Scientific committee
Christophe Pittet (Université d'AixMarseille, France)
Tullia Dymarz (University of Wisconsin, USA)
Manjusha Majumdar (University of Calcutta, India)
Scientific program
Titles of the courses
Course 1: "Prerequisites on Riemannian Geometry", Arindam Bhattacharyya (Jadavpur University, India)
Course 2: "Hyperbolic Geometry and Mostow Rigidity", Kingshook Biswas (Indian Statistical Institute, India) and Krishnendu Gongopadhyay (Indian Institutes of Science Education and Research, India)
Course 4: "Word Hyperbolic Groups", Indira Chatterji (Université Côte d'Azur, France)
Course 6: "Ergodic Theorems and Unitary Representations of Lie Groups and their Lattices", Christophe Pittet (Université d'AixMarseille, France)
Course 7: "Large scale geometry of nilpotent and solvable Lie groups", Tullia Dymarz (University of Wisconsin, USA)
The courses are divided into two categories: four introductory courses and three advanced courses. Training sessions will complement the advanced courses.
Introductory courses
Course 1: "Prerequisites on Riemannian Geometry", Arindam Bhattacharyya (Jadavpur University, India)
Abstract of the course. We shall introduce the basic geometric objects of Riemannian geometry to provide some background: definition of a Riemannian manifold, its associated distance and group of isometries with their elementary properties. Emphasis will be given on examples, including surfaces and Lie groups.
Course 2: "Hyperbolic Geometry and Mostow Rigidity", Kingshook Biswas (Indian Statistical Institute, India) and Krishnendu Gongopadhyay (Indian Institutes of Science Education and Research, India)
Abstract of the course. We shall give a gentle introduction to hyperbolic geometry, insisting on the hyperbolic plane, before considering higher dimensional spaces. The rest of the lectures will be devoted to sketching Sullivan's proof of the Mostow rigidity theorem, which states that if X, Y are closed hyperbolic nmanifolds with n at least three, then any isomorphism between their fundamental groups is induced by an isometry between the manifolds.
Abstract of the course. We will discuss the notion of quasiisometry and present some standard examples of invariants, such as ends, volume growth, finite presentability, etc.. We should also describe BassSerre theory from a topological view if time allows.
Course 4: "Word Hyperbolic Groups", Indira Chatterji (Université Côte d'Azur, France)
Abstract of the course. I will discuss Cayley graphs, then growth and hyperbolicity in metric spaces and groups. I will discuss concrete examples to see which ones are hyperbolic and which ones are not.
Advanced courses
Abstract of the course. We will define and discuss the Gromov boundary of a hyperbolic group. This is an extremely useful topological space associated to a hyperbolic group. We will give many examples of boundaries, and describe some properties of the boundary which are reflected in the group.
Course 6: "Ergodic Theorems and Unitary Representations of Lie Groups and their Lattices", Christophe Pittet (Université d'AixMarseille, France)
Abstract of the course. Ergodic theorems can be deduced from operator norm estimates. In the case of Lie groups and their lattices, the theory of unitary representations, in particular estimates of the HarishChandra (spherical) functions, lead to very precise convergence rate estimates. (Priority will be given to examples rather than to the general theory.)
Course 7: "Large scale geometry of nilpotent and solvable Lie groups", Tullia Dymarz (University of Wisconsin, USA)
Abstract of the course.
The goal of these talks is to introduce students to the basics of large scale geometry and metric structures of nilpotent and solvable Lie groups. The first lecture will review the notion of quasiisometry and gives basics of nilpotent and solvable groups. The second will focus on aspects of the metric geometry of nilpotent Lie groups. The third will look at the metric geometry of certain family of solvable Lie groups. We will assume some familiarity with Riemannian geometry and the basic definitions of Lie groups and Lie algebras.
Training sessions
Besides the first hour providing some very elementary background on Riemannian geometry, we wish to organize the lectures based on the "learningbydoing"
method. To implement this, the lectures have been grouped in halfdays. A portion of the time is used to introduce definitions and some results (with or without proofs). For the rest of the time, the students will be organized into small groups, and we should make them work on examples and find proofs of some results. To have a lot of time is supposed to help the students get acquainted with the objects and methods on their own.
Schedule
DAY1 18012022 (Tuesday) 
Inauguration 01:30 pm  2:00 pm 
Arindam Bhattacharyya 02:00 pm 03:00 pm 
Peter Haïssinsky 03:30 pm 04:30 pm 
Krishnendu Gongopadhyay 05:00 pm 06:00 pm 

DAY2 19012022 (Wednesday) 
Peter Haïssinsky & Tutorial 10:30 am 11:30 am 
Krishnendu Gongopadhyay & Tutorial 11:45 am 12:45 pm 
LUNCH 
Indira Chatterji & Tutorial 01:30 pm 03:15 pm 
Peter Haïssinsky & Tutorial 03:45 pm 05:30 pm 
DAY3 20012022 (Thursday) 
Indira Chatterji & Tutorial 01:30 pm 03:15 pm 
Peter Haïssinsky & Tutorial 03:45 pm 05:30 pm 
Krishnendu Gongopadhyay & Tutorial 06:00 pm 07:00 pm 


DAY4 21012022 (Friday) 
Indira Chatterji & Tutorial 01:30 pm 03:15 pm 
Krishnendu Gongopadhyay & Tutorial 03:45 pm 06:00 pm 



DAY5 22012022 (Saturday) 
Krishnendu Gongopadhyay & Tutorial 11:30 am 12:30 pm 
LUNCH 
Indira Chatterji & Tutorial 01:30 pm 03:15 pm 
Peter Haïssinsky & Tutorial 03:45 pm 04:45 pm 
Krishnendu Gongopadhyay & Tutorial 05:00 pm 06:00 pm 

DAY6 24012022 (Monday) 
Tullia Dymarz & Tutorial 09:00 am 11:00 am 
LUNCH 
Christophe Pittet & Tutorial 01:30 pm 03:15 pm 
Kingshook Biswas 03:45 pm 06:00 pm 
Genevieve Walsh 06:30 pm  07:00 pm 
DAY7 25012022 (Tuesday) 
Tullia Dymarz & Tutorial 09:00 am 11:00 am 
LUNCH 
Genevieve Walsh & Tutorial 01:30 pm  02:30 pm 
Christophe Pittet & Tutorial 03:30 pm 05:15 pm 
Genevieve Walsh 06:30 pm  07:00 pm 
DAY8 26012022 (Wednesday) 
Tullia Dymarz & Tutorial 09:00 am 11:00 am 
LUNCH 
Genevieve Walsh & Tutorial 01:30 pm  02:30 pm 
Christophe Pittet & Tutorial 03:30 pm 05:15 pm 
Genevieve Walsh 06:30 pm  07:00 pm 
DAY9 27012022 (Thursday) 
Kingshook Biswas 09:00 pm 11:15 pm 
LUNCH 
Genevieve Walsh & Tutorial 01:30 pm  03:45 pm 
Christophe Pittet & Tutorial 04:00 pm 05:45 pm 
Valedictory Session 

Links

CIMPA.
Sponsors
Cimpa
Centre international de mathématiques pures et appliquées.
IMU
International Mathematical Union
Calcutta Mathematical Society
I2M
Institut de mathématiques de Marseille