# William Thurston Lectures

### 2019 Thurston Lectures

We are excited to announce that the third installment of our annual Thurston Lectures, named after Fields Medalist and former UC Davis mathematician William Thurston and made possible by a generous donation, will be delivered this Spring 2019 quarter by Andrei Okounkov.

Event details: Professor Okounkov will be visiting the UC Davis Department of Mathematics during the week of May 13-17 and will deliver 3 lectures on "Multivariate special functions and duality from the point of view of enumerative geometry":

- Lecture 1: Tuesday, May 14, 4-5pm (Colloquium) in MSB 1147, preceded by a reception at 3:30pm.
- Lecture 2: Wednesday, May 15, 1-2pm (Algebraic Geometry seminar), in MSB 1147.
- Lecture 3: Thursday, May 16, 3-4pm (lecture) in MSB 1147.

**Abstract**:

Special functions in this lecture series will be generalizations of characters of irreducible representations of Lie groups, spherical functions of symmetric spaces, and more general Macdonald-type hypergeometric functions. They are not all that special from the point of view of analysis, because they satisfy certain linear differential or q-difference equations. However, these difference equations have a very delicate structure involving roots, coroots, and the like. In particular, they enjoy a certain powerful Langlands-like duality, which in the Lie groups context would interchange the arguments of the functions, that is, an element in the maximal torus of the groups G with the label of the function, which has to do with the highest weight and the dual torus. In this lecture series, my goal is to explain this phenomenon from the point of view of enumerative geometry and related modern high-energy physics. This seems to be a natural generality in which to consider these questions, in particular, it is much broader than the domain of the traditional Lie theory.

**Speaker Bio**

Prof. Okounkov is a Samuel Eilenberg Professor of Mathematics at Columbia University. He previously held positions at Princeton University, UC Berkeley and University of Chicago. In 2006, he received the Fields Medal "for his contributions to bridging probability, representation theory and algebraic geometry".

### 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

For questions, contact Gladis Lopez-Lytle at mso@math.ucdavis.edu.