Sidney Martin Webster Explained

Sidney Martin Webster (born 12 November 1945 in Danville, Illinois) is an American mathematician, specializing in multidimensional complex analysis.^[1]

After military service, Webster attended the University of California, Berkeley as an undergraduate and then as a graduate student, receiving a PhD in 1975 under the supervision of Shiing-Shen Chern^[1] with thesis Real hypersurfaces in complex space. Webster was a faculty member at Princeton University from 1975 to 1980 and at the University of Minnesota from 1980 to 1989. In 1989 he became a full professor at the University of Chicago. He has held visiting positions at the University of Wuppertal, Rice University, and ETH Zurich.^[1]

Webster was a Sloan Fellow for the academic year 1979–1980. In 1994 in Zurich he was an invited speaker of the International Congress of Mathematicians.^[2] In 2001 he received, jointly with László Lempert, the Stefan Bergman Prize from the American Mathematical Society.^[1] In 2012 Webster was elected a Fellow of the American Mathematical Society.

In 1977 he proved a significant theorem on biholomorphic mappings between algebraic real hypersurfaces.^[3] Using his expertise on Chern-Moser invariants, he developed a theory that provides a complete set of invariants for nondegenerate real hypersurfaces under volume-preserving biholomorphic transformations.^[4] He used the edge-of-the-wedge theorem to prove an extension theorem that generalized a 1974 theorem of Charles Fefferman.^{[5] [1]}

Selected publications

• The rigidity of C-R hypersurfaces in a sphere. Indiana University Mathematics Journal. 28. 3. 1979. 405–416. 24892266. Webster. S. M.. 10.1512/iumj.1979.28.28027. free.
• Inventiones Mathematicae. 1979. 51. 2. 155–169. Biholomorphic mappings and the Bergman kernel off the diagonal. 10.1007/BF01390226. Webster. S. M.. 1979InMat..51..155W . 119485248.
• with Klas Diederich: A reflection principle for degenerate real hypersurfaces. Duke Math. J.. 47. 1980. 4. 835–843. 10.1215/S0012-7094-80-04749-3. Diederich. K.. Webster. S. M..
• with Jürgen K. Moser: Acta Mathematica. 150. 1983. 255–296. Normal forms for real surfaces in C ² near complex tangents and hyperbolic surface transformations. 10.1007/BF02392973. free. Moser. Jürgen K.. Webster. Sidney M..

References

1. Jackson, Allyn. Lempert and Webster Receive 2001 Bergman Prize. Notices of the AMS. 49. 9. 998–999. October 2001.
2. Book: Geometric and dynamical aspects of real submanifolds of complex spaces. Proceedings of the International Congress of Mathematicians, Zürich, 1994. 1995. 917–921. 10.1007/978-3-0348-9078-6_84. Webster. Sidney M.. 978-3-0348-9897-3.
3. Webster, S. M.. On the mapping problem for algebraic real hypersurfaces. Inventiones Math.. 43. 53–68. 1977. 10.1007/BF01390203. 1977InMat..43...53W . 122533957.
4. Webster, S. M.. Pseudo-Hermitian structures on a real hypersurface. Journal of Differential Geometry. 13. 1. 1978. 25–41. 10.4310/jdg/1214434345. free.
5. Webster, S. M.. On the reflection principle in several complex variable. Proc. Amer. Math. Soc.. 71. 1. August 1978. 26–28. 10.1090/S0002-9939-1978-0477138-4. free.