**The 2022 Cantrell Lecture Speaker will be Professor Akshay Venkatesh. **

Dr. Venkatesh is a professor at the Institute for Advanced Study in Princeton.Among many other honors, in 2018, he was awarded the Fields Medal for his synthesis of analytic number theory, homogeneous dynamics, topology, and representation theory. The citation describes him as having "made profound contributions to an exceptionally broad range of subjects in mathematics" and recognizes him for having "solved many longstanding problems by combining methods from seemingly unrelated areas, presented novel viewpoints on classical problems, and produced strikingly far-reaching conjectures."

**Lecture 1**

**May 2nd @ 4pm- Miller Learning Center Room 0148 **

**Number theory and 3-dimensional geometry. **

There is a wonderful analogy between the theory of numbers, and 3-dimensional geometry. For example, prime numbers behave like knots! I will explain some of the history of this analogy and how it is evolving.

**Lecture 2**

**May 3rd @ 4pm- Boyd Room 0328**

**Symplectic L-functions and their topological analogues. **

The topology of the symplectic group enters into many different areas of mathematics. After discussing a couple of “classical” manifestations of this, I will explain a new one, in the theory of L-functions, as well as a purely topological analogue of the statement. I am not going to assume any familiarity with the theory of L-functions for the talk. Joint work with Amina Abdurrahman.

**Lecture 3**

**May 4th @ 2pm- Boyd Room 0328**

**Relative Langlands duality. **

If we are given a compact Lie group G acting on a space X, a powerful tool in “approximately” decomposing the G-action on functions on X is the orbit method. I will describe this method and how it sometimes refines to an exact algebraic statement which involves a “dual” group G^ and dual space X^. This is part of a joint work with David Ben-Zvi and Yiannis Sakellaridis about duality in the relative Langlands program. I will do my best to make the talk comprehensible without any familiarity with the framework of the Langlands program.