• The problem set 3 has been updated (again).

Problem Sets:

  • Problem Set 1: [link]
  • Problem Set 2: [link]
  • Problem Set 3: [link]


The schedule for the course is somewhat irregular, so please take notes of the weeks and dates. The room is always MaD355 and we usually meet on Tuesdays from 10am to 12pm and Thursdays from 2pm to 4pm according to the following list: 
  • Week X: Tuesday (Y.Z) and Thursday (Y+2.Z)
  • Week 12: Course (20.3) and Course (22.3)
  • Week 13: (Easter break: no course/problem session)
  • Week 14: (No course/problem session)
  • Week 15: Course (10.4) and Problem Session (12.4)
  • Week 16: Course (17.4) and Course (19.4) 
  • Week 17: (No course/problem session)
  • Week 19: Course (1.5) and Problem Session (3.5) and Course (4.5)
  • Week 19: Course (8.5) and Problem Session (10.5) (11.5)
  • Week 20: Course (15.5) and Problem Session (17.5)

Course Material:

We will mainly follow the book edited by Ghys and de la Harpe, but I included some extra references. You may also consult Gromov's original papers at your own risks [link].

  • Etienne Ghys, Pierre de la Harpe (editors): Sur les groupes hyperboliques d'après Mikhael Gromov, Progress in Mathematics, 83, Birkhaüser, 1990. (French [link] & English translation [link])
  • Etienne Ghys, Pierre de la Harpe: Infinite groups as geometric objects (after Gromov), (in the book edited by T. Bedford, M. Keane, C. Series, Ergodic Theory, Symbolic Dynamics and Hyperbolic spaces), [link].
  • Cornelia Drutu, Michael Kapovich, Geometric Group Theory, [link]
  • Martin Bridson, André Haefliger, Metric Spaces of Non-Positive Curvature, [link]

Further reading: (Optional)

  • Eero asked after the lectures if quasi-isometric f.g. groups are necessarily bilipschitz equivalent. The same question was first asked by de la Harpe in his book Topics in Geometric Group Theory and answered by Tullia Dymarz in the following paper [link].  Examples of discrete subsets of the Euclidean plan quasi-isometric but not bilipschitz equivalent to the plane were known earlier. Those examples were not f.g. groups.
  • Švarc was actually Jewish German Russian. His name was changed from the German from "Schwarz" to the Russian equivalent then back to the English form "Švarc". The accent is on the "S" (not on the "c"). [link]

Thibaut Dumont,
Mar 28, 2018, 2:22 AM
Thibaut Dumont,
May 15, 2018, 8:40 AM
Thibaut Dumont,
May 30, 2018, 4:50 AM
Thibaut Dumont,
Mar 26, 2018, 6:33 AM