Large genus bounds for the distribution of triangulated surfaces in moduli space


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April 29, 2020 4:00 pm - 5:30 pm
via Zoom Video Conferencing

Sahana Vasudevan - MIT

Triangulated surfaces are compact (hyperbolic) Riemann surfaces that admit a conformal triangulation by equilateral triangles. Brooks and Makover started the study of the geometry of random large genus triangulated surfaces. Mirzakhani later proved analogous results for random hyperbolic surfaces. These results, along with many others, suggest that the geometry of triangulated surfaces mirrors the geometry of arbitrary hyperbolic surfaces especially in the case of large genus asymptotics. In this talk, I will describe an approach to show that triangulated surfaces are asymptotically well-distributed in moduli space.

via Zoom: