Boris Venkov’s theory of lattices and spherical designs. (English) Zbl 1298.11002

Nebe, Gabriele

Chan, Wai Kiu (ed.) et al., Diophantine methods, lattices, and arithmetic theory of quadratic forms. Proceedings of the international workshop, Banff International Research Station (BIRS), Alberta, Canada, November 13–18, 2011. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-8318-1/pbk; 978-0-8218-9503-0/ebook). Contemporary Mathematics 587, 1-19 (2013).

From the Introduction: Boris Venkov passed away on November 10, 2011, just 5 days before his 77th birthday. His death overshadowed the conference “Diophantine methods, lattices, and arithmetic theory of quadratic forms”, November 13-18, 2011, at the BIRS in Banff (Canada), where his important contributions to the theory of lattices, modular forms and spherical designs played a central role. This article gives a short survey of the mathematical work of Boris Venkov in this direction.
For the entire collection see [Zbl 1260.11002].

MSC:

11-03	History of number theory
01A70	Biographies, obituaries, personalia, bibliographies
05B30	Other designs, configurations
11E12	Quadratic forms over global rings and fields
11H06	Lattices and convex bodies (number-theoretic aspects)
11H50	Minima of forms
11H56	Automorphism groups of lattices
11H71	Relations with coding theory
11F11	Holomorphic modular forms of integral weight
11F46	Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms

Keywords:

obituary; survey of Venkov’s mathematical work; spherical design; unimodular lattices; eutactic lattices; extremal lattices