Seminars and Colloquia by Series

Smooth structures on 4-manifolds and corks

Series: Geometry Topology Working Seminar
Time: Friday, September 23, 2016 - 14:00 for 1.5 hours (actually 80 minutes)
Location: Skiles 006
Speaker: John Etnyre – Georgia Tech

I will discuss a process called a cork twist for relating homeomorphic but not diffeomorphic smooth 4-manifolds. This involves finding a contractible submanifold of a given 4-manifold, removing it, and re-gluing by a diffeomorphism of the boundary. This is a surprisingly simple way of relating non-diffeomorphic manifold that was discovered in the 1990s but has recently been getting a lot of attention.

Geometric Small Cancellation

Series: Geometry Topology Working Seminar
Time: Wednesday, September 21, 2016 - 10:05 for 1 hour (actually 50 minutes)
Location: Skiles 005
Speaker: Justin Lanier – Georgia Tech

In this lecture series, held jointly (via video conference) with the University of Buffalo and the University of Arkansas, we aim to understand the lecture notes by Vincent Guirardel on geometric small cancellation. The lecture notes can be found here: https://perso.univ-rennes1.fr/vincent.guirardel/papiers/lecture_notes_pcmi.pdf This week we will compete the first of two steps in proving the small cancellation theorem (Lecture 3).

Geometric Small Cancellation

Series: Geometry Topology Working Seminar
Time: Monday, September 12, 2016 - 10:05 for 1 hour (actually 50 minutes)
Location: Skiles 005
Speaker: Justin Lanier – Georgia Tech

In this lecture series, held jointly (via video conference) with the University of Buffalo and the University of Arkansas, we aim to understand the lecture notes by Vincent Guirardel on geometric small cancellation. The lecture notes can be found here: https://perso.univ-rennes1.fr/vincent.guirardel/papiers/lecture_notes_pcmi.pdf This week we will finish the section on rotating families (Lecture 3).

Models for Mapping Class Groups II

Series: Geometry Topology Working Seminar
Time: Friday, September 9, 2016 - 14:05 for 1.5 hours (actually 80 minutes)
Location: Skiles 006
Speaker: Dan Margalit – Georgia Institute of Technology

A celebrated theorem of Nikolai Ivanov states that the automorphism group of the mapping class group is again the mapping class group. The key ingredient is his theorem that the automorphism group of the complex of curves is the mapping class group. After many similar results were proved, Ivanov made a metaconjecture that any “sufficiently rich object” associated to a surface should have automorphism group the mapping class group. In joint work with Tara Brendle, we show that the typical normal subgroup of the mapping class group (with commuting elements) has automorphism group the mapping class group. To do this, we show that a very large family of complexes associated to a surface has automorphism group the mapping class group.