Anish Ghosh: Values of quadratic forms at integer points (NTWS 100)
Channel: Number Theory Web Seminar
Date: 02/09/2023

Abstract: A famous theorem of Margulis, resolving a conjecture of Oppenheim, states that an indefinite, irrational quadratic form in at least three variables takes a dense set of values at integer points. Recently there has been a push towards establishing effective versions of Margulis's theorem. I will explain Margulis's approach to this problem which involves the ergodic theory of group actions on homogeneous spaces. I will then discuss some new effective results in this direction. These results use a variety of techniques including tools from ergodic theory, analytic number theory as well as the geometry of numbers.

Number Theory Web Seminar: https://www.ntwebseminar.org

Original air date: 
Thursday, September 30, 2021 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, October 1, 2021 (1am AEST, 4am NZDT)