Monday, March 10 2025, 4 - 5pm Tuesday, March 11 2025, 4 - 5pm Wednesday, March 12 2025, 4 - 5pm 148 Miller Learning Center and 328 Boyd Larry Guth Claude E. Shannon Professor of Mathematics MIT 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 primes in an interval. This simple formula isn't perfect, so we can study how the true number of primes deviates from the approximation.Do the deviations look random, like stock prices?Do they behave predictably like pendulums?How accurately can we predict the number of primes in an interval using an algebraic formula?This talk is aimed at a general mathematical audience, including math majors and high school math teachers. Lecture 2 Tuesday, March 11, in 328 Boyd The Riemann zeta function and the Riemann hypothesis Abstract: 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. Lecture 3 Wednesday, March 12, in 328 Boyd Recent work on the zeroes of the Riemann zeta functionAbstract: I will discuss my recent work with James Maynard estimating the number of zeroes of the zeta function in different regions. Larry Guth is the 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. He has received multiple international prizes, which point to his broad contributions to mathematics: The Salem Prize in Mathematics, for outstanding contributions to analysis; the New Horizons in Mathematics Prize "for ingenious and surprising solutions to long standing open problems in symplectic geometry, Riemannian geometry, harmonic analysis, and combinatorial geometry”; the Bôcher Memorial Prize of the AMS, for his “deep and influential development of algebraic and topological methods for partitioning the Euclidean space and multi-scale organization of data, and his powerful applications of these tools in harmonic analysis, incidence geometry, analytic number theory, and partial differential equations”; and the Maryam Mirzakhani Prize in Mathematics (formerly the NAS Award in Mathematics), “for developing surprising, original, and deep connections between geometry, analysis, topology, and combinatorics, which have led to the solution of, or major advances on, many outstanding problems in these fields.” He received a Sloan Fellowship in 2010 and gave an Invited Address (geometry section) at the International Congress of Mathematicians; and a Plenary Address at the 2022 International Congress of Mathematicians.
