He is currently the William Caspar Graustein Professor of Mathematics at Harvard University.Yau's work is mainly in differential geometry, especially in geometric analysis.
His contributions have influenced both physics and mathematics, and he has been active at the interface between geometry and theoretical physics.
His proof of the positive energy theorem in general relativity demonstrated—sixty years after its discovery—that Einstein's theory is consistent and stable.
His proof of the Calabi conjecture allowed physicists to show, using Calabi–Yau compactification, that string theory is a viable candidate for a unified theory of nature.
Calabi–Yau manifolds are part of the standard toolkit for string theorists today.