Pavlo Yatsyna: Quadratic forms and totally real number fields

Abstract.

In this talk, I'll share recent progress in the study of quadratic forms defined over rings of integers. Specifically, we'll zero in on the question of what integers a given quadratic form represents and when it represents all of them. In the second half, I will discuss what we know about totally real number fields, which have quadratic forms with rational integer coefficients that represent all totally positive integers.