Phillip Griffiths

thumb|Phillip Griffiths in 2010 Phillip Griffiths Phillip Augustus Griffiths IV (born October 18, 1938) is an American mathematician, known for his research on complex manifolds, algebraic geometry, and partial differential equation. He was elected in 1979 a Member the National Academy of Sciences. In 2008 he was awarded (jointly with Pierre Deligne and David Mumford) the Wolf Prize. At the 2014 International Congress of Mathematicians, Griffiths received the Chern Medal. Quotes The theory of exterior differential systems in approximately one century old, although its origin may be traced back much further. As originally formulated by Élie Cartan Cartan and subsequently used throughout his work, the theory was intended as a tool to be used in the study of geometric problems. After two periods of theoretical development, one in the 1930s and the other in the 1960s, there has recently been a renewed interest in exterior differential systems as providing a systematic framework for the study of geometric problems. It is my opinion that this development is just beginning, and that exterior differential systems should become a standard tool for geometers, especially for questions where the differential equations expressing the problem are overdetermined systems, and for global questions. When used properly, the theory has a marvelous ability to reveal the underlying geometry in a complicated problem. Some aspects of exterior differential systems Complex geometry and Lie theory (Sundance, UT, 1989) Proceedings of Symposia in Pure Mathematics, volume 53 151-173 1991 Providence, Rhode Island American Mathematical Society https://books.google.com/books?id=EVEECAAAQBAJ&pg=PA151doi=10.1090/pspum/053/1141201 1141201 (quote from p. 151) One of the points I have tried to make is that mathematics is extremely useful to our society. If this is true, one would think that we as a society would vigorouly support the research that leads to new uses and that students would be at an all time high. Today that is not the case. The mathematics community has yet to effectvely demonstrate to the public and their elected representatives that our subject is dfferent from the sciences. We do not design widgets or cure diseases, yet our impact on engineering and medicine is enabling and significant. But the community has dwelled so long in splendid isolation that the public poorly understands what we do. April 3, 1993 Mathematics—From Servant to Partner https://albert.ias.edu/server/api/core/bitstreams/79bdc6b2-a769-4840-96f0-e648df6eace5/content (lecture given at the Institute for Advanced Study) Hodge theory for a smooth algebraic curve includes both the Hodge structure (period matrix) on cohomology and the use of that Hodge structure to study the geometry of the curve, via the Jacobian variety. W. V. D. Hodge Hodge extended the theory of the period matrix to smooth algebraic varieties of any dimension, defining in general a Hodge structure on the cohomology of the variety. He gave a few applications to the geometry of the variety, but these did not attain the richness of the Jacobian variety. In recent years, Hodge theory has been successfully extended to arbitrary varieties, and to families of varieties. Hodge theory and geometry Bulletin of the London Mathematical Society Wiley 36 06 2004-10-19 0024-6093 10.1112/s0024609304003728 721–757 External links Category:1938 births Category:Living people Category:Academics from the United States Category:Mathematicians from the United States Category:Wolf Prize in Mathematics laureates Category:Princeton University alumni Category:University of California, Berkeley faculty Category:Princeton University faculty Category:Harvard University faculty Category:Members of the American Philosophical Society Category:People from Raleigh