Annual Progress Seminar Time: 02:00 PM -- 02:35 PM Host: Sourav Pal Speaker: Priyanka Aroda Title: Contractions and their dilations Abstract: A contraction is an operator on a Hilbert space which has norm atmost 1. We study Sz.-Nagy's dilation theorem which models contractions as a part of nicer operators on larger spaces. We also discuss a more direct and explicit construction of a unitary dilation of a contraction, which is due to Schaffer. We study an analogue to Sz.-Nagy's dilation theorem, due to Ando, for a pair of commuting contractions.