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Suggestions for reading before bed
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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 geometer,
Proc. Sympos. Pure Math., 95 171-197, AMS, Providence, RI, 2017;
arXiv:1602.02260
Andrei Bud and Dawei Chen, Moduli of Differentials and Teichmüller dynamics,
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, 459-471, Springer, Berlin, 2002
Comprehensive surveys (risk to delay your going to bed):
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
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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.
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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):
(beware: risk to provoke psychedelic dreams)
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; arXiv:1705.05190.
Vincent Delecroix, Elise Goujard, Peter Zograf, Anton Zorich,
Higher genus meanders and Masur–Veech volumes (2023), arXiv:2304.02567.