**Date & Time:** Thursday, July 31, 2014, 16:00-17:00.

**Venue:** Ramanujan Hall

**Title:** Effective Quantitative Oppenheim for almost every quadratic form

**Speaker:** Jayadev Athreya, UIUC

**Abstract:** In 1986, Margulis, using methods from dynamics, proved A. Oppenheim's
1929 conjecture that for every indefinite irrational quadratic form in at least
three variables, the values it takes at integer lattice points form a dense
subset of the real line. Subsequently, Eskin-Margulis-Mozes proved an associated
counting result, giving polynomial asymptotics for the number of lattice points
of norm at most $T$ which get mapped to a fixed interval. In joint work with
Margulis, we give an effective version if this result for almost every quadratic
form.