Moduli Spaces of Riemann Surfaces (Fall 2025)

 

What is this course about?

For discussing moduli of Riemann surfaces, besides via algebraic geometry only, one can enter this subject as well via complex analysis, differential geometry and combinatorial topology. We will touch on all of them in this course.​

 

Prerequisite

Basic knowledge of differentiable manifolds.

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Literature

[1] Eduard Looijenga, Moduli spaces of Riemann surfaces.

[2] Joe Harris, Ian Morrison, Moduli of curves.

[3] Enrico Arbarello, Maurizio Cornalba, Phillip A. Griffiths, Geometry of algebraic curves, volume II.

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Place and time

Tuesdays, 08:50-12:15; Venue: A3-1a-204

Zoom: 787 662 9899, PW: BIMSA

Starting from Sep. 16

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WeChat Group

We have created a WeChat Group for communication​. You could write to me if you would like to join.

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Material covered

Sep. 16: Mapping class groups, conformal structures, uniformization.

Sep. 23: Hyperbolic geometry in dimension 2, T_{0,3}, \Gamma_{0,3},T_{1,1}, \Gamma_{1,1}.

Sep. 30: Hyperbolic surfaces, pants decompositions.

Oct. 7: Holiday.

Oct. 14: Fenchel-Nielsen parametrizations for Teichmuller spaces.

Oct. 21: Quadratic differentials.

Oct. 28: Jenkins-Strebel differentials, ribbon graphs, thickened Teichmuller spaces.

Nov. 4: Ideal triangulation of thickened Teichmuller spaces, barycentric subdivision, homotopy type of M_{g,P}, Dolbeault cohomology.

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