Universität Wien

250090 VO Geometric and asymptotic group theory (2014W)

4.00 ECTS (2.00 SWS), SPL 25 - Mathematik

MALV

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 07.10. 10:00 - 12:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 14.10. 10:00 - 12:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 21.10. 10:00 - 12:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 28.10. 10:00 - 12:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 04.11. 10:00 - 12:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 11.11. 10:00 - 12:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 18.11. 10:00 - 12:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 25.11. 10:00 - 12:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 02.12. 10:00 - 12:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 09.12. 10:00 - 12:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 16.12. 10:00 - 12:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 13.01. 10:00 - 12:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 20.01. 10:00 - 12:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 27.01. 10:00 - 12:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The purpose of this course is to give an introduction to coarse embeddings of infinite graphs and groups.

A coarse embedding is a far-reaching generalization of an isometric embedding. The concept was introduced by Gromov in 1993. It plays a crucial role in the study of large-scale geometry of infinite groups and the Novikov higher signature conjecture. Coarse amenability, also known as Guoliang Yu's property A, is a weak amenability-type condition that is satisfied by many known metric spaces. It implies the existence of a coarse embedding into a Hilbert space.

Coarse embeddings and related constructions find applications in modern geometric group theory, algebraic topology, and theoretical computer science.

In this introductory course, we discuss the interplay between infinite expander graphs, coarse amenability, and coarse embeddings. We present several 'monster' constructions in the setting of metric spaces of bounded geometry and finitely generated groups.

The course is open to students of all degrees (Bachelor, Master or PhD). The knowledge of the following fundamental concepts is required: graph, group, free group, presentation of a group by generators and relators, fundamental group.

Assessment and permitted materials

Presentation or test.

Minimum requirements and assessment criteria

Examination topics

Reading list

Association in the course directory

Last modified: Mo 07.09.2020 15:40