This talk focuses on pointwise ergodic theorems and their connection to Bourgain's path to his Fields Medal. We aim to cover four key milestones:
Part One: We investigate the norm convergence of ergodic averages, concluding with an explanation of the Baby Spectral Theorem.
Part Two: We examine the pointwise ergodic theorem established by Birkhoff in 1931. Depending on the time available, we will cover at least one proof, exploring Calderon's transference in the process.
Part Three: This section delves into the circle method and its comparison to the continuous Fourier Transform. We will also discuss several properties of prime numbers and provide an approximation for averages along primes.
Part Four: We introduce the concept of oscillation and present a proof of the pointwise ergodic theorem along primes. Time permitting, we will explore further developments post-1990.

The references are uploaded in the following link:
https://drive.google.com/drive/folders/1_zIDuDybfkfYuHhrlLtwe-rd6SdpraPZ?usp=drive_link