University teaching

"Topology extras" lecture course at Independent University of Moscow (IUM), Fall 2020 [youtube | problems]

"Toric Topology" lecture course at IUM, Fall 2016. [mathnet | conspectus | exam | youtube]

"Topology-3" (manifolds and characteristic classes) lecture course at IUM, Spring 2016 and Spring 2017. [mathnet | conspectus | problems | youtube (2016) | youtube (2017)]

"Combinatorics, topology and algebra of simplicial complexes", lecture course at Steklov Math. Institute, Spring 2016 [mathnet | conspectus | exam | youtube]

"Convex polytopes and discrete geometry" at HSE, spring 2023 [yandex disk | youtube]

"Topological data analysis", elective course at HSE for students of Faculty of Computer Science and Yandex Data School, spring 2024, [github | youtube]

General info for students could be found at HSE website.

"Calculus-1" and "Calculus-2" lecture course at Faculty of Computer Science HSE, 2016-2022. For 2021-22 [official | faculty wiki] 

"Differential equations" at HSE I was seminar instructor in 2017 and 2018. Here is the wonderful interactive textbook by Ilya Schurov who was the lecturer in 2018.

"Introduction to mathematics-1" (Calculus) at Neapolis University Paphos, 2023 [materials]

Handbook on homology (in Russian) [pdf]

My game to compute and play with persistence homology in browser. You can create your own pointcloud with up to 40 points by copying python arrays there. Only desktop version is available.

Interactive mega-talk "Matrix Odyssey: from computational algebra to toric topology and back" at the ATA Lab's seminar, 2022: [link to html slides | github]

Autumn school "Toric topology, combinatorics, and data analysis", Saint-Petersburg, 2022, mini-course "Evasive oracles, and homology of moment-angle complexes" [Lecture 1 | Lecture 2]

Yandex Data School, mini-course "Hodge operators and basics of topological data analysis", Moscow, 2022, by V.Chernyshev and A.A. My part [Lecture1 | Lecture2 | Lecture3]

Autumn school "Toric topology and combinatorics", Sochi, SMC, 2021, mini-course "Introduction to Stanley-Reisner algebras" [LabPage | YouTube] Some research projects were proposed to students. 

Summer school "Mathematics, theoretical physics, and mathematical methods of data analysis in neuroscience", Sochi, SMC, 2021, lecture "Persistent homology and its relation to fractal features" [slides | youtube]

Summer school "Contemporary Mathematics" Dubna, 2021, mini-course "Finite topologies" [mccme | mathnet | problems]

"Outdoor seminar on machine learning'' organized in Voronovo by FCS HSE 2021, lecture "Diagonalization algorithms, Morse theory, and spaces of matrices" [slides]

Autumn online school "Applications of topology and geometry", FCS HSE, Moscow+Zoom, 2020, mini-course "Topology of properties and group actions". [Lecture1 | Lecture2 | Lecture3]

Summer school "Contemporary Mathematics" Dubna 2019, mini-course "Around g-theorem" [mccme | mathnet | problems | youtube]

"Geometry, Topology, and Mathematical Physics", in Chernogolovka, 2019, lecture "Combinatorial geometry of the Toda flow and the permutohedral tiling of Euclidean space" [dubrovinlab]

Summer school "Contemporary Mathematics" Dubna 2018, mini-course "Polytopes and spaces of matrices" [mccme | mathnet | conspectus | problems | youtube]

Some notes about homology of finite spaces [pdf]

Introductory notes about Toda flows [pdf]

A note on the analogue of chromatic polynomial for Buchstaber number [pdf] 

A note on Macaulay duality [pdf]

A note about preperiodicity property of real Buchstaber invariant and its relation to integer programming (my attempts to understand this paper) [pdf] 

A note about Bier spheres prepared for some talk [pdf]

A scary diagram which proves that polyhedral functors in general categories form an operad [pdf]