Lecture 1: Monday, March 16, in 150 Miller Learning Center The (algebraic) geometry of the Mandelbrot set Lecture 2: Tuesday, March 17, in 328 Boyd Elliptic curves, periodic points, and bifurcations Lecture 3: Wednesday, March 18, in 328 Boyd From abelian varieties to dynamical rigidity: a unifying conjecture     Abstract: One of the most famous (and still not fully understood) objects in mathematics is the Mandelbrot set. …

Recent work on the zeroes of the Riemann zeta functionI will discuss my recent work with James Maynard estimating the number of zeroes of the zeta function in different regions.

The Riemann zeta function and the Riemann hypothesisIn Talk 1, we learned about some strange patterns in the prime numbers.  In this talk, we try to explain where these strange patterns come from.  This leads us to the Riemann zeta function.  We also introduce an important open question called the Riemann hypothesis, and discuss how it relates to prime numbers and why it is hard to prove.

Lecture 1 Monday, March 10, in 148 Miller Learning Center Prime numbers: probability, physics, and computation Abstract: This talk is about how prime numbers are distributed.  As we look at bigger numbers, primes slowly get rarer.  We can measure this precisely by counting how many primes there are in different intervals.  There is a simple formula, discovered around 1800, that gives a pretty good approximation for the number of…