Celebration In Honor of the Frank C. and Florence S. Professorship
In recognition of the work of Mathematician and Member of IAS (1968-69), Andrew P. Ogg
WELCOME by David Nirenberg | Director and Leon Levy Professor, Institute for Advanced Study
WELCOME by Akshay Venkatesh | Robert and Luisa Fernholz Professor, Institute for Advanced Study
THOUGHTS ABOUT ANDREW OGG’S (TORSION) CONJECTURE
2:15 PM, Barry Mazur | Gerhard Gade University Professor, Harvard University
Ogg’s celebrated conjecture can be paraphrased as saying that rational points (on the modular curves that parametrize torsion points on elliptic curves) exist if and only if there is a good geometric reason for them to exist. Ogg’s mathematical viewpoint has inspired an increasingly broad array of results and conjectures. B. Mazur’s talk will discuss this and recent related work.
MODULAR CURVES, MODULAR FORMS AND HECKE OPERATORS: OLD AND NEW
3:00 PM, Winnie Li | Distinguished Professor of Mathematics, Penn State University
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.
A GUIDE TO MOONSHINE
4:15 PM, John Duncan | Associate Professor, Emory University and Research Fellow, Academia Sinica
J. Duncan will explain how the works of Andrew Ogg—especially his questions—have guided the maturation of moonshine from its inception to the present, and continue to shape its future perspective.