Effective density for values of generic quadratic forms

INFORMAL GEOMETRY AND DYNAMICS

Speaker:

Dubi Kelmer - Boston College

via Zoom Video Conferencing: https://harvard.zoom.us/j/972495373

The Oppenheim Conjecture, proved by Margulis, states that any irrational quadratic form, has values (at integer coordinates) that are dense on the real line. However, obtaining effective estimates for any given form is a very difficult problem. In this talk I will discuss recent results, where such effective estimates are obtained for generic forms using a combination of methods from dynamics and analytic number theory. I will also discuss some results on analogous problems for inhomogenous forms and more general higher degree polynomials.