Recent work on the zeroes of the Riemann zeta function

I 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 hypothesis

In 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.

Larry Guth is a Claude E. Shannon Professor of Mathematics at MIT.  He is a member of the US National Academy of Sciences and has made significant contributions to metric geometry, harmonic analysis, extremal combinatorics, and number theory.