Mixing Surfaces, Algebra, and Geometry

Explore the fascinating intersection of surfaces, algebra, and geometry in this 51-minute AMS Maryam Mirzakhani Lecture delivered by Dan Margalit from Georgia Institute of Technology at the 2022 Joint Mathematics Meetings. Delve into topics such as simple curves on surfaces, Mirzakhani's theorem, taffy pullers, and the Nielsen-Thurston Classification. Examine concepts like pseudo-Anosov maps, the mapping class group, and the classification of 3-manifolds. Investigate moduli space, Lehmer's Problem, and Penner's examples. Discover the connections between small stretch factors and 3-manifolds, and explore Long's Question and multiple fiberings. Gain insights into the map of mathematics and the intriguing world where surfaces, algebra, and geometry converge.

Intro
THE MAP OF MATHEMATIC
Simple Curves on Surfaces
A Theorem of Mirzakhani
Taffy Pullers
3-Pronged Taffy Puller
Why the Same Stretch Factor?
The Nielsen-Thurston Classification
Pseudo-Anosov Maps
The Mapping Class Group
Mapping torus
The Classification of 3-Manifolds
Moduli space
Lehmer's Problem
What is small?
Penner's examples
Long's Question
Multiple Fiberings
Small stretch factors and 3-manifolds
Where are the small stretch factors?