Misha Schmalian, University of Oxford
Event Date
2026-03-20
Event Time
02:00 pm ~ 03:00 pm
Event Location
University of Pennsylvania, room DRL A2
PATCH Seminar (joint with Bryn Mawr, Haverford, Penn, and Swarthmore)
Abstract: One of the crowning achievements of modern mathematics is the Geometrization Theorem of Thurston and Perelman, which provides a structural description of all 3-dimensional manifolds. In the morning session, we will have discussed an operation called Dehn filling, and the results presented there will rely heavily on Geometrization.
The goal of this talk is to give an overview of Geometrization and its interaction with Dehn fillings. As motivation, we will discuss a recent algorithm that decides whether a given 3-manifold can be obtained from another given manifold via Dehn filling. We will see how Geometrization allows us to reduce this topological question to a classical result about Diophantine quadratic equations.
In the morning background talk (10am, in DRL A6), I will give an introduction to Dehn surgery and discuss the question of (non-) uniqueness of this construction.