Akshay Venkatesh, Robert and Luisa Fernholz Professor in the School of Mathematics, and a 2018 recipient of the Fields Medal, will deliver the public lecture “Primes and Knots” on October 25, 2019, at 5:30 p.m. in Wolfensohn Hall.

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Venkatesh is a number theorist who has made contributions to numerous fields of study, including representation theory, dynamics, and algebraic topology, and has often united disparate areas of research. During his public lecture, Venkatesh will explore the surprising parallels that exist between prime numbers and mathematical knots.

Number theory is a branch of mathematics focused primarily on the study of integers—those numbers that can be written without a fraction. Prime numbers are some of the most intriguing integers. Prime numbers—such as 2, 3, 5, and 7—are only divisible by 1 and themselves; they serve as the building blocks for all other numbers. Yet despite this foundational nature, primes are deceivingly hard to predict, and there is no quick way to decompose a number into its prime factors.

Mathematical knots exist in the three-dimensional space of Euclidean geometry. Unlike the knot of a shoelace, mathematical knots do not have ends, instead making a continuous loop. However, mathematical knots are similar in the sense that they, too, can quickly become a tangled jungle of twists and turns that only the most determined among us may attempt to unravel.

How do these abstract concepts relate, and what do they tell us about mathematics and the world in which we live? These are a few of the questions Venkatesh will seek to answer. Participants in the program will be able to share in the effort to bring clarity to these enduring puzzles.

Venkatesh earned a B.Sc. in Mathematics and Physics at the University of Western Australia (1997) and a Ph.D. in Mathematics at Princeton University (2002). Most recently a Professor at Stanford University (2008–18), he was C.L.E. Moore Instructor (2002–04) at the Massachusetts Institute of Technology, a Member (2005–06) in the Institute’s School of Mathematics, and Associate Professor (2005–08) at New York University’s Courant Institute of Mathematical Sciences. His research has been recognized with many awards, including the Fields Medal, Ostrowski Prize, the Infosys Prize, and the Salem Prize. He was recently elected a Fellow of the Royal Society.

IAS public lectures are an opportunity for educational exchange with the broader community and the transmission of knowledge to empower human thought both locally and globally.