John E. Jayne (born 29 May 1943) is an American-born mathematician and Professor Emeritus of Mathematics at University College London. His research is in descriptive set theory, functional analysis, topology, Baire functions, Borel sets, measurable selections, K-analytic sets and Banach space theory. He is associated with the Jayne-Rogers Theorem, a result in descriptive set theory that has been strengthened, reproved and extended in later work by other mathematicians. Jayne founded the International Mathematics Competition for University Students (IMC) in 1994 and has served as its President since that time.
Early life and education Jayne was born in Davenport, Iowa, United States. He received an A.B. degree in mathematics from the University of California, Berkeley in 1965, an M.A. from Columbia University in 1967, a Ph.D. from Columbia University in 1971, and a D.Sc. from the University of London in 1986.
Academic career Jayne has been associated with the Department of Mathematics at University College London, where he is Professor Emeritus of Mathematics. His UCL departmental page lists him as Professor of Mathematics in the Department of Mathematics at University College London. His professional appointments and visiting positions have included the Scuola Normale Superiore in Pisa, the Czechoslovak Academy of Sciences in Prague, the Steklov Institute in Moscow, the University of Paris VI, the Polish Academy of Sciences, the University of Rome II, Johannes Kepler University in Linz, the University of Washington, the University of Murcia and the University of Iowa.
Research Jayne's research has focused on descriptive set theory, general topology, functional analysis and Banach space theory. His publications include work on analytic spaces, Baire functions, Borel isomorphisms, measurable selections, upper semicontinuous multifunctions, K-analytic sets, fragmentability and Banach spaces. Together with C. A. Rogers, Jayne proved what became known as the Jayne–Rogers Theorem, which characterizes certain first-level Borel measurable functions in terms of piecewise continuity. The theorem has subsequently been strengthened and generalized. Solecki obtained a stronger result for separable metric spaces, Motto Ros and Semmes later gave a new proof, and subsequent work extended the theorem to broader classes of spaces. The Jayne-Rogers Theorem has also influenced work in computable analysis and effective descriptive set theory. Pauly and de Brecht studied non-deterministic computation in relation to the Jayne-Rogers Theorem, while Kihara developed decompositions of Borel functions in work motivated by generalisations of the theorem. Jayne's work with Rogers and others also includes research on K-analytic sets and measurable selectors.
Books Jayne was one of the authors of Analytic Sets, published by Academic Press in 1980. The book is cited in later descriptive set theory literature, including standard references in the subject. With C. A. Rogers, Jayne wrote Selectors, published by Princeton University Press in 2002. Google Books lists a later electronic edition of Selectors published by Princeton University Press. The MacTutor History of Mathematics Archive, in its biography of C. A. Rogers, lists Selectors among Rogers's books.
International Mathematics Competition Jayne is the founder and President of the International Mathematics Competition for University Students. The IMC website lists him as a contact for the competition and describes the competition's evaluation process and international structure. Jayne is also listed by Huawei as a member of the Expert Committee of the IMC Challenge sponsored by Huawei. Huawei describes the IMC Challenge as an international programme jointly initiated by Huawei and the International Mathematics Competition for University Students to connect mathematical research with industrial problems.
Honours Jayne received an honorary D.Sc. from Sofia University in 1996 and an honorary D.Sc. from Shumen University in 1998.
Selected publications Jayne, J. E. (1973). "Characterisations and metrization of proper analytic spaces". Inventiones Mathematicae. 22: 51–62. doi:10.1007/BF01425478. Jayne, J. E. (1974). "The space of class Œ± Baire functions". Bulletin of the American Mathematical Society. 80: 1151–1156. doi:10.1090/S0002-9904-1974-13652-9. Jayne, J. E.; Rogers, C. A. (1977). "The extremal structure of convex sets". Journal of Functional Analysis. 26 (3): 251–288. doi:10.1016/0022-1236(77)90027-1. Jayne, J. E.; Rogers, C. A. (1982). "First level Borel functions and isomorphisms". Journal de Mathématiques Pures et Appliquées. 61: 177–205. Jayne, J. E.; Hansell, R. W.; Rogers, C. A. (1983). "K-analytic sets". Mathematika. 30 (2): 189–221. doi:10.1112/S0025579300010524. Jayne, J. E.; Rogers, C. A. (1985). "Borel selectors for upper semi-continuous set-valued maps". Acta Mathematica. 155: 41–79. doi:10.1007/BF02392537. MR 0793237. Zbl 0588.54020. Dellacherie, Claude; Hoffmann-J√∏rgensen, J√∏rgen; Jayne, J. E.; Kechris, Alexander S.; Martin, Donald A.; Rogers, C. A.; Stone, A. H.; Tops√∏e, Flemming (1980). Analytic Sets. London: Academic Press. Jayne, J. E.; Rogers, C. A. (2002). Selectors. Princeton: Princeton University Press. ISBN 9780691096285.
See also Descriptive set theory Functional analysis Banach space Baire function International Mathematics Competition for University Students
References
External links Official website John E. Jayne profile, University College London John E. Jayne publications, University College London International Mathematics Competition for University Students
