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Vol 76, No 1 (2021)
- Year: 2021
- Articles: 8
- URL: https://journal-vniispk.ru/0042-1316/issue/view/7520
Questions in algebra and mathematical logic. Scientific heritage of S. I. Adian
Abstract
This is a survey of results on the Burnside problem and properties of Burnside groups, the finite basis problem for group identities, periodic products of groups and Malcev's problem, construction of groups with special properties (Tarski monsters), constructive bounds in the Burnside–Magnus problem, and algorithmic problems: the problem of recognition of group properties, the word problem for semigroups with one relation, and semi-Thue systems. The focus is on the most important results obtained in papers of Adian and his students.Bibliography: 81 titles.
Uspekhi Matematicheskikh Nauk. 2021;76(1):3-30
3-30
On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry
Abstract
In this paper, we give a survey of the known results concerning the tensor rank of multiplication in finite extensions of finite fields, enriched with some unpublished recent results, and we analyze these to enhance the qualitative understanding of the research area. In particular, we identify and clarify certain partially proved results and emphasise links with open problems in number theory, algebraic geometry, and coding theory.Bibliography: 92 titles.
Uspekhi Matematicheskikh Nauk. 2021;76(1):31-94
31-94
Newton polytopes and tropical geometry
Abstract
The practice of bringing together the concepts of ‘Newton polytopes’, ‘toric varieties’, ‘tropical geometry’, and ‘Gröbner bases’ has led to the formation of stable and mutually beneficial connections between algebraic geometry and convex geometry. This survey is devoted to the current state of the area of mathematics that describes the interaction and applications of these concepts.Bibliography: 68 titles.
Uspekhi Matematicheskikh Nauk. 2021;76(1):95-190
95-190
Sergei Ivanovich Adian (obituary)
Uspekhi Matematicheskikh Nauk. 2021;76(1):191-194
191-194
Non-Abelian $\mathfrak{so}_3$ Euler top
Uspekhi Matematicheskikh Nauk. 2021;76(1):195-196
195-196
The law of large numbers for the bigraded Betti numbers of a random simplicial complex
Uspekhi Matematicheskikh Nauk. 2021;76(1):197-198
197-198
Extreme points of the set of quantum states with bounded energy
Uspekhi Matematicheskikh Nauk. 2021;76(1):199-200
199-200
Vasilii Mikhailovich Babich (on his ninetieth birthday)
Uspekhi Matematicheskikh Nauk. 2021;76(1):201-202
201-202