Reading Seminar

Teichmüller Theory


Fall Semester 2021

University of Fribourg, Switzerland

ABOUT THIS SEMINAR

This seminar is a team effort - we want to learn the basics of Teichmüller Theory in order to understand some of its powerful implications in Analysis, Geometry, and Topology. Please join us!

Here is a brief outline of what we plan to cover: after a first introductory talk by the organizers, we will read Chapters 4-7 in the first volume of Hubbard’s book series on Teichmüller theory (see below for more info on the book). This main part of the seminar will consist of a total of 11 talks. The last two talks are reserved for applications. Tentatively, this will be either the classification of surface homeomorphisms or the topological characterisation of rational maps. Both these theorems are due to Thurston and we can base our discussion on the second volume of Hubbard’s book series.

This seminar is organized by: Giuliano Basso, Annina Iseli, Livio Liechti, and Stefan Wenger.


Cover picture: https://www.youtube.com/watch?v=FHzPgarTkqI
by Sam Wells and Aidan Donahue (Geometry Lab, George Mason University, Fairfax)


DATES, TIMES, AND LOCATION

The seminar will take place weekly on Tuesdays 15-17h during the entire fall semester which is Sept. 21 - Dec. 2021. The meetings will be held at University of Fribourg, Switzerland in room 2.301 in the Géosciences building.

We plan to hold this seminar in person (non-hybrid) if the Covid situation allows for it.

TENTATIVE SCHEDULE


  • Meeting 1 - 21.Sept. Introductory talk (******) Livio Liechti

  • Meeting 2 - 28.Sept. Quasiconformal maps and Grötzsch’s theorem (4.1-4.3) Giuliano Basso

  • Meeting 3 - 5.Okt. Normal Families and Quasisymmetric maps (4.4-4.5) Damaris Meier

  • Meeting 4 - 12.Okt. The mapping theorem (4.6-4.7) Elia Bubani

  • Meeting 5 - 19.Okt. Beltrami forms and complex structures (4.8) Patrick Ghanaat

  • Meeting 6 - 26.Okt. Boundary values and the Douady-Earle extension (4.9-5.1) Julia Münch

  • Meeting 7 - 2.Nov. AUSFALL

  • Meeting 8 - 9.Nov. Teichmüller extremal mappings (5.3) Giuliano Basso

  • Meeting 9 - 16.Nov. Spaces of quadratic differentials (5.4) Annina Iseli

  • Meeting 10 - 23.Nov. Quasiconformal surfaces, Teichmüller spaces (6.1 & 6.4) Livio Ferretti

  • Meeting 11 - 30.Nov. The Schwarzian derivative (6.3) Elia Bubani

  • Meeting 12 - 7.Dez. Analytic structure on Teichmüller space (6.4 & 6.5) Livio Liechti

  • Meeting 13 - 14.Dez. Tangent spaces & Contractibility (6.6-6.7) Patrick Ghanaat

  • Meeting 14 - 21.Dez. Geometry of finite dimensional Teichmüller spaces (7.1-7.3) Giuliano Basso

  • Meeting 15 - Jan.2022 Classification of surface homeomorphisms (8.1 & 8.4)


HUBBARD'S BOOKS

As mentioned in the outline of the seminar, we will base the main part of this seminar on Volume 1 of Hubbard's book series about Teichmüller Theory. It can be ordered for example here: http://matrixeditions.com/orders.html
It can likely also be purchased through your University's book store or you can ask University's library whether they would we willing to purchase it and add it to their catalogue.

The table of contents is freely accessible here.


GET IN TOUCH!

Please reach out with questions, comments, or to let us know that you are planning on joining our reading seminar:

annina.iseli[the-symbol]math.unifr.ch