The Metric Geometry/Geometric Group Theory Student Seminar meets weekly on Mondays at 5:30pm in Cockins Hall 312.
This is a learning seminar aimed at the general math grad student population intended to introduce topics via listening to other students give talks, and giving talks yourself. Each week, one student will present a talk, either on a specific paper or general subject, and the topic will vary from week-to-week.
Very little typically needs to be assumed of the audience’s background to make talks understandable; usually basic algebra and some algebraic topology suffices. So in particular, if you are a new(er) grad student, you shouldn’t have any issues keeping up or delivering talks, and this should be a great way to learn about different topics if you’re unsure what you would like to pursue in grad school. (Of course, grad students of all years are welcome as well!)
The fields of Metric Geometry and Geometric Group Theory are very broad with many applications to other branches of math, but they’re typically united by the core concept of negatively or non-positively “curved” spaces. Some examples of topics which could be covered, in no particular order, include:
- Generalizations of negative/non-positive curvature to metric spaces and groups,
- Aspherical (or “K(G,1)”) spaces,
- Small cancellation theory,
- Aspects of functional analysis (e.g. von Neumann algebras, amenability, Property (T), the Haagerup property),
- Thurston’s 8 geometries and the classification of 3-manifolds (see http://www.3-dimensional.space/ for a neat visualization),
- Higher dimensional graphs of groups/spaces (aka “complexes of groups/spaces”),
- Lie theory (e.g. lattices in Lie groups),
- Coarse geometry (e.g. quasi-isometries, Morse boundaries),
- Algorithmic group theory (including (bi)automaticity of groups),
- Dynamics and ergodic theory on negatively/non-positively curved metric spaces,
- Arithmetic groups and applications to number theory,
- Mapping class groups,
- Alexandrov spaces (in particular, their use in Perelman’s proof of the Poincare conjecture),
- Kahler geometry, and
- Random complexes/groups,
among others. Some standard references for Metric Geometry and Geometric Group Theory can be found here and here, respectively.
If you’re interested in joining or learning more, visit our sign up page.