• Suggestions for reading before bed 

  • Related lecture courses.

    • Bram Petri, Introduction to moduli spaces of Riemann surfaces,
    • Paul Apisa, Dynamics on moduli spaces - notes and problems

  • Part I. Flat world.

     Short survey papers in the spirit of geometric topology:
    • Alex Wright, From rational billiards to dynamics on moduli spaces, Bull. AMS 53 (2016), no. 1, 41-56; arXiv:1504.08290
    • Anton Zorich, The magic wand theorem of A. Eskin and M. Mirzakhani, Gazette des mathématiciens 142 (2014), 39-54; arXiv:1502.05654

     Short survey papers in the spirit of algebraic geometry:
    • Dimitri Zvonkine, Translation surfaces and moduli spaces, Lond. Math. Soc. Newsl. 480 (2019), 23-27
    • Dawei Chen, Teichmüller dynamics in the eyes of an algebraic geometery, Surveys on recent developments in algebraic geometry, 171-197, Proc. Sympos. Pure Math., 95, Amer. Math. Soc., Providence, RI, 2017; arXiv:1602.02260
    • Andrei Bud and Dawei Chen, Moduli of Differentials and Teichmüller dynamics, to be published in the proceedings of the MATH+ Fall School on Algebraic Geometry; arXiv:2004.05762.

     Short introduction to square-tiled surfaces:
    • Square tiled surfaces and Teichmüller volumes of the moduli spaces of abelian differentials, Rigidity in dynamics and geometry (Cambridge, 2000), 459-471, Springer, Berlin, 2002

     Comprehensive surveys:
    • Carlos Matheus and Giovanni Forni, Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards, J. Mod. Dyn. (2014), no. 3-4, 271-436; arXiv:1311.2758
    • Anton Zorich, Flat surfaces, Frontiers in number theory, physics, and geometry. I, 437-583, Springer, Berlin, 2006; arXiv:math/0609392

  • Part II. Hyperbolic world.
    •  Short introduction to train tracks:
    • Benson Farb and Dan Margalit, A Primer on Mapping Class Groups, Chapter 15.1 "A Fundamental Example", pp. 424-434

     Short survey of early works of Maryam Mirzakhani:
    • Anton Zorich, The work of Maryam Mirzakhani, Extended version of "The work of the 2014 Fields medalists", Notices AMS, 62 (2015), no. 11, 1334-1349.

     More comprehensive survey of works of Maryam Mirzakhani:
    • Alex Wright, A tour through Mirzakhani's work on moduli spaces of Riemann surfaces, Bull. AMS 57 (2020), no. 3, 359-408; arXiv:1905.01753

     Original paper of Maryam Mirzakhani:
    • Maryam Mirzakhani, Growth of the number of simple closed geodesics on hyperbolic surfaces, Annals of Math. 168 (2008), no. 1, 97-125.

     Comprehensive introduction to multicurves and measured laminations:
    • Francis Bonahon, Closed Curves on Surfaces.

  • Part III. Bridges between different worlds.

     Short introductions to moduli spaces, Deligne-Mumford compactification, Witten-Kontsevich correlators:
    • Ravi Vakil, The moduli space of curves and its tautological ring, Notices AMS, 50 (2003), no. 6, 647-658.
    • Dimitri Zvonkine, An introduction to moduli spaces of curves and their intersection theory, Handbook of Teichmüller theory. Volume III, 667-716, IRMA Lect. Math. Theor. Phys., 17, Eur. Math. Soc., Zürich, 2012

     An ample exercise of computation of degrees of line subbundles of the Hodge bundle - Section 3 of:
    • Alex Eskin, Maxim Kontsevich, Anton Zorich, Lyapunov spectrum of square-tiled cyclic covers, Journal of Modern Dynamics 5 (2011), no. 2, 319-353.

     Research papers on enumeration of square-tiled surfaces and on large genus asymptotics (Lecture 8):
    • Vincent Delecroix, Elise Goujard, Peter Zograf, Anton Zorich, Masur–Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves, Duke Math Journal, 170:12 (2021), 2633–2718; arXiv:2011.05306.
    • Amol Aggarwal, Large Genus Asymptotics for Intersection Numbers and Principal Strata Volumes of Quadratic Differentials Inventiones math. 226:3 (2021), 897–1010, arXiv:2004.05042.
    • Vincent Delecroix, Elise Goujard, Peter Zograf, Anton Zorich, Large genus asymptotic geometry of random square-tiled surfaces and of random multicurves (2023), arXiv:2304.02567. Inventiones math. 230:1 (2022), 123–224, arXiv:2007.04740.

     Introduction to meanders (Lecture 9):
    • Alexander Zvonkin, Meanders: A personal perspective, to appear in European Journal of Combinatorics; special issue dedicated to memory of Pierre Rosenstiehl.

     Research papers on enumeration of meanders (Lecture 9):
    • Vincent Delecroix, Elise Goujard, Peter Zograf, Anton Zorich, Enumeration of meanders and Masur–Veech volumes Forum of Mathematics Pi, 8:4 (2020), 80pp.
    • Vincent Delecroix, Elise Goujard, Peter Zograf, Anton Zorich, Higher genus meanders and Masur–Veech volumes (2023), arXiv:2304.02567.