Gopal Prasad

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Gopal Prasad (2006)

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

Life

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

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

He is a US citizen. 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). In 1998/99 he was a Guggenheim Fellow and in 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 .

He has been the Editor of the Michigan Mathematical Journal and Associate Editor of the Asian Journal of Mathematics and Associate Editor of Annals of Mathematics since 1998.

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Among other things, he dealt with grids in Lie groups and expanded the Mostow rigidity theorem .

With Sai-Kee Yeung he succeeded in the first explicit construction of 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 it? That this is not the case - in the case of the wrong planes mentioned - was proven in 1979 by David Mumford (he also showed that there are only a finite number), but a construction only succeeded Prasad and Yeung. Previously, S.-T. Yau showed that such false levels must be quotients of the complex 2-dimensional unit ball with respect to a discrete subgroup of the Lie group PU (2,1). According to Mumford, there were also further proofs of existence for special false planes with certain automorphism groups, but no explicit construction. Prasad and Yeung also gave an almost complete classification of the False Planes (that is, they found 28 classes and five possible more, but which later turned out to be nonexistent).

With Andrei Rapinchuk he also made a significant advance in the spectral theory of Riemannian manifolds. In the case of arithmetic locally symmetric manifolds with non-positive curvature, they solved the question to what extent these are determined by their spectral data.

Another significant advance he made in the mid-1990s with Allen Moy in representation theory of p-adic groups. There they introduced a new invariant and solved an old problem of connecting their representation theory with finite Lie groups. They used methods of the Bruhat-Tits theory. Their methods were influential in further research in this area.

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

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
  2. ↑ Prasad Strong rigidity of Q-rank 1 lattices , Inventiones Mathematicae, Volume 21, 1973, pp. 255-286
  3. ↑ That is, there is a biholomorphic mapping between the two. Severi originally asked about the existence on the projective plane of homeomorphic surfaces, which are also biholomorphic, which S.-T. Yau 1977 said no.
  4. ^ Prasad, Yeung Fake projective planes , Inventiones Mathematicae, Volume 168, 2007, pp. 321-370. Addendum Volume 182, 2010, 213-227
  5. ↑ The classification was completed by Donald I. Cartwright, Tim Steger Enumeration of the 50 fake projective planes , Comptes Rendus Mathematique, Volume 348, 2010, pp. 11-13
  6. ↑ Prasad, Rapinchuk Weakly commensurable arithmetic groups and isospectral locally symmetric spaces , Publ.Math.IHES 109 (2009), 113-184
  7. ↑ Moy, Prasad Unrefined minimal K-types for p-adic groups , Inventiones Math. 116 (1994), 393-408, Prasad, Moy Jacquet functors and unrefined minimal K-types , Commentarii Math. Helv. 71 (1996), 98 -121
  8. ^ Conrad, Gabber, Prasad Pseudo-reductive groups , Cambridge University Press 2010
personal data
SURNAME Prasad, Gopal
BRIEF DESCRIPTION Indian-American mathematician
DATE OF BIRTH July 31, 1945
PLACE OF BIRTH Ghazipur