Reading course on Coarse Geometry
Coarse geometry cares (only) about the large scale structure.
This reading course is aimed at master students, phd students, and researchers interested to learn more about coarse geometry, particularly with a view towards geometric group theory. Prerequisites are previous encounters with concepts such as quasi-isometries and Gromov-hyperbolicity, for instance as in a GGT-lecture.
If you are interested to join, send a message to
rappenzeller (at) mathi.uni-heidelberg.de
Each week we will read some pages of a book or paper and then discuss together what we have read.
Possible topics include:
- Coarse structures, this captures the large scale geometry in a categorical way. Coarse groups can then be considered analogously to topological groups, ... [1,2]
- Asymptotic cones, with relations to affine buildings and/or lacunary hyperbolic groups and small cancellation theory. [3,4,2]
- Boundary theory including Gromov-boundary (for hyperbolic spaces), visual boundary (for CAT(0)-spaces) and Morse boundary, .. [5,2]
- Asymptotic dimension, generalizing the topological dimension. [2]
We meet weekly on Wednesdays, 9:15-10:15. First meeting 15. April in Seminarrom 7 to discuss details and outline.
Related literature:
[1] Leitner, Vigolo, An Invitation to Coarse Groups, 2023.
[2] Roe, Lectures on Coarse Geometry, 2003.
[3] Sisto, Separable and tree-like asymptotic cones of groups, 2012.
[4] Olshanskii Oisin Sapir, Lacunary hyperbolic groups, 2009.
[5] Cordes, Morse boundaries of proper geodesic metric spaces, 2023.
