Yair Minsky - Virginia Mathematics Lectures - November 13-15, 2017

Event start date: Monday, November 13, 2017

Virginia Mathematics Lectures »
Yair Minsky Poster

Yair Minsky (Yale University)
  • Lecture 1. Hyperbolic 3-manifolds, their structure and deformations
  • Lecture 2. Between 2 and 3 dimensions: Teichmuller theory, pleated surfaces, and the complex of curves
  • Lecture 3. Quantitative models, Thurston's skinning map, and beyond

Hyperbolic 3-manifolds, their structure and deformations

Lecture 1: November 13, 2017. Time and location: 5-6pm, Physics 203

Abstract: Hyperbolic geometry is the richest and most interesting of Thurston’s eight geometries for 3-manifolds. A good understanding of the ways in which hyperbolic geometry interacts with topology in three dimensions also informs our understanding of many related fields, such as geometric group theory and complex dynamics. We will give a brief introduction to this subject, trying to focus on examples, geometric intuition and overall structure.

Between 2 and 3 dimensions: Teichmuller theory, pleated surfaces, and the complex of curves

Lecture 2: November 14, 2017. Time and location: 5-6pm, Rouss 410

Abstract: One can probe the geometry of a 3-manifold by mapping in surfaces in different ways: conformal boundaries at infinity give us a parametrization of families of 3-manifolds using classical Teichmuller space, and Thurston’s pleated surfaces relate the varying geometry on the interior to 2-dimensional combinatorial and geometric structures. We will explore these notions and explain a little about how they provide a complete set of invariants for deformation spaces of 3-manifolds.

Quantitative models, Thurston’s skinning map, and beyond

Lecture 3: November 15, 2017. Time and location: 5-6pm, Rouss 410

Abstract: While the theory has had many successes, we are still far from having a complete “effective” recipe for predicting the geometry of a hyperbolic 3-manifold from its topological description. I will describe some ongoing work in this direction, and some remaining questions.

Last updated: Friday, September 29, 2017