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NOTICES of the AMS 599 People.Qxp 5/30/01 10:36 AM Page 600 people.qxp 5/30/01 10:36 AM Page 599 Mathematics People Vakil’s research is in the 2001–2002 AMS Centennial field of algebraic geometry. Fellowships Awarded His main work to date has been on the geometry of The AMS has awarded four Centennial Fellowships for algebraic curves and maps of 2001–2002. The recipients are IVAN DIMITROV, RAVI VAKIL, algebraic curves, as well as JIAHONG WU, and MEIJUN ZHU. The amount of the fellowship the intersection theory of is $40,000, with an additional expense allowance of $1,600. moduli spaces, especially of curves and stable maps. His Ivan Dimitrov current interests involve the Ivan Dimitrov received his Ph.D. in 1998 from the Univer- interactions of algebraic sity of California, Riverside, under the supervision geometry with nearby fields, of Ivan Penkov. Since then including enumerative geom- Dimitrov has been a Hedrick etry, mathematical physics, Assistant Professor at the Ravi Vakil number theory, and combi- University of California, Los natorics. Angeles. He also visited He plans to use the Centennial Fellowship to visit the the Max-Planck-Institut für Mathematical Sciences Research Institute in Berkeley as well Mathematik in Bonn (summer as Stanford University, where he will take up an assistant 1999). During the 2001–02 professorship. academic year he will spend a semester at Yale University Jiahong Wu and a semester at the Mathe- matical Sciences Research Jiahong Wu received his Ph.D. in 1996 from the University Institute in Berkeley. of Chicago under the supervision of Peter Constantin. Dimitrov’s research area is After a year at the Institute representation theory of Lie for Advanced Study, he spent Ivan Dimitrov algebras and Lie superalge- three years at the University of bras. Among the problems he Texas at Austin as an in- has worked on are the algebraic and geometric aspects of structor. In the fall of 2000 representations of direct limit Lie algebras and classifica- he moved to Oklahoma State tion of weight representations of Lie superalgebras. His cur- University, where he is cur- rent research projects are centered on various extensions rently an assistantprofessor. of the theory of Harish-Chandra modules to complex Lie Wu’s research has been in algebras and real Lie superalgebras. nonlinear partial differential He plans to use part of the Centennial Fellowship to visit equations, especially those Yale University. arising in the study of fluid mechanics. His work includes the study of zero-dissipation Ravi Vakil limits for various equations Ravi Vakil received his Ph.D. in 1997 from Harvard Uni- Jiahong Wu arising in the description of versity under the direction of Joe Harris. Vakil was an in- physical systems and analyt- structor at Princeton University (1997–98) and is currently ical results related to magneto-hydrodynamic turbulence a C.L.E. Moore Instructor at the Massachusetts Institute of (e.g., turbulence in the outer layers of the sun). His recent Technology (1998–2001). work is on the global existence of smooth solutions for the JUNE/JULY 2001 NOTICES OF THE AMS 599 people.qxp 5/30/01 10:36 AM Page 600 Mathematics People 2D quasi-geostrophic equation, an evolution equation that Citation describes the large-scale motion of the atmosphere and ocean in certain regimes, the zero viscosity limit of the The Bergman Prize was classical Navier-Stokes equations in bounded domains, awarded to Professor Masa- and several initial-boundary-value problems for model take Kuranishi of Columbia equations in nonlinear, dispersive media. University for his numerous He plans to use the Centennial Fellowship for visits to fundamental contributions to the University of Chicago and the University of Texas at the theory of complex mani- Austin. folds and Cauchy-Riemann structures. Meijun Zhu Of his voluminous work Meijun Zhu received his Ph.D. from Rutgers University in we highlight two results: one 1996 under the direction of Yan Yan Li. Zhu was a post- from complex manifold doctoral fellow at the theory on locally complete Masatake Kuranishi University of British Columbia deformation of compact and at the Pacific Institute for complex manifolds, and one the Mathematical Sciences from Cauchy-Riemann structures on the local embedding (1996–98), and a postdoctoral problem. fellow at McMaster University His result on locally complete deformation of (1998–99). Since 1999 he has compact complex manifolds is one of the pivotal results in been an assistant professor the long history of the study of deformation of complex at the University of Oklahoma. structures. Zhu’s research area is par- Deformation theory has its origin in the work of Riemann, tial differential equations. He which, for a compact Riemann surface of genus at least two, has worked mainly on non- determined the number of complex deformation parame- linear elliptic equations in- ters to be three times its genus minus three. volving critical Sobolev expo- In the late 1950s Kodaira and Spencer pioneered the nents, curvature equations, study of the local moduli of compact complex manifolds Meijun Zhu