2024 Gentry Lectures

Department of Mathematics 2024 Gentry Lectures 

Hyperbolic Knots and Links
April 11, 2024
Mathematics Colloquium
11:00  AM
016 Manchester Hall

We will define and discuss hyperbolic knots and links, and explore what is known about the minimal volume hyperbolic links with various numbers of components.

“The Markov theorem and the punctured modular torus”
April 11, 2024
Public Lecture
5:00 PM
016 Manchester Hall

A classic topic in number theory asks: which numbers are hard to approximate by rationals? A sequence of numbers, starting with the golden ratio, was defined by Lagrange as the hardest to approximate. Subsequently Markov showed that these numbers are associated to integer solutions to the Markov equation a2 +Ir+ c2 = 3abc. V.7e will discuss the relation of these topics with continued fractions, the hyperbolic plane, the modular group PSL2 (Z) and simple curves on the punctured modular torus. Then we will describe a proof of Markov’s theorem using loops on the modular torus and curvature flow.  Reception with light refreshments will follow the talk at 6:15 in the Green Room.

 

Bio: Ian Agol graduated with a B.S. in mathematics from the California Institute of Technology in 1992 and obtained his Ph.D. in 1998 from the University of California, San Diego. Dr. Agol’s long list of accomplishments includes being named a Guggenheim Fellow (2005), an American Mathematical Society Fellow (2012), and being awarded the Oswald Veblen Prize in Geometry (2013). In 2015, he was awarded the 2016 Breakthrough Prize in Mathematics, “for spectacular contributions to low dimensional topology and geometric group theory, including work on the solutions of the tameness, virtually Haken and virtual fibering conjectures.” In 2016, he was elected to the National Academy of Sciences. Formerly a professor at the University of Illinois, Chicago, Ian Agol is currently a professor at the University of California, Berkeley. His research interests are 3-manifold topology and hyperbolic geometry.