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Prof. Habib’s research focus is in Differential Geometry  (geometry of submanifolds, of Kählerian and Sasaki manifolds, of Riemannian foliations), analysis on manifolds (spectral geometry of Dirac-type operators) and functional analysis (Müntz spaces). Over the months of March and April, Prof. Habib will deliver a set of lectures, intended primarily for students at Ì©¹ú²ÊƱand the Lebanese University, exploring Foliations Theory and introducing Riemannian Geometry as per the following description and timeline:

- Foliation Theory: In this course, we will study foliations on manifolds. First, we start solving differential equations and review Cauchy problem which was the main motivation to define foliations. Second, we review the notion of a differentiable manifold and study some of its properties. In the third part, we define foliations on manifolds and see several examples that are used in normal life. In the fourth part, we study conditions to impose on manifolds in order to carry foliations of particular codimensions. In the last part, we consider the notion of basic cohomology on foliations and relate it to the de Rham cohomology of the manifold.

Dates: March 7, 14, 28 and April 11, 25

Timing: 2pm till 3:30pm

Location: Nicely 321 & online [via °Â​e²ú·¡³æ]

- Introduction to Riemannian Geometry: The aim of this course is to introduce the theory of Riemannian foliations on Riemannian manifolds. In the first chapter, we define vector bundles on manifolds and the notion of a linear connection acting on sections on such bundles. We study the properties of such objects and establish the Bianchi identity for the curvature of the connection. We then see how connections can define parallel transport on vector bundles and holonomy groups in order to characterize the triviality of vector bundles. The second chapter is devoted to introducing foliations on manifolds. In this set up, we give the notion of foliated local charts that provide the local structure of a foliation. In particular, we define basic forms as being differential forms on the manifold that are constant along the leaves of a foliation and study the properties of the corresponding de Rham cohomology by using analytic tools.

Dates: every Monday and Wednesday starting March 10 till April 30 

Timing: 3:30pm till 5:30pm

Location: Nicely 321 & online [via WebEx]