Topics in Geometric Group Theory
Seminar Course
Winter Semester 2022/23
with Dr. Bakul Sathaye
This is a seminar course aimed at Masters students with some background in group theory and geometry. This would be well suited for students who took the sequence on “Geometric Group Theory” in 2021-22. However the topics are very broad and would be interesting to all students who have adequate knowledge of basic concepts in topology, algebraic topology, group theory, and geometry.
Prerequisites: Students in or past their 5th semester in mathematics (BSc or MSc) can take this course. The prerequisites are basic courses in algebra and analysis, point-set topology, metric spaces, fundamental groups, simplicial and CW complexes.
Course Structure: The course will be run as a seminar course, where the participants will present different topics from the course material. The presentations will be given in English. We will follow the book “Office hours with a Geometric Group Theorist” by Matt Clay and Dan Margalit. Depending on the number of participants, their backgrounds, and their interests, the participants will have a change to choose a topic from the book to give a seminar talk on. In order to assist preparation of your presentations and better understanding of the material, we will work in pairs.
Seminar Talks
The course will take place on Wednesdays from 11:00 to 12:00 in SRZ 214. Each talk will be 50 minutes long with 10 minutes for questions and discussion at the end.
Talk 1. (19.10.22) Sihar Mohammed - Free groups and Folding Slides
Talk 2. (26.10.22) Bowen Jin - Ping-pong Lemma Slides
Talk 3. (2.11.22) Raquel Murat - Small cancellation theory Notes
Talk 4. (9.11.22) Judit Jansat - Quasi-isometries Slides and Notes
Talk 5. (16.11.22) Pranav Asrani - Hyperbolic groups Notes
Talk 6. (23.11.22) Amir Hosseini - Asymptotic Dimension Slides
Talk 7. (30.11.22) Jan Raring - Growth of Groups Slides
Talk 8. (7.12.22) Rabi Kumar Chakraborty - Group cohomology I Slides
Talk 9. (14.12.22) Anupam Datta - Group cohomology II Notes
Talk 10. (21.12.22) Grzegorz Kozera - Mapping Class groups I Slides
Talk 11. (11.1.23) Ludovic Pedro de Lemos - Mapping Class groups II Slides
Talk 12. (18.1.23) Jonas Pinke - Braid groups Notes
Talk 13. (25.1.23) Zhengqing He - Ampleness and free groups
References:
M. Clay and D. Margalit, Office hours with a geometric group theorist
C. Löh, Geometric Group Theory
C. Löh, Group Cohomology and Bounded Cohomology: An Introduction for Topologists
B. Farb and D. Margalit, A primer on Mapping Class Groups