Keith M. Ball

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Keith M. Ball (* 1960 ) is a British mathematician who specializes in geometry, functional analysis and probability theory. He is a professor at Warwick University .

Keith Ball, Oberwolfach 2009

Ball studied mathematics at Cambridge University with a bachelor's degree in 1982 and a doctorate in 1987 with Béla Bollobás ( Isometric problems in and sections of convex sets ). He then went to Texas A&M University before becoming a Lecturer at University College London in 1990 , where he became Professor of Mathematics in 1996 and Astor Professor in 2006 . He is a professor at the University of Warwick and since 2010 Director of the International Center for Mathematical Sciences (ICMS) in Edinburgh.

He was visiting scholar at the Massachusetts Institute of Technology , the Institut des Hautes Études Scientifiques , Princeton University , Microsoft Research , the University of Michigan and the Institut Henri Poincaré .

With Shiri Artstein, Franck Barthe and Assaf Naor , he solved the problem of the monotonous increase in the entropy of the normalized sums of n random variables with the number n, first investigated by Claude Shannon . Shannon himself showed in the 1940s that the entropy of the sum of two state variables is greater than or equal to that of a random variable. The theorem is an analog of the Second Law of Thermodynamics for sums of random variables.

Ball dealt with various problems of discrete and convex geometry. As part of his doctoral thesis in 1986 a. a. how big the maximum section through an n-dimensional cube is. In 1991 he proved the plank theorem in real Banach spaces, which, according to Ball, can be understood as a generalization of Hahn and Banach's theorem , as a sharp quantitative version of the Banach-Steinhaus theorem and as a geometric version of the drawer principle . In 1991 he gave an improved lower bound (compared to the bound by Harold Davenport and Claude Rogers ) for the density of optimal lattice packing of spheres in n-dimensional Euclidean spaces. The barrier is the best known so far.

He also wrote a popular science math book.

In 1992 he received the Whitehead Prize and was a Leverhulme Fellow from 2003 to 2004. In 2010 he received an honorary professorship at the University of Edinburgh when he became Scientific Director of the International Center for Mathematical Sciences (ICMS). In 2013 he became a member of the Royal Society . He is a Fellow of the American Mathematical Society and the Royal Society of Edinburgh .

He is married to the historian Sachiko Kusukawa.

Fonts

  • Strange curves, counting rabbits and other mathematical explorations , Princeton University Press 2003, review by Anita Barnes, Plus Magazine
  • Editor with Vitali Milman Convex geometric analysis , Cambridge University Press 1999
  • An elementary introduction to modern convex geometry , in Silvio Levy (editor) Flavors of Geometry , MSRI Lecture Notes, Cambridge University Press 1997
  • Convex Geometry and Functional Analysis , in William Johnson, Joram Lindenstrauss (Editor) Handbook of Banach Spaces , Elsevier 2001
  • An elementary introduction to monotone transportation , in Vitali Milman, Gideon Schechtman (Eds.): Israel Seminar on GAFA (Geometric Aspects of Functional Analysis), 2002–2003, Springer Verlag 2004, Lecture Notes in Mathematics
  • Ball, Pools of Blood, Plus Magazine

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
  2. ↑ Artstein, Barthe, Naor, Ball Solution of Shannon's problem on the monotonicity of entropy , Journal of the American Mathematical Society, Volume 17, 2004, pp. 975-982
  3. ↑ Shannon, Weaver A mathematical theory of communication , University of Illinois Press 1949. Strict evidence was provided by Elliott Lieb (1978), who formulated the general conjecture, and AJ Stam (1959).
  4. ↑ Ball Cube Slicing in , Proc. AMS, vol 97, 1986, pp. 465-473.
  5. ↑ Ball The plank problem for symmetric bodies , Inventiones Mathematicae, Volume 104, 1991, pp. 535-543. For Hilbert dreams already proven by T. Bang 1951.
  6. ↑ Ball A lower bound for the optimal density of lattice packings , International Mathematical Research Notes, 1992, No. 10, p. 217, Duke Math. J., Volume 68, 1992, pp. 217-221
  7. ^ New Fellows 2013 of the Royal Society (royalsociety.org); Retrieved May 7, 2013
personal data
SURNAME Ball, Keith M
BRIEF DESCRIPTION British mathematician
DATE OF BIRTH 1960