Talk, Study Seminar on Abstract Homotopy Theory and Applications, Independent University of Moscow, Zoom
We consider a generalization of principal bundles and gerbes following the paper by Thomas Nikolaus, Urs Schreiber and Danny Stevenson.
Talk, Study Seminar on Abstract Homotopy Theory and Applications, Higher School of Economics, Independent University of Moscow, Zoom
We introduce the category $\mathsf{BornCoarse}$ of bornological coarse spaces, define the category of motivic coarse spaces $\mathrm{Spc}\, \chi$, consider some examples of coarse homology theories, including coarse ordinary homology, equivariant ordinary homology and equivariant coarse topological $K$-theory. We discuss also connections with index theory. This series of talks is based on the book by Ulrich Bunke and Alexander Engel “Homotopy Theory with Bornological Coarse Spaces”. Read more
Talk, Study Seminar on Abstract Homotopy Theory and Applications, Higher School of Economics, Independent University of Moscow, Zoom
In this series of talks, we will learn about $\infty$-cosmoi in the sense of Emily Riehl and Dominic Verity. Read more
Talk, Conference 'SIMC Youth Race', Steklov Mathematical Institute of RAS
In 1971, S. P. Novikov and V. M. Buchstaber gave the construction, predicted by characteristic classes. This construction describes a multiplication, with a product of any pair of elements being a non-ordered multiset of $n$ points. It led to the notion of $n$-valued groups. Soon after that, V. M. Buchstaber gave the axiomatic definition of $n$-valued groups, obtained the first results on their algebraic structure, and began to develop the theory. At present, a number of authors are developing $n$-valued (finite, discrete, topological or algebra geometric) group theory together with applications in various areas of Mathematics and Mathematical Physics. In this talk, we will give some key notions of $n$-valued group theory and discuss the author’s recently obtained results, which are related to multivalued discrete dynamical systems. We will describe some connections with famous results on symbolic dynamics, combinatorics on words and constructions of quasicrystals
Talk, Seminar on Geometry, Topology and Their Applications, Sobolev Institute of Mathematics, Zoom
Slides of the talk (in Russian), the page of the seminar
Talk, Study Seminar on Abstract Homotopy Theory and Applications, Independent University of Moscow, Zoom
This is a concise intro to the theory of homotopy (co-)limits. Read more
Talk, Laboratory of Algebraic Topology and Applications Seminar, High School of Economics
Talk, Knot Theory and Lower Dimensional Topology Seminar, Lomonosov Moscow State University
Talk, 29th International Scientific Conference for Undergraduate and Graduate Students and Young Scientists Lomonosov, Lomonosov Moscow State University