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Flat Surfaces
Summer Semester 2021
You can find here the information for the course Flat Surfaces for bachelor and master students during the summer term 2021.
Due to Covid19 pandemic, the lessons are provided online, as scheduled below.
If you have any questions, please write an email to Yiu Man Wong
Course description:
A polygon presentation of a Riemann surface with parallel side identifications carries with it the additional information of a holomorphic differential on the Riemann surface. Any pair of Riemann surface and holomorphic differential is known as a flat surface and the natural action of SL(2,R) on any such polygon presentation provides flat surfaces that share many interesting dynamical and algebraic properties. Recent decades have seen dynamical properties of billiards in polygons, square tiled surfaces (torus covers or Hurwitz spaces), and piecewise isometries of the interval motivate many developments in the study of the orbits and properties of the SL(2,R)-action, known broadly as Teichmueller dynamics. This course aims to give an accessible, example-driven introduction to this exciting area of current research.
Prerequisites:
It is suggested that this course be taken concurrently with Complex Geometry.
Schedule:
The first lecture is proposed to start at 10 a.m. on 20th April 2021 (Tue) and there will be one lecture per week. The lectures will be held via Zoom and the links and videos are available on the OLAT page.
Literature:
Anton Zorich, FLAT SURFACES (pdf)
Alex Wright, TRANSLATION SURFACES AND THEIR ORBITCLOSURES:AN INTRODUCTION FOR A BROAD AUDIENCE (pdf)
Dawei Chen, Andrei Bud, MODULI OF DIFFERENTIALS AND TEICHMULLER DYNAMICS (pdf)
