American mathematician (born 1937)
Irwin Kra (born January 5, 1937) is an American mathematician, who works on thefunction theory incomplex analysis .
Kra studied atPolytechnic Institute of Brooklyn (bachelor's degree in 1960) and atColumbia University , where he graduated in 1964 and received his doctorate in 1966 under supervision ofLipman Bers (Conformal Structure and Algebraic Structure). After that, he was from 1966 to 1968 aC.L.E. Moore instructor atMassachusetts Institute of Technology and then at theState University of New York at Stony Brook , where he chaired from 1975 to 1981 the Faculty of Mathematics. From 1991 to 1996, there, he was Dean of the Division of Physical Sciences and Mathematics. Since 2004 he has been Professor Emeritus. He was a visiting professor at theHebrew University inJerusalem (where he collaborated withHershel M. Farkas ), theUniversity of Perugia inSantiago de Chile , theTohoku University , theFudan University inShanghai (1987). From 2004 to 2008 he was Director of Math for America, a private organization that is dedicated to the improvement of college education in mathematics in the United States. He currently lives in New York City. In 2010 he taught at theNorthwestern University .
From 1972 to 1973 he was a Guggenheim Fellow. In 2012 he became a fellow of theAmerican Mathematical Society .[ 1]
Kra studiesRiemann surfaces and their moduli spaces (Teichmüller spaces ) and their connection withKleinian groups and associated automorphic forms and their applications for example in number theory.
WithBernard Maskit in 1998, he published the collected works ofLipman Bers on function theory.
Irwin Kra has three children. He is the father of mathematicianBryna Kra ,[ 2]
With Jane P. Gilman,Rubí E. Rodríguez Complex Analysis in the spirit of Lipman Bers With Hershel M. FarkasRiemann Surfaces , Springer Verlag, 1980,[ 3] 2nd edn. August 1992 With Farkas:Theta constants, Riemann surfaces, and the modular group: an introduction with applications to uniformization theorems, partition identities and combinatorial number theory With Lipman Bers (editors):Crash course on Kleinian Groups , Springer 1974 Automorphic forms and Kleinian Groups , Benjamin 1972Lipman Bers, a Life in Mathematics , Eds. I. Kra, R. Rodriguez, L. Keen, Amer. Math. Soc., Providence, RI, 2015."On the ring of functions on an open Riemann surface" .Trans. Amer. Math. Soc .132 :231– 244. 1968.doi :10.1090/s0002-9947-1968-0226043-5 MR 0226043 .Kra, I. (July 1969)."Cohomology of Kleinian groups" .Proc Natl Acad Sci U S A .63 (3):655– 660.Bibcode :1969PNAS...63..655K .doi :10.1073/pnas.63.3.655 PMC 223501 PMID 16591774 . Kra, Irwin (1971)."A generalization of a theorem of Poincaré" .Proc. Amer. Math. Soc .27 (2):299– 302.doi :10.1090/s0002-9939-1971-0301189-7 MR 0301189 . withB. Maskit :Kra, I.; Maskit, B. (1972)."Involutions on Kleinian groups" .Bull. Amer. Math. Soc .78 (5):801– 805.doi :10.1090/s0002-9904-1972-13042-8 MR 0301190 . Kra, Irwin (1981)."Canonical mappings between Teichmüller spaces" .Bull. Amer. Math. Soc. (N.S.) .4 (2):143– 179.doi :10.1090/s0273-0979-1981-14870-9 MR 0598682 . Kra, Irwin (1983)."On the vanishing of Poincaré series of rational functions" .Bull. Amer. Math. Soc. (N.S.) .8 :63– 66.doi :10.1090/s0273-0979-1983-15085-1 MR 0682823 . Kra, Irwin (1989)."Accessory parameters for punctured spheres" .Trans. Amer. Math. Soc .313 (2):589– 617.doi :10.1090/s0002-9947-1989-0958896-0 MR 0958896 . "Horocyclic coordinates for Riemann surfaces and moduli spaces. I: Teichmüller and Riemann spaces of Kleinian groups" .J. Amer. Math. Soc .3 :499– 578. 1990.doi :10.1090/s0894-0347-1990-1049503-1 MR 1049503 .with Hershel M. Farkas:Farkas, Hershel M.; Kra, Irwin (1999)."On the quintuple product identity" .Proc. Amer. Math. Soc .127 (3):771– 778.doi :10.1090/S0002-9939-99-04791-7 MR 1487364 . "Cusp forms associated to rank 2 subgroups of Kleinian groups" .Proc. Amer. Math. Soc .111 :803– 814. 1991.doi :10.1090/s0002-9939-1991-1056679-1 MR 1056679 .withC. J. Earle and S. L. Krushkal´:Earle, C. J.; Kra, I.; Krushkalь, S. L. (1994)."Holomorphic motions and Teichmüller spaces" .Trans. Amer. Math. Soc .343 (2):927– 948.doi :10.1090/s0002-9947-1994-1214783-6 MR 1214783 . The original article was a translation of the corresponding German article.
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