Riemann Zeta Function

This lecture covers the Riemann zeta function, focusing on its properties and applications in number theory and algebraic geometry. The instructor explains the concept of zeta functions, rationality, and the Weil conjectures. The lecture also delves into the functional equation and the Riemann hypothesis, providing insights into the behavior of the zeta function at different points. Additionally, the lecture discusses Betti numbers and their significance in understanding algebraic varieties. Throughout the lecture, various analogies and mathematical formulations are presented to deepen the understanding of the Riemann zeta function.