# The Clay Mathematics Institute

**CMI at 20**

Oxford, 24-26 September, 2018

A conference to celebrate the foundation of the Clay Mathematics Institute in 1998 and its contributions to the international mathematical community over the past 20 years. The conference will highlight the outstanding work of some of the mathematicians whose research CMI has supported. Speakers: Manjul Bhargava, Ben Green, Elon Lindenstrauss, John Morgan, Ngô Bảo Châu, Andrei Okounkov, Peter Scholze, Stanislav Smirnov, Claire Voisin, Andrew Wiles.

## Millennium Problems

The answer to this conjecture determines how much of the topology of the solution set of a system of algebraic equations can be defined in terms of further algebraic equations. The Hodge conjecture is known in certain special cases, e.g., when the solution set has dimension less than four. But in dimension four it is unknown.