Teichmuller Theory

Student Reading Seminar


  FALL 2015

Tuesdays 1-2 PM
MATH 350

   
This is, in some sense, a continuation of the seminar from the summer.

Schedule of talks:

 August 25
  Steve Preston
 Organizational meeting
 September 1
  Steve Preston  Riemannian geometry, metrics and geodesics.
 September 8
  Pearce Washabaugh
  Introduction to infinite dimensional geometry.
 September 15
  Steve Preston  Riemannian geometry, curvature, normal and isothermal coordinates, the basic constant curvature spaces, and the uniformization theorem for surfaces.
 September 22
  Steve Preston  Riemannian geometry, connections, curvature, harmonic theory, metrics on Lie groups.
 September 29
  Yano Casalalaina  Complex geometry, definition of a complex manifold, tangent bundles.
 October 6
  Yano Casalalaina  Complex geometry, connections on a complex manifold.
 October 13
  Yano Casalalaina  Complex geometry, curvature and Kahler--Einstein metrics.
 October 20
  Boramay Chhay
  Teichmuller theory, space of metrics, subspace of metrics with constant curvature, quotient by the diffeomorphism group, relationship to the space of almost complex structures, and descending the natural metrics to the Weil--Petersson metric on the quotient, Teichmuller space.
 October 27
  Boramay Chhay  Teichmuller theory continued.
 November 3
  Steve Preston
  Genus 1 example
 November 10
  Steve Preston
  Genus at least 2 
 November 17
 Lucas Simon  Deformations of complex structure, and quadratic differentials.
 November 24
 NO MEETING
   THANKSGIVING BREAK
 December 1
 NO MEETING
  NO MEETING
 December 8
 Jae Min Lee Properties of the Weil--Petersson metric as a Kähler metric, and formulas for the sectional curvature.


References:
  1. Geometry of Algebraic Curves, Volume 2, E. Arbarello, M. Cornalba, and P. Griffiths.
  2. Introduction to Teichmuller spaces, by Y. Imayoshi and M. Taniguchi.
  3. Teichmuller Theory and Quadratic Differentials, by F. Gardiner.
  4. Teichmuller Theory in Riemannian Geometry, by A. Tromba.
  5. Geometry and Spectra of Compact Riemann Surfaces, by P. Buser.
  6. Families of Riemann Surfaces and Weil-Petersson Geometry, by Scott Wolpert.
  7. Teichmuller theory and dynamical systems, lecture notes from Jeremy Kahn.
  8. Univalent functions and Teichmuller spaces, Olli Lehto,
  9. Kahler Geometry of Loop Spaces, Sergeev.
  10. Quasiconformal Teichmuller theory, Gardiner and Lakic.


This seminar is being organized by Stephen Preston and Sebastian (Yano) Casalaina-Martin.  This webpage is yet another example of a shameless (indirect) copying of a webpage of Pasha Belorousski's at the University of Michigan.