Stephen Rallis
| Stephen Rallis | |
|---|---|
Stephen Rallis
|
|
| Born | Stephen Rallis 17 May 1942 Bennington, Vermont |
| Died | 17 April 2012 (aged 69) |
| Residence | United States |
| Nationality | American |
| Fields | Mathematics |
| Institutions | |
| Alma mater |
Massachusetts Institute of Technology Harvard University |
| Doctoral advisor | Bertram Kostant |
| Doctoral students |
|
| Known for |
Rallis Inner Product Formula Ginzburg-Rallis-Soudry Automorphic Descent Method |
Stephen James Rallis (May 17, 1942 – April 17, 2012) was an American mathematician who worked on group representations, automorphic forms, the Siegel–Weil formula, and Langlands L-functions.
Rallis received a B.A. in 1964 from Harvard University, a Ph.D. in 1968 from the Massachusetts Institute of Technology, and spent 1968–1970 at the Institute for Advanced Study in Princeton. After two years at Stony Brook, two years at Universite de Strasbourg, and several visiting positions, he joined the faculty at Ohio State University in 1977 and stayed there for the rest of his career.
Rallis's ideas had a significant and lasting impact on the theory of automorphic forms. His mathematical life was characterized by several long term collaborations with the mathematicians David Ginzburg, Stephen Kudla, Herve Jacquet, Ilya Piatetski-Shapiro, Gerard Schiffmann, David Soudry, etc., and he was just as prolific with his junior post-doctoral students.
Beginning in the 1970s, Rallis and Schiffmann wrote a series of papers on the Weil Representation. This led to Rallis's work with Kudla in which they developed a far-reaching generalization of the Siegel-Weil formula: the regularized Siegel-Weil formula and the first term identity. These results have prompted other mathematicians to extend Siegel-Weil to other cases. Rallis's 1984 paper giving proofs of certain examples of the Howe duality conjecture was the start of his work on what is now known as "The Rallis Inner Product Formula" which relates the inner product of a pair of theta functions to a special value or residue of a Langlands L-function. This cornerstone of what Wee Teck Gan et al. term the Rallis program on the theta correspondence has found wide applications. Rallis then adapted the classical idea of doubling a quadratic space to create the "Piatetski-Shapiro and Rallis Doubling Method" for constructing integral representations of L-functions, and thus they obtained the first general result on L-functions for all classical groups. The 1990 Wolf Prize to Piatetski-Shapiro cites this work with Rallis as one of Piatetski-Shapiro's main achievements. Whereas it had previously been assumed that all the L-functions constructed by the Rankin-Selberg integral method were a subset of those constructed by the Langlands-Shahidi method, the 1992 paper by Rallis with Piatetski-Shapiro and Schiffmann on the Rankin-Selberg integrals for the group G_2 showed this was not the case and opened the way for determining many new examples of L-functions represented by Rankin-Selberg integrals.
...
Wikipedia