"From the proceedings of the AMS special session with related papers, January 4-5, 1995, San Francisco, California."

Includes bibliographical references.

External geometries / Peter Sarnak -- Extremal Riemann surfaces with a large number of systoles / Paul Schmutz Schaller -- On arithmetic genus 2 subgroups of triangle groups / M. NÌaÌatÌanen and T. Kuusalo -- Some lattices obtained from Riemann surfaces / M. Bernstein and N.J.A. Sloane -- Jacobian of the Picard curve / J.R. Quine -- Fermat's quartic curve, Klein's curve, and the terahedron / Rubí E. Rodríguez and Víctor Gonzáles-Aguilera -- Riemann surfaces admiting large automorphism groups / Ravi S. Kulkarni -- The splitting of some Jacobi varieties using their automorphism groups / John F.X. Ries -- Number theory, theta identities, and modular curves / Robert Brooks, Hershel M. Farkas, and Irwin Kra -- Uniformization of some quotients of modular curves / Robert Brooks and Yaacov Kopeliovich -- Teichmúller disks and Veech's F-structures / Clifford J. Earle and Frederick P. Gardiner -- On the geometry and spectral asymptotics of degenerating hyperbolic three manifolds / Józef Dodziuk and Jay Jorgenson -- Differential equations for the quadratic periods of abelian differentials / Debra Curtis and Marvin Tretkoff -- Zeta functions on Carlo Morpugo -- A minimum problem for heat kernels of flat tori / Albert Baernstein II.