Irwin Kra (born January 5, 1937) is an American mathematician, who works on the

function Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-oriente ...

theory in

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...

Life and work

Kra studied at

Polytechnic Institute of Brooklyn The New York University Tandon School of Engineering (commonly referred to as Tandon) is the engineering and applied sciences school of New York University. Tandon is the second oldest private engineering and technology school in the United Sta ...

(bachelor's degree in 1960) and at

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

, where he graduated in 1964 and received his doctorate in 1966 under supervision of

Lipman Bers Lipman Bers ( Latvian: ''Lipmans Berss''; May 22, 1914 – October 29, 1993) was a Latvian-American mathematician, born in Riga, who created the theory of pseudoanalytic functions and worked on Riemann surfaces and Kleinian groups. He was also kn ...

(Conformal Structure and Algebraic Structure). After that, he was from 1966 to 1968 a C.L.E. Moore instructor at

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

and then at the

State University of New York at Stony Brook Stony Brook University (SBU), officially the State University of New York at Stony Brook, is a public research university in Stony Brook, New York. Along with the University at Buffalo, it is one of the State University of New York system's ...

, 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 the

Hebrew University The Hebrew University of Jerusalem (HUJI; he, הַאוּנִיבֶרְסִיטָה הַעִבְרִית בִּירוּשָׁלַיִם) is a public research university based in Jerusalem, Israel. Co-founded by Albert Einstein and Dr. Chaim Weiz ...

Jerusalem Jerusalem (; he, יְרוּשָׁלַיִם ; ar, القُدس ) (combining the Biblical and common usage Arabic names); grc, Ἱερουσαλήμ/Ἰεροσόλυμα, Hierousalḗm/Hierosóluma; hy, Երուսաղեմ, Erusałēm. i ...

(where he collaborated with

Hershel M. Farkas Herschel or Herschell may refer to: People * Herschel (name), various people Places * Herschel, Eastern Cape, South Africa * Herschel, Saskatchewan * Herschel, Yukon * Herschel Bay, Canada * Herschel Heights, Alexander Island, Antarctica * ...

), the

University of Perugia University of Perugia (Italian ''Università degli Studi di Perugia'') is a public-owned university based in Perugia, Italy. It was founded in 1308, as attested by the Bull issued by Pope Clement V certifying the birth of the Studium Generale. Th ...

Santiago de Chile Santiago (, ; ), also known as Santiago de Chile, is the capital and largest city of Chile as well as one of the largest cities in the Americas. It is the center of Chile's most densely populated region, the Santiago Metropolitan Region, whose ...

, the

Tohoku University , or is a Japanese national university located in Sendai, Miyagi in the Tōhoku Region, Japan. It is informally referred to as . Established in 1907, it was the third Imperial University in Japan and among the first three Designated National ...

, the

Fudan University Fudan University () is a national public research university in Shanghai, China. Fudan is a member of the C9 League, Project 985, Project 211, and the Double First Class University identified by the Ministry of Education of China. It is als ...

Shanghai Shanghai (; , , Standard Mandarin pronunciation: ) is one of the four direct-administered municipalities of the People's Republic of China (PRC). The city is located on the southern estuary of the Yangtze River, with the Huangpu River flow ...

(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 the

Northwestern University Northwestern University is a private research university in Evanston, Illinois. Founded in 1851, Northwestern is the oldest chartered university in Illinois and is ranked among the most prestigious academic institutions in the world. Charte ...

. From 1972 to 1973 he was a Guggenheim Fellow. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. Kra studies

Riemann surface In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed vers ...

s and their moduli spaces (

Teichmüller space In mathematics, the Teichmüller space T(S) of a (real) topological (or differential) surface S, is a space that parametrizes complex structures on S up to the action of homeomorphisms that are isotopic to the identity homeomorphism. Teichmülle ...

s) and their connection with

Kleinian group In mathematics, a Kleinian group is a discrete subgroup of the group (mathematics), group of orientation-preserving Isometry, isometries of hyperbolic 3-space . The latter, identifiable with PSL(2,C), , is the quotient group of the 2 by 2 complex ...

s and associated automorphic forms and their applications for example in number theory. With

Bernard Maskit Bernard Maskit is an American mathematician known for his expertise in Kleinian groups. The Maskit slice through the moduli space of Kleinian groups is named after him; he is the author of the book ''Kleinian Groups'' (Grundlehren der Mathematisc ...

in 1998, he published the collected works of

on function theory.

Family relations

Irwin Kra has three children. He is the father of mathematician

Bryna Kra Bryna Rebekah Kra (born 1966) is an American mathematician and Sarah Rebecca Roland Professor at Northwestern University who is on the board of trustees of the American Mathematical Society and was elected the president of American Mathematical So ...

Writings

Books

*With Jane P. Gilman, Rubí E. Rodríguezbr>''Complex Analysis in the spirit of Lipman Bers''
Springer Verlag, 2007 *With Hershel M. Farkas ''Riemann Surfaces'', Springer Verlag, 1980,
August 1992 *With Farkas

Providence, American Mathematical Society 2001 *With Lipman Bers (editors): ''Crash course on Kleinian Groups'', Springer 1974 *''Automorphic forms and Kleinian Groups'', Benjamin 1972
Lipman Bers, a Life in Mathematics
Eds. I. Kra, R. Rodriguez, L. Keen, Amer. Math. Soc., Providence, RI, 2015.

Selected articles

* * * *with B. Maskit: * * * * *with Hershel M. Farkas: * *with C. J. Earle and S. L. Krushkal´:

References

portrait on the sides of Math for America
The original article was a translation of the corresponding German article. {{DEFAULTSORT:Kra, Irwin 1937 births Living people 20th-century American mathematicians 21st-century American mathematicians Polytechnic Institute of New York University alumni Columbia University alumni Massachusetts Institute of Technology School of Science faculty Stony Brook University faculty Fellows of the American Mathematical Society