From the proceedings of the AMS special session with related papers, January 45, 1995, San Francisco, California.

Includes bibliographical references.

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