Keith Martin Ball

Keith M. Ball ( born 1960 ) is a British mathematician who is concerned with geometry, functional analysis and probability theory. He is Professer at the University of Warwick.

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

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

With Shiri Artstein, Franck Barthe and Assaf Naor he solved the problem of monotonic increase of 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 analogue 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, he proved in 1986, among other things, how big is the maximum section of a n- dimensional cube. In 1991 he proved the plank set in real Banach spaces which can be perceived by ball both as a generalization of the theorem of Hahn and Banach, as a sharp quantitative version of the theorem of Banach - Steinhaus and as a geometric version of the drawer principle. He gave in 1991 an improved (compared to the bound of Harold Davenport and Claude Rogers ) lower bound for the optimal density of lattice packings of spheres in n-dimensional Euclidean spaces. The barrier is the best ever known.

He also wrote a popular science math book.

In 1992 he was awarded the Whitehead Prize and was 2003-2004 Leverhulme Fellow. In 2010 he received an honorary professorship at the University of Edinburgh when he was scientific director of the International Centre 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.

Writings

  • Strange curves, counting rabbits and other mathematical explorations, Princeton University Press, 2003 Review by Anita Barnes, Plus Magazine
  • Publisher 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 (Eds. ) Handbook of Banach Spaces, Elsevier 2001
  • An elementary introduction to monotone transportation, in Vitali Milman, Gideon Schechtman (ed.): Israel Seminar on GAF (Geometric Aspects of Functional Analysis), 2002-2003, Springer Verlag 2004, Lecture Notes in Mathematics
  • Ball, Pools of Blood, Plus Magazine
Béla Bollobás
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