**Speaker:** Abhay Jindal (Int. PhD)

**Date:** 26 October, 2021

**Time: **9:15pm-10:15pm

**Abstract:** Does every operator on an infinite-dimensional Hilbert space have a non-trivial invariant subspace? The question is still unanswered. A possible approach is to classify all invariant subspaces of all known operators in the hope of getting an insight that will lead to proof or a counterexample. Beurling’s theorem is a step in that direction. In this talk, we aim to prove Beurling’s theorem which gives a complete characterization of the invariant subspaces of the Hardy shift.

**Prerequisite:** Familiarity with Complex Analysis and Hilbert Spaces.