Yves Colin de Verdière

Yves Colin de Verdière is a French mathematician who deals with differential geometry, analysis, graph theory and mathematical physics.

Colin de Verdière studied from 1964 at the École normale supérieure and obtained his PhD in 1973 with Marcel Berger at the University of Paris VII Denis Diderot. He was until his retirement in 2006 Professor at the Institute Fourier Grenoble University.

It deals with, among other semiclassical approximations to wave equations (and the Schrödinger equation ) and spectra of graphs ( eigenvalues ​​of the Laplace operator on graphs ) and Riemannian manifolds, where he found a correlation with the length of closed geodesics. Colin de Verdière proved that with ergodic geodesic flow almost all eigenfunctions are uniformly distributed. In 1990, he introduced a new, named after him graph invariant and a Planaritätskriterium for graphs.

In 1991 he became a member of the Institut universitaire de France. In 1999 he was awarded the Ampere Prize of the French Academy of Sciences. He became a member of the National Academy of Sciences of the United States in 2005. In 1986 he was invited speaker at the ICM, Berkeley ( Spectres de variétés riemannienne et specters de graphes ).

Writings

• Spectres de Autographes, 1998