Seminars and Colloquia by Series

The profinite topology on a group

Series
Geometry Topology Seminar Pre-talk
Time
Monday, February 6, 2023 - 12:30 for 1 hour (actually 50 minutes)
Location
Speaker
Tam Cheetham-WestRice University

The finite index subgroups of a finitely presented group generate a topology on the group. We will discuss using examples how this relates to the organization of a group's finite quotients, and introduce the ideas of profinite rigidity and flexibility. 

Morse functions on surfaces, the pants complex, and 4-manifolds

Series
Geometry Topology Seminar Pre-talk
Time
Monday, December 5, 2022 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Gabriel IslambouliUC Davis

We show how to obtain a decomposition of an arbitrary closed, smooth, orientable 4-manifold from a loop of Morse functions on a surface or as a loop in the pants complex. A nice feature of all of these decompositions is that they can be encoded on a surface so that, in principle, 4-manifold topology can be reduced to surface topology. There is a good amount to be learned from translating between the world of Morse functions and the world of pants decompositions.  We will allude to some of the applications of this translation and point the interested researcher to where they can learn more. No prior knowledge of these fields is assumed and there will be plenty of time for questions.

From walls to cube complexes by Abdul Zalloum

Series
Geometry Topology Seminar Pre-talk
Time
Monday, September 19, 2022 - 13:00 for 1 hour (actually 50 minutes)
Location
Speaker
Abdalrazzaq (Abdul) ZalloumUniversity of Toronto

A geodesic metric space is said to be CAT(0) if triangles are at most as fat as triangles in the Euclidean plane. A CAT(0) cube complex is a CAT(0) space which is built by gluing Euclidean cubes isometrically along faces. Due to their fundamental role in the resolution of the virtual Haken's conjecture, CAT(0) cube complexes have since been a central object of study in geometric group theory and their study has led to ground-breaking advances in 3–manifold theory. The class of groups admitting proper cocompact actions on CAT(0) cube complexes is very broad and it includes hyperbolic 3-manifolds, most non-geometric 3 manifold groups, small cancelation groups and many others. 

 

A revolutionary work of Sageev shows that the entire structure of a CAT(0) cube complexes is encoded in its hyperplanes and the way they interact with one another. I will discuss Sageev's theorem which provides a recipe for constructing group actions on CAT(0) cube complexes using some very simple and purely set theoretical data.

From little things big things grow by Tyrone Ghaswala

Series
Geometry Topology Seminar Pre-talk
Time
Monday, March 22, 2021 - 13:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Tyrone GhaswalaCIRGET, Université du Québec à Montréal

This pre-talk will be an introduction to infinite-type surfaces and big mapping class groups. I will have a prepared talk, but it will be extremely informal, and I am more than happy to take scenic diversions if the audience so desires!

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