Semyon Alesker

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Semyon Alesker, Oberwolfach 2010

Semyon Alesker ( Hebrew סמיון אלסקר; *  1972 ) is an Israeli mathematician who made fundamental contributions in the field of convex geometry and integral geometry.

Alesker received his PhD in 1999 from Vitali Milman at Tel Aviv University and is now a professor at that university.

Alesker dealt in particular with evaluations of convex sets , i.e. on these defined additive functionals that generalize measures . The roots of the theory lie in the attempts (since Max Dehn ) to solve the 3rd  Hilbert problem for the decomposition equality of polyhedra. He expanded the theory of Hugo Hadwiger (1957) to characterize intrinsic volumes (constant evaluations that are invariant under rigid movements ) on the one hand with regard to pure translational invariance, and on the other hand with regard to pure rotational invariance. He approximated rotation-invariant continuous evaluations by polynomial evaluations, which he characterized with methods of representation theory of the orthogonal group . For continuous translation-invariant evaluations (which Hadwiger characterized for dimension 1, 2), he proved a conjecture by Peter McMullen in 2001 that mixed volumes lie close to translation-invariant continuous evaluations (or, in other words, that translation-invariant continuous evaluations can be represented by linear combinations of mixed volumes) . Alesker also defined new operations for evaluations, products, and Fourier and Radon transforms for translation-invariant continuous evaluations. In a number of papers he also introduced a theory of valuations on manifolds (instead of on convex sets, as is usually the case).

In 2004 he received the Erdős Prize and in 2000 the EMS Prize . In 2002 he was invited speaker at the International Congress of Mathematicians (ICM) in Beijing (Algebraic structures on valuations, their properties and applications).

Web links

Individual evidence

  1. ^ Albrecht Pietsch: History of Banach spaces and linear operators. Birkhäuser 2007, p. 613.
  2. ↑ They can also be complex valued. The most important property is the "modularity" .
  3. ↑ Examples are Lebesgue measures, but also mixed volumes that do not correspond to the usual measures.
  4. ↑ Alesker: Continuous rotationally invariant valuations on convex sets. Annals of Mathematics, Vol. 149, 1999, pp. 977-1005.
  5. ↑ Alesker: On P. McMullen's Conjecture on translation invariant valuations. Advances in Mathematics, Vol. 155, 2000, pp. 239-263. Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture. Geom. Funct. Analysis, Vol. 11, 2001, pp. 244-272.
  6. ↑ Alesker: The multiplicative structure on polynomial continuous valuations. Geom. Funct. Analysis, Vol. 14, 2004, pp. 1-26.
  7. ↑ Alesker: Theory of valuation on manifolds- a survey. Preprint 2006
  8. ↑ Alesker: Algebraic Structures on Valuations, Their Properties and Applications. ICM Lecture, PDF.
personal data
SURNAME Alesker, Semyon
ALTERNATIVE NAMES סמיון אלסקר (Hebrew)
BRIEF DESCRIPTION Israeli mathematician
DATE OF BIRTH 1972