## 2024 Thurston Lectures

The Thurston Lectures are named after Fields Medalist and former UC Davis mathematician William Thurston. The next Thurston Lecture series will be given by Alex Kontorovich (Rutgers University) on May 6-8, 2024.

**Series title:** *To Be Announced.*

**Detailed schedule:**

Lecture I. The Shape of Math to Come — Monday, May 6, 4:10-5pm in MSB 1147 with reception to follow

Lecture II. The Koebe-Andreev-Thurston Theorem and Arithmetic Polyhedra — Tuesday, May 7, 4:10-5pm in MSB 1147

Lecture III. Local-Global Problems in Orbits — Wednesday, May 8, 4:10-5pm in MSB 1147

**Abstracts:**

*The Shape of Math to Come* — We will discuss some ongoing experiments at the interface of human and computer mathematics that may have a meaningful impact on what research mathematics might look like in a decade (if not sooner).

*The Koebe-Andreev-Thurston Theorem and Arithmetic Polyhedra* — The KAT theorem takes a combinatorial polyhedron P and geometrizes it to one having a midsphere. There is a natural process by which this geometrization gives rise to a finite area hyperbolic 3-manifold M(P). We say that a polyhedron P is "arithmetic" if the 3-manifold M(P) is. We will discuss progress on the following basic question: which polyhedra are arithmetic?

*Local-Global Problems in Orbits* — We will discuss some recent advances in our understanding of local-global principles in orbits, as well as applications to graph theory, polygonal billiards, and number theory.

## About the speaker

Alex Kontorovich is a Distinguished Professor of Mathematics at Rutgers University. Kontorovich received his BA from Princeton and Ph.D. from Columbia, after which he taught at Brown, Stony Brook, and Yale before moving to Rutgers. In 2013, he received the American Mathematical Society’s Levi L. Conant Prize for mathematical exposition. Kontorovich’s research has received numerous honors, including an Alfred P. Sloan Research Fellowship, a Simons Foundation Fellowship, an NSF CAREER award, and a von Neumann Fellowship at the Institute for Advanced Study in Princeton. In 2017, Kontorovich became a Kavli Fellow of the National Academy of Sciences and was elected Fellow of the American Mathematical Society. He is a Founding Member and Member, Board of Directors, Association for Mathematical Research. He was the 2020–2021 Distinguished Professor for the Public Dissemination of Mathematics at the National Museum of Mathematics.

### About William Paul Thurston

William Paul Thurston (October 30, 1946 – August 21, 2012) was among the most original and influential mathematicians of the twentieth century. He transformed the mathematics of foliations, low-dimensional topology, hyperbolic manifolds, the theory of rational maps, and geometric group theory. His work led to a fundamental rethinking of the structure of 3-dimensional spaces.

Thurston received a bachelor's degree from New College in 1967 and a Ph.D. in Mathematics from UC Berkeley in 1972. He spent a year at the Institute for Advanced Study and a year at MIT before being appointed Professor of Mathematics at Princeton University in 1974. In 1991 he moved to UC Berkeley and in 1993 he was appointed Director of the Mathematical Sciences Research Institute. In 1996 he moved again, this time to UC Davis, where he was a Professor of Mathematics until 2003, when he moved to Cornell. Bill was in the process of returning to UC Davis in 2012 when he tragically passed away.

Thurston’s work revealed the unexpectedly central role played by hyperbolic geometry in the study of low-dimensional manifolds. His Geometrization Conjecture, which he solved in many cases, changed the fundamental viewpoint from which mathematicians approached the study of manifolds.

Thurston was awarded the Veblen Prize in Geometry in 1976, the Fields Medal at the 1983 International Congress of Mathematicians in Warsaw and the Leroy P. Steele Prize for seminal contribution to research in 2012. Thurston had numerous Ph.D. students, many of whom became leading mathematicians themselves.

*"Mathematics is a process of staring hard enough with enough perseverence at the fog of muddle and confusion to eventually break through to improved clarity."*

–Bill Thurston, "About me" on MathOverflow