Celebration In Honor of the Frank C. and Florence S. Professorship

A. Ogg is well-known for his numerous accomplishments: the Grothendieck-Ogg-Shafarevich formula; the N\’eron-Ogg-Shafarevich criterion; Ogg’s formula for the conductor of an elliptic curve; the rational torsion conjecture for elliptic curves; and his insight connecting finite groups and modular forms, which started the moonshine theory. In this talk, W. Li shall discuss a different aspect—namely the impact of his work on modular forms through personal encounters, including the newform theory and the Rankin-Selberg convolution of modular forms. Li will introduce a new method to compute the traces of Hecke operators on the space of even weight (cusp) forms for certain triangle groups, a joint work with J. Hoffman, L. Long, and F-T. Tu. This explicit trace formula is especially interesting when the triangle group is cocompact—that is, its fundamental domain is a Shimura curve.