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Sep 25, 2014 | Atlanta, GA *

The 2014 speaker is Sir Vaughan Frederick Randal Jones, a New Zealand mathematician, known mostly for his work on von Neumann algebras and his famous knot polynomial. He is currently on the faculty of Vanderbilt University as a distinguished professor of mathematics.

Vaughan was awarded the Rutherford Medal by the Royal Society of New Zealand in 1991, and the Fields Medal in 1990. Also in 1990 he was elected a Fellow of the Royal Society. In the Queen's Birthday Honours 2002, he was appointed Distinguished Companion of The New Zealand Order of Merit for services to mathematics. In the Special Honours 2009, he redesignated his DCNZM to a Knight Companion of The New Zealand Order of Merit. In 2012 he became a fellow of the American Mathematical Society. Vaughan was elected to the Australian Academy of Science in 1992 as a Corresponding Fellow.

His work on knot polynomials, with the discovery of what is now called the Jones polynomial, was from an unexpected direction with origins in the theory of von Neumann algebras, an area of analysis already much developed by Alain Connes. It led to the solution of a number of the classical problems of knot theory, and marked the beginning of quantum topology.

In his free time, Vaughan can be found wind surfing.

There will be two lectures. The general audience lecture will be on September 25, at 4:35 pm, in the Clary Theater, Student Success Center. The math lecture will be at 11:05 am on September 26 in Skiles 006.

Lecture 1: General Audience

### How quantum theory and statistical mechanics gave a polynomial of knots

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We will see how a result in von Neumann algebras (a theory developed by von Neumann to give the mathematical framework for quantum physics) gave rise, rather serendipitously, to an elementary but very useful invariant in the theory of ordinary knots in three dimensional space. Then we'll look at some subsequent developments of the theory, and talk about a thorny problem which remains open.

Lecture 2: Mathematics Lecture

### Some unitary representations of Thompson's groups F and T