Gopal Prasad

Gopal Prasad ( born July 31, 1945 in Ghazipur ) is an Indian- American mathematician who is primarily concerned with Lie groups and algebraic and arithmetic groups and their representations, differential geometry, algebraic geometry, number theory and ergodic theory.

Life

Prasad made ​​in 1963 of Magadh University ( Jain College) with a BA in 1965 and his master 's degree from Patna University. He was briefly the Indian Institute of Technology, Kanpur, and then went in 1966 to the Tata Institute of Fundamental Research, where he began his collaboration with MS Raghunathan, where he received his doctorate at the University of Mumbai 1976 ( Discrete subgroups of real and p- adic semisimple groups). In 1979 he became associate professor and in 1984 professor at the Tata Institute, where he was in 1990/91 Dean of Mathematkfakultät. In 1992 he was a professor at the University of Michigan, where he is Raoul Bott Professor of Mathematics.

He was a visiting scholar at the University of Bonn (1977 ) and at the Max Planck Institute for Mathematics in Bonn, at the IHES, repeatedly at the Institute for Advanced Study (1973 /74 1980/81, 1987/88, 1998/99, 2005/2006), at Yale University (1972 /73), in Bielefeld, the MSRI, the ETH Zurich and the University of Notre Dame.

He has U.S. citizenship. Prasad is a member of the Indian National Science Academy and the Indian Academy of Sciences.

In 1990 he was invited speaker at the International Congress of Mathematicians in Kyoto (Semi -Simple Groups and Arithmetic subgroups ). 1998/99 he was a Guggenheim Fellow and 2006 he received the Humboldt Research Award. In 1989 he received the mathematics prize of the Council for Industrial and Scientific Research in India. He is a Fellow of the American Mathematical Society.

Since 1998 he is editor of the Michigan Mathematical Journal and co-editor of the Asian Journal of Mathematics and Associate Editor for Annals of Mathematics.

Work

It dealt among other things with lattices in Lie groups, and expanded the Mostow rigidity theorem - ..

With Sai - Kee Yeung him the first explicit construction of projective planes succeeded wrong (Fake Projective Planes ). They arise from an aggravation of an old problem of algebraic geometry by Francesco Severi: Are projective algebraic surfaces with the same Betti numbers ( topological invariants ) as the complex projective plane identical to this? That this is not the case - just at the wrong levels mentioned - was proved in 1979 by David Mumford ( he also showed that there are only finitely many are ), but it was not until a construction Prasad and Yeung. Earlier, S.-T. Yau shown that such falsity levels must be the quotient of the complex 2-dimensional unit ball with respect to a discrete subgroup of the Lie group PU (2,1). It gave Mumford also other existence proofs for special Incorrect levels with certain automorphism groups, but no explicit construction. Prasad and Yeung also gave an almost complete classification of the wrong levels ( that is, they found 28 classes and five other possible, but were later found to be non-existent ).

With Andrei Rapinchuk He also managed a significant advance in the spectral theory of Riemannian manifolds. They solved in the case of arithmetic locally symmetric manifolds of positive curvature is not the question to what extent these are determined by their spectral data.

Another important step forward was made him the mid-1990s with Allen Moy in the representation theory of p- adic groups. They led there a new invariant and solved an old problem of the connection of its representation theory with finite Lie groups. They used methods of Bruhat - Tits theory. Their methods were influential for the further research in this area.

With Brian Conrad and Ofer Gabber he classified pseudoreduktive nonabelian algebraic groups over fields of odd characteristic.