space M/\mathcal{F},  then  G acts smoothly on the leaf space, as long as \mathcal{F} is a closed orbit-like foliation on a compact manifold M.

This talk is based on a joint work with Dr. Marco Radeschi (wwu- Munster).

Friday - November 22

Time

Room

Speaker/Title/Abstract

9:30 - 11:30

BBL 308

Hessel Posthuma - Geometry and topology of quotients of proper Lie groupoids

Abstract:   Proper Lie groupoids are natural generalizations of proper actions of Lie groups on manifolds that play an important role various parts of geometry. In this talk I shall discuss joint work with M. Pflaum and X. Tang about the geometric and topological structure of the underlying quotient spaces of proper Lie groupoids. I will cover several aspects of this: the stratification of the quotient, basic cohomology and metric properties.

13:00 - 15:00

BBL 308

Matias del Hoyo - Riemannian structures on Lie groupoids

Abstract:  Lie groupoids are geometric objects generalizing Lie group actions, smooth fibrations, pseudogroups and principal bundles, among others. Every Lie groupoid has an underlying singular foliation, whose leaves are the points linked by an arrow, so we may think of a groupoid as a singular foliation endowed with extra algebraic data. In this talk I will discuss a joint work with R. Fernandes, where we define metrics for Lie groupoids as metrics compatible with the underlying foliation and the extra algebraic data. We show how to construct these metrics, and we use them to achieve linearization theorems, generalizing previous linearization theorems for groupoids, and local Reeb stability for foliations.

15:30 - 17:30

BBL 308

Marco Zambon - Singular foliations and Lie groupoids

Abstract: We consider  singular foliations, meant as a suitable submodule of vector fields on a manifold. We will review the ingenious construction  by Androulidakis-Skandalis of  a groupoid H, called holonomy groupoid, associated to any singular foliation. H is only a topological groupoid, but we will show that the restriction of H to any leaf is a smooth Lie groupoid. Further, we will relate H to the holonomy transformations of the singular

foliation, thus justifying the name "holonomy groupoid". We will also discuss an algebraic characterization of singular

foliations. Finally, we will sketch how the holonomy groupoid of a singular foliation is related to an integration problem involving Lie algebroids, in analogy to the work of Moerdijk-Mrcun in the regular case.