Langlands Program

Writing for NRC Handelsblad, Robbert Dijkgraaf, IAS Director and Leon Levy Professor, likens IAS Professor and Abel Prize Laureate Robert Langlands’s program, “a deep connection between two completely different parts of mathematics: on the one hand, numbers and their relations, on the other hand, geometrical patterns and their symmetries,” to a mathematical Rosetta Stone.

In 2006, Edward Witten, Charles Simonyi Professor in the School of Natural Sciences, cowrote with Anton Kapustin a 225-page paper, “Electric-Magnetic Duality and the Geometric Langlands Program,” on the relation of part of the...

We felt like we were in uncharted territory: no mathematicians we knew had ever received grants of this magnitude before. Normally, mathematicians receive relatively small individual grants from the National Science Foundation. This sounded a bit scary . . .  We turned to the Institute for Advanced Study as the place to foster innovation. As they say, the rest is history.

The fundamental lemma has been described as a gross understatement. Says Andrew Wiles, a Visitor in the School of Mathematics and an Institute Trustee, “At first, it was thought to be a minor irritant, but it subsequently became clear that it was not a lemma but rather a central problem in the field.”

It has been said that the goals of modern mathematics are recon­struction and development.1 The unifying conjectures between number theory and representation theory that Robert Langlands, Professor Emeritus in the School of Mathematics...

Born on October 6, 1936, in British Columbia, Robert Langlands grew up in a small town where his father owned a building supply store. “When I was a child I liked to add and subtract,” says Langlands. “In our store, my mother worked. And I...

The Langlands program is incredibly vast and far-reaching. The deepest aspect of it, as far as we know, involves the number theory setting where Langlands started close to forty years ago. However, the...