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.

Spis treści:
Preface
1. Rank and determinant functions for matrices over semi-rings A. E. Guterman
2. Algebraic geometry over Lie algebras I. V. Kazachkov
3. Destabilization of closed braids A. V. Malyutin
4. n-dimensional local fields and adeles on n-dimensional schemes D. V. Osipov
5. Cohomology of face rings, and torus actions T. E. Panov
6. Three lectures on the Borsuk partition problem A. M. Raigorodskii
7. Embedding and knotting of manifolds in Euclidean spaces A. B. Skopenkov
8. On Maxwellian and Boltzmann distributions V. V. Ten.