2002–2003 Erdős Colloquium:
Benedict H. Gross

Automorphisms of even unimodular lattices

Speaker: Benedict H. Gross, Harvard University
Date and time: Monday, February 24, 2003, 4:00–5:00 p.m.
Location: Little Hall, Room 121
Opening remarks: Pierre Ramond, Distinguished Professor of Physics
Refreshments: 3:30 p.m. and after the lecture, Little Hall, Room 339 (the Atrium)

Abstract

An even unimodular lattice L is an orthogonal space over the integers. If the quadratic form is indefinite, these lattices are determined by their signature (p, q) over the reals, which must satisfy \(p\equiv q\pmod{8}\). However, the orthogonal group O(L) is still mysterious. I will describe properties of the characteristic polynomials of orthogonal transformations, and give sufficient conditions on an integral monic polynomial for it to appear in this manner. This is a report on joint work with Curt McMullen, who encountered the problem in an investigation of dynamics on K3 surfaces.

About the speaker

Benedict H. Gross is George Vasmer Leverett Professor of Mathematics at Harvard University. He has been awarded Cole Prize of the American Mathematical Society in 1987, and he is a Fellow of the American Academy of Arts and Sciences since 1992. He is Dean for Undergraduate Education of Harvard University. Professor Gross has made fundamental contributions to mathematics, in particular in number theory and algebraic geometry.

Related seminar talk

Professor Gross will also give a lecture entitled “On the exceptional series of Lie groups” at the Algebra Seminar, Tuesday, February 25, 2003, 9:35–10:25 a.m., Little Hall, Room 339.