and geometric inequalities. by the methods of elliptic systems of partial differential Recently he has been work- equations. The problem was to prove the existence of a ing on sharp Sobolev inequalities and various isoperimet- locally complete deformation of any compact complex ric inequalities on Riemannian manifolds. He plans to use manifold. A locally complete deformation means a local the Centennial Fellowship to visit Princeton University. holomorphic deformation such that any other local holo- morphic deformation can be obtained as a pullback of it. Please note: Information about the competition for the Kodaira, Spencer, and Nirenberg proved its existence under 2002–2003 AMS Centennial Fellowships will be published the additional assumption of the vanishing of the second in the “Mathematics Opportunities” section of an cohomology group of the tangent bundle. In such a case upcoming issue of the Notices. the local moduli space is regular. —Allyn Jackson In 1962 Kuranishi constructed a locally complete holo- morphic deformation of any compact complex manifold. His local moduli space is in general a complex-analytic set Kuranishi Receives 2000 that may have singularities. His deformation is also locally complete at points of the parameter space sufficiently Bergman Prize near the reference point. Kuranishi’s work is of great fundamental importance in the theory of holomorphic MASATAKE KURANISHI has been awarded the Stefan Bergman deformation. His work, building upon that of Kodaira- Prize for 2000. The prize, established in 1988, recognizes Spencer, ushered in the development of local deformation mathematical accomplishments in the areas of research in theory in the following two decades in which the work of which Stefan Bergman worked. The amount of the 2000 a long list of mathematicians, Douady, Grauert, Palam- Bergman Prize is $26,000. odov, Forster, Knorr, Tyurina, Bingener, and many others, The previous Bergman Prize winners are: David W. Catlin completed the theory of semi-universal deformation of (1989), Steven R. Bell and Ewa Ligocka (1991), Charles analytic objects. A semi-universal deformation allows nilpo- Fefferman (1992), Yum Tong Siu (1993), Jon Erik Fornæss tent elements in the structure sheaf of the local moduli (1994), Harold P. Boas and Emil J. Straube (1995), David E. space and requires that the tangent space of the moduli Barrett and Michael Christ (1997), and John P. D’Angelo space at the reference point agrees with the space of (1999). On the selection committee for the 2000 prize were first-order infinitesimal deformations, which in the case of Frederick Gehring, J. J. Kohn (chair), and Yum Tong Siu. a compact complex manifold is the first cohomology group What follows is the citation prepared by the committee, of the tangent bundle. a brief biographical sketch, and some background about Kuranishi’s result on the local embedding problem of the Bergman prize. Cauchy-Riemann structures concerns the realization of 600 NOTICES OF THE AMS VOLUME 48, NUMBER 6 people.qxp 5/30/01 10:36 AM Page 601 Mathematics People abstract real submanifolds endowed with some partial connections to put in better perspective the local embed- complex structures called Cauchy-Riemann structures. ding problem and the techniques of its solution. For a local smooth real submanifold in complex The impact of Kuranishi’s work on complex manifolds Euclidean space, the tangent space inherits the complex and Cauchy-Riemann structures has been deep and structure of the ambient space, and a subspace of it is far-reaching. a complex vector space. When the dimension of the max- imum complex vector subspace of the tangent space is Biography constant, the local smooth real submanifold is a Cauchy- Masatake Kuranishi was born on July 19, 1924, in Tokyo. Riemann manifold (or CR manifold). The restrictions to it He received his Ph.D. in 1952 fom Nagoya University, where of local holomorphic functions on the ambient space are he became a lecturer (1951–52), associate professor the CR functions. When the local smooth real submanifold (1952–58), and professor (1958–61). Between 1956 and is a real hypersurface, it is said to be strongly pseudoconvex 1961 he also held visiting positions at the University of at a point if after a local biholomorphic coordinate change Chicago, the Massachusetts Institute of Technology, and it becomes strictly convex. Strong pseudoconvexity is Princeton University. In the summer of 1961 he assumed equivalent to the complex Hessian of its defining function his present position as professor of mathematics at being positive or negative definite when restricted to the Columbia University. He was a fellow of the Guggenheim maximum complex vector space of its tangent space. This Foundation in 1975. notion of strong pseudoconvexity is also defined for the higher codimension case, using the positivity of the About the Prize so-called Levi form, which is the generalization of the The Bergman Prize honors the memory of Stefan Bergman, complex Hessian of the defining function of the hyper- best known for his research in several complex variables surface case.
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