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
 December 1
 December 8
Jae Min Lee Properties of the Weil--Petersson metric as a Kähler metric, and formulas for the sectional curvature.

  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.