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An introduction to flat surfaces - I

Introductory Workshop: Holomorphic Differentials in Mathematics and Physics August 19, 2019 - August 23, 2019

August 19, 2019 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Elise Goujard (Université de Bordeaux I)
Location: SLMath: Eisenbud Auditorium
Tags/Keywords

  • Flat surfaces

  • Teichmüller theory

  • moduli spaces

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

g-flatsurfaces
Abstract

Holomorphic differentials equip naturally Riemann surfaces with a flat structure. Motivated by the study of billiards in polygons, I will review the geometry and dynamics of moduli spaces of flat surfaces: their statification, the GL(2,R) action, and the Teichmüller flow, and then focus on several invariants such as Masur-Veech volumes of strata, Siegel-Veech constants (related to the counting of closed geodesics), Lyapunov exponents, and their interconnection.
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Video/Audio Files

g-flatsurfaces

H.264 Video 895_27259_8047_895_27259_7867_2dfdf-Goujard.mp4
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