Virtual Math Seminar: Jarek Kwapisz (MSU): "Rational Maps and Teichmuller Space".
- Monday, September 28, 2020 from 4:00pm to 5:30pm
- WebEx meeting number: 120 112 3734 . Password: math
Virtual Math Seminar.
Monday 28 September 4:10-5:15pm
WebEx link, meeting, and password:
Dr. Jarek Kwapisz
Rational Maps, Teichmuller Space, and Elastic Graphs after Bill and Dylan Thurston
Rational functions of the Riemann sphere are quotients of two complex polynomials. Remarkably, one can often uniquely define such a function in terms of soft data given by its homotopy class relative a finite set of points. What homotopy classes work is a subject of two hallmark results separated by nearly 50 years and due to Bill Thurston and his son Dylan Thurston. The older is the famous Thurston's obstruction, heralding flight to infinity in the Teichmuller space. The newer result, published this summer in Annals of Mathematics, gives a relatively more elementary positive certificate via maps of graphs with rubber band edges, which generate a surface skeleton of the rational function when allowed to pull tight.
I will attempt to give an informal description of this rich subject, offering a fascinating mix of topology, geometry, and analysis. This talk is a prequel to Lukas' talk (and also loosely connects with my own study of conformal dimension via p-resistance).
- Department of Mathematical Sciences