Counting Lattice Points in Moduli Spaces of Quadratic Differentials

Explore the intricate world of lattice point counting in moduli spaces of quadratic differentials through this 47-minute lecture by Peter Zograf. Delve into the methodology for enumerating lattice points represented by square-tiled surfaces in moduli spaces of meromorphic quadratic differentials with simple poles on complex algebraic curves. Discover the versatility of lattice point counting through three distinct examples: evaluating Masur-Veech volumes of moduli spaces of quadratic differentials, computing asymptotic frequencies of geodesic multicurves on hyperbolic surfaces, and asymptotically enumerating meanders with a fixed number of minimal arcs. Gain insights into complex mathematical concepts and their applications in algebraic geometry and topology. Access accompanying slides for visual aid and further understanding of the presented material.