This volume collects contributions from participants in the IWOTA conference held virtually at Lancaster, UK, originally scheduled in 2020 but postponed to August 2021. It includes both survey articles and original research papers covering some of the main themes of the meeting.

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.