# The Clay Mathematics Institute

## Call for Nominations

The Clay Mathematics Institute calls for nominations for its competition for the 2021 Clay Research Fellowships. The primary selection criteria for the Fellowship are the exceptional quality of the candidate's research and the candidate's promise to become a mathematical leader. All Fellows are recent PhDs, and most are selected as they complete their thesis work. **Nominations close October 15, 2020.**

## Millennium Problems

In 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. This question, the Poincaré conjecture, was a special case of Thurston's geometrization conjecture. Perelman's proof tells us that every three manifold is built from a set of standard pieces, each with one of eight well-understood geometries.