Masser's conjecture on equivalence of integral quadratic forms

Han Li

Wesleyan University

Brandeis University

Thursday, March 24, 2016

Talk at 4:30 p.m. in 317 Goldsmith Hall

Tea at 4:00 p.m. in 100 Goldsmith Hall


Abstract: A classical problem in the theory of quadratic forms is to decide whether two given integral quadratic forms are equivalent. Stated in terms matrices the problem asks for given symmetric n-by-n integral matrices A and B whether there is a unimodular integral matrix X satisfying A=X'BX, where X' is the transpose of X. For definite forms one can construct a simple decision procedure. Somewhat surprisingly, no such procedure was known for indefinite forms until the work of C. L. Siegel in the early 1970s. In the late 1990s D. W. Masser conjectured for n at least 3, there exists a polynomial search bound for X in terms of the heights of A and B. In this talk we shall discuss our recent resolution of this conjecture based on a joint work with Professor Gregory A. Margulis.

Home Web page: Alexandru I. Suciu Posted: September 7, 2015
Comments to: URL: