Spencer Bloch

Spencer Janney Bloch ( May 22nd, 1944 in New York) is an American mathematician who is engaged in algebraic geometry and number theory.

Bloch studied until his bachelor's degree in 1966 at Harvard University and in 1971 received his doctorate at Columbia University with Steven Kleiman with the dissertation Algebraic Cohomology Classes on Algebraic Varieties. After that, he was at Princeton University, from 1973 as an assistant professor. From 1974 to 1976 he was an associate professor at the University of Michigan and then at the University of Chicago, where he was professor from 1979 and he remained ever since, except for visiting professorships in Cologne, Kyoto, Bonn, Cambridge and Paris. Today he is there RM Hutchins Distinguished Service Professor Emeritus.

Bloch was Sloan Fellow (and later in the selection committee ). He is a member of the National Academy of Sciences, the American Academy of Arts and Sciences (since 2009) and received the 1996 Humboldt Research Award in 1994. He was invited speaker at the International Congress of Mathematicians (ICM ) in Helsinki 1978 ( Algebraic K- theory and zeta functions of elliptic curves ) and Kyoto 1990 ( Plenary Lecture: Algebraic K -theory, Motives and Algebraic Cycles ). 1982 to 1989 he was associate editor of the Bulletin of the American Mathematical Society and the American Journal of Mathematics. He is a Fellow of the American Mathematical Society.

Bloch worked on algebraic cycles, Algebraic - theory and motives. From introduced him higher Chow groups provided candidates for the Alexander Beilinson 1982 suspected motivic theory of algebraic varieties over number fields. The Bloch- Kato conjectures make statements about the values ​​of functions of projective algebraic varieties over number fields at integer points. The importance of analytical functions to obtain information about the algebraic structure of number fields, shows up in older records ( such as Dirichlet's analytic class number formula ) and assumptions (such as the conjecture of Birch and Swinnerton - Dyer ), which are generalized strong here. Refine the Beilinson conjecture of 1984.

In the 1990s and 2000s he worked among others with algebraic - geometric formulation of Chern - Simons theory and perturbative renormalization in quantum field theories.

Writings

  • Lectures on algebraic cycles (lectures Duke University 1979, 1980 published by the Duke University ), Cambridge University Press 2010
  • Higher regulators, K - theory and Zeta Functions of Elliptic Curves, American Mathematical Society, Providence 2000
  • Publisher: Algebraic Geometry, Bowdoin, 1985 ( Summer Research Institute in Algebraic Geometry ), 2 volumes, American Mathematical Society, Providence 1987
  • Algebraic cycles and higher K -theory, Advances in Mathematics, Volume 61, 1986, pp. 267-304
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