Department of Mathematics - Master Calendar

Graduate Geometry-Topology Seminar

Event Type

Seminar/Symposium

Sponsor

Department of Mathematics

Location

Altgeld Hall 347

Date

Mar 29, 2024 4:00 pm

Speaker

Brevan Ellefsen

Cost

n/a

Contact

Anthony D'Arienzo

E-Mail

apd6@illinois.edu

Views

Originating Calendar

Graduate Student Seminars in Mathematics

Speaker: Brevan Ellefsen

Introduction to Haken Manifolds
In dimension 2, surfaces are commonly classified by cutting and gluing along curves. Similar techniques turn out to work in dimension 3 with spheres, but there are now many more shapes to cut along. Perhaps the nicest are the Haken manifolds, which contain a very nice surface one can repeatedly cut along. Not every 3-manifold is Haken, but it turns out every 3-manifold almost is: the surface can merely be twisted a finite number of times. The proof of this was a major milestone in 21st century mathematics. In the first of two talks discussing the proof of this result, we present an introduction to the classical theory at an introductory level. Intended for a general audience with some knowledge of algebraic topology.