Introduction to geometry, dynamics, and moduli in low dimensions - LMS-CMI Research School 2017

Under construction!

Some references (survey papers and lecture notes)

photo Howard Masur - Ergodic theory of translation surfaces,
   Handbook of Dynamical Systems, Vol. 1B pdf

photo Alex Wright - Translation surfaces and their orbit closures: An introduction for a broad audience,
   EMS Surv. Math. Sci. 2015 pdf

photo Giovani Forni and Carlos Matheus - Introduction to Teichm├╝ller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards,
   ArXiV pdf

photo Sebastien Gouëzel and Erwan Lanneau - Un théorème de Kerckhoff, Masur et Smillie : Unique ergodicité sur les surfaces plates,
   Séminaires et Congrès 20 (2010) pdf

photo Howard Masur and Serge Tabachnikov - Rational billiards and flat structures,
   Handbook of dynamical systems, Vol. 1A, North-Holland, Chapter 13 (2002) dvi | pdf (with figures).

photo Marcelo Viana - Dynamics of interval exchange maps and Teichmüller flows,
   Lecture notes of graduate courses taught at IMPA in 2005 and 2007 pdf.

photo Martin Möller - Affine groups of flat surfaces,
   Handbook of Teichmüller Theory, Volume 2, Chapter 10 pdf.

photo Martin Möller -Teichmüller curves from an algebraic viewpoint,
   Park City Lecture notes (2011) pdf.

photo John Smillie -The dynamics of billiard flows in rationnal polygons,
   Dynamical System Ergodic Theory and Applications (2000) pdf.

photo John Smillie and Barak Weiss - Finiteness results for flat surfaces: a survey and problem list,
   Proceedings of a conference, Fields Institute, Toronto (2006) pdf.

photo Yaroslav Vorobets - Planar structures and billiards in rational polygons: the Veech alternative,
   Russian Mathematical Surveys pdf.

photo Jean-Christophe Yoccoz - Échanges d'Intervalles et Surfaces de Translation,
   Séminaire BOURBAKI 60ème année, 2007-2008, no 996 (2008) pdf.

photo Jean-Christophe Yoccoz - Interval exchange maps and translation surfaces,
   Pisa Lectures (2007) pdf.

photo Jean-Christophe Yoccoz - Échanges d'Intervalles,
   Cours au Collège de France (2005) pdf. See also Matheus's Weblog.

photo Jean-Christophe Yoccoz - Cours et séminaires au Collège de France,
   Page du Collège de France html.

(Some) Previous schools

Les Houches School: Frontiers in Number Theory, Geometry and Physics, proceedings of the Spring School at Les Houches (2003)
photo Anton Zorich - Flat surfaces pdf.
photo Jean-Christophe Yoccoz - Continued Fraction Algorithms for Interval Exchange Maps: an Introduction pdf.

Luminy (2003): Handbook of Dynamical Systems (Vol 1, Part B, 2006):
photo Pascal Hubert and Thomas Schmidt - Chapter 6: An introduction to veech surfaces pdf.
photo Howard Masur - Chapter 7: Ergodic Theory of Translation surfaces pdf.
photo Giovanni Forni - Chapter 8: On the lyapunov exponents of the Kontsevich-Zorich cocycle pdf.
photo Alex Eskin - Chapter 9: Counting problems in moduli space pdf.

Problem lists

photo P. Hubert, H. Masur, T. Schmidt and A. Zorich - Problems on billiards, flat surfaces and translation surfaces,
   Problems on Mapping Class Groups and Related Topics Proc. Sympos. Pure Math., 74, Amer. Math. Soc., Providence, RI, (2006) pdf.

photo J. Smillie and B. Weiss - Finiteness results for flat surfaces: a survey and problem list,
   Partially hyperbolic dynamics, laminations, and Teichmüller flow Proceedings of a conference, Fields Institute, Toronto (2006) pdf.

EXERCISES

photo Alex Wright - EXERCISES TO ACCOMPANY TRANSLATION SURFACES AND THEIR ORBIT CLOSURES,
   pdf.
More lectures on Alex's web page: here.

photo Vincent Delecroix and Samuel Lelievre - School at Morelia,
   here.