Large-scale Geometry of Lie Groups

Introduction to some notions of large-scale geometry that turn out to be relevant in the geometric study of Lie groups: One is the notion of quasi-isometry, another related one is the notion of sublinearly bilipschitz equivalence. Introduction to the notion of asymptotic cone of a metric space. Presentation of Pansu's result that one can identify the asymptotic cone of a simply connected nilpotent Lie group to its Carnot-graded group, which is another nilpotent Lie group, with a special metric. Descriptions of the asymptotic cone for various other Lie groups. Introduction to Gromov-hyperbolicity, and characterization, among connected Lie groups, of those that are Gromov-hyperbolic.

Course leader

Lecturer: Prof. Yves de Cornulier (CNRS and University Lyon 1 Claude Bernard, France)
Coordinator: Enrico Le Donne (University of Jyväskylä)

Target group

Jyväskylä Summer School offers courses to advanced Master's students, graduate students, and post-docs from the field of Mathematics and Science and Information Technology.

Prerequisites: basic knowledge of Lie groups and general topology

Course aim

Learning outcomes: An overview of basic concepts of large-scale geometry, which are useful much beyond the realm of Lie groups; an acquaintance with the geometry of Lie groups.

Fee info

EUR 0: Participation in the Summer School courses is free of charge, but students are responsible for covering their own meals, accommodation and travel costs as well as possible visa costs.

Scholarships

Jyväskylä Summer School is not able to grant Summer School students financial support.