MA2: Coarse Geometry of the Laplacian and Other Analytic Quantities

label Diverse autorenew 2025-09-29, 17:01 history_edu Diana Ignat
The goal of these lectures is to discuss the quasi-invariance under quasi-isometries of analytic quantities like for example the isoperimetric constant, the Cheeger constant, p-parabolicity, or the eigenvalues of the Laplacian. As applications I will for instance discuss (1) the recurrence properties of the simple random walk on planar graphs, or (2) prove that every Riemannian manifold whose fundamental group surjects onto a free group admits a tower of covers which forms an expander. To a large extent the methods are rather elementary, although some familiarity with Riemannian geometry should be helpful.

Period
11-08-2014 - 15-08-2014 (1 weeks)

Target group
The course is aimed at graduate students, but strong advanced undergraduate students with the appropriate background might find it suitable. Although there are no formal prerequisities, knowledge on metric (and Riemannian) geometry and elementary algebraic topology will be useful.

Course aim
The most important aims of the Summer School are to develop post-graduates scientific readiness and to offer students the possibility to study in a modern, scientific environment and to create connections to the international science community.



Credits
2.0 ECTS credits

Course fee
EUR 0[Convert to USD]Participating the Summer School is free of charge, but student have to cover the costs of own travel, accommodation and meals at Jyvskyl.

Course leader
Coordinator: Dr. Pekka Pankka (University of Jyvskyl, Finland)Lecturer: Prof. Juan Souto (IMRAR, University of Rennes, France)

Scholarships
The 24th Jyvskyl Summer School is not able to grant any Summer School students financial support. In order to ensure your participation, we recommend that you take steps to secure your own funding, for example, by turning first to your home institution

University of Jyvaskyla Faculty of Mathematics and Science and Faculty of Information Technology
Address: Jyvaskyla Summer School, Faculty of Mathematics and Science P.O.Box 35 (YK312), FIN-40014 University of Jyvaskyla, Finland
Postal code: FIN-40014
City: Jyvaskyla
Country: Finland
Website: http://www.jyu.fi/summerschool
E-mail: jss@jyu.fi
Phone: +358505818351