University of Colorado Boulder

Fiftieth Annual DeLong Lecture Series

Department of Mathematics

Professor Benedict H. Gross

Harvard University

January 15, 2014
5:00-6:00 pm RAMY C250 The rank of elliptic curves
The problem of finding rational solutions to cubic equations is central in number theory, and goes back to Fermat. I will discuss why these equations are particularly interesting, and the modern theory of elliptic curves that has developed over the past century, including the Mordell-Weil theorem and the conjecture of Birch and Swinnerton-Dyer. I will end with a description of some recent results of Manjul Bhargava on the average rank.

Following Wednesday's lecture, there will be a reception in honor of Professor Gross at the Koenig Alumni Center, 1202 University Avenue (the SE corner of Broadway and University).
January 16, 2014
5:00-6:00 pm RAMY C250 The arithmetic of hyperelliptic curves
Hyperelliptic curves over Q have equations of the form y2 = F(x), where F(x) is a polynomial with rational coefficients which has simple roots over the complex numbers. When the degree of F(x) is at least 5, the genus of the hyperelliptic curve is at least 2 and Faltings has proved that there are only finitely many rational solutions. In this talk, I will describe methods which Manjul Bhargava and I have developed to quantify this result, on average.

Benedict H. Gross

Benedict H. Gross

Benedict (Dick) Gross is the George Vasmer Leverett Professor of Mathematics at Harvard University. Before he joined the Harvard mathematics faculty, Professor Gross taught at Princeton University, the University of Paris, and Brown University. He is a member of the American Academy of Arts and Sciences and the National Academy of Sciences.

Gross's research interests are primarily in number theory and representation theory. Together with Don Zagier, he proved a formula relating the heights of Heegner divisors to the first derivatives of Rankin L-functions at s=1. Their work provided some insight into the conjecture of Birch and Swinnerton-Dyer, and was awarded the Cole Prize in Number Theory of the American Mathematical Society. Dick has had over 30 PhD students, and has enjoyed working jointly with many of his students and colleagues. Over the past two years he has been collaborating with Manjul Bhargava on the arithmetic of hyper elliptic curves.

DeLong Lecture Series

This Lecture Series is funded by an endowment given by Professor Ira M. DeLong, who came to the University of Colorado in 1888 at the age of 33. Professor DeLong essentially became the mathematics department by teaching not only the college subjects but also the preparatory mathematics courses. Professor DeLong was a prominent citizen of the community of Boulder as well as president of the Mercantile Bank and Trust Company, organizer of the Colorado Education Association, and president of the charter convention that gave Boulder the city manager form of government in 1917. After his death in 1942 it was decided that the bequest he made to the mathematics department would accumulate interest until income became available to fund DeLong prizes for undergraduates and DeLong Lectureships to bring outstanding mathematicians to campus each year. The first DeLong Lectures were delivered in the 1962-63 academic year.

Previous DeLong Lecturers