Surveys in contemporary mathematics

Young scientists in Russia are continuing the outstanding tradition of Russian mathematics in their home country, in spite of the post-Soviet diaspora. This collection, the second of two, showcases the recent achievements of young Russian mathematicians and the strong research groups they are associated with. The first collection focused on geometry and number theory; this one concentrates on combinatorial and algebraic geometry and topology. The articles are mainly surveys of the recent work of the research groups and contain a substantial number of new results. Topics covered include algebraic geometry over Lie groups, cohomological aspects of toric topology, the Borsuk partition problem, and embedding and knotting of manifolds in Euclidean spaces. The authors are A. E. Guterman, I. V. Kazachkov, A. V. Malyutin, D. V. Osipov, T. E. Panov, A. M. Raigorodskii, A. B. Skopenkov and V. V. Ten.

A. E. GutermanI. V. KazachkovA. V. MalyutinD. V. OsipovT. E. PanovA. M. RaigorodskiiA. B. SkopenkovV. V. Ten

Preface	p. vii
Rank and determinant functions for matrices over semirings	p. 1
Algebraic geometry over Lie algebras	p. 34
Destabilization of closed braids	p. 82
n-dimensional local fields and adeles on n-dimensional schemes	p. 131
Cohomology of face rings, and torus actions	p. 165
Three lectures on the Borsuk partition problem	p. 202
Embedding and knotting of manifolds in Euclidean spaces	p. 248
On Maxwellian and Boltzmann distributions	p. 343

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