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

**Date:** 29th November 2022

**Time: **9:15 PM-10:15 PM

**Abstract:** We shall give two proofs of the following approximation theorem due to Carathéodory.

*Any holomorphic function from the open unit disc to the closed unit disc can be approximated locally uniformly by finite Blaschke products. *

We’ll also discuss some generalizations of this theorem and recent advances. We’ll conclude the talk with some open problems.

**Prerequisites**: First Course in Complex Analysis