3:45 pm Tuesday, October 8, 2019
Junior Geometry: Symplectic volumes of moduli spaces of curves by
Charles Reid (UT Austin) in RLM 12.166
Moduli spaces of surfaces have fascinated people for a while now, partly because their study brings together so many areas of math. In my talk we will discuss the Moduli Space of hyperbolic surfaces with geodesic boundary. This space has a natural symplectic form called the Weil-Peterson symplectic form. More precisely, for every genus g, number of boundary components n, and boundary lengths L_1,...,L_n, the moduli space M_g,n(L_1,...,L_n) has a symplectic form. This means that it has a a symplectic volume. In the early 2000's Mirzakhani found an inductive formula for computing these symplectic volumes. I will give an idea of where the formula comes from, and we will apply her strategy to get the volume of M_1,1(L). If time permits, I might talk about why these volume formulas have a lot to say about the intersection theory of moduli space. Submitted by
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