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Fedor Vylegzhanin

@fedor-vylegzhanin

Algebraic and toric topology; Steklov Institute, HSE University

1 follower5 works
About

Fedor Evgenievich Vylegzhanin is a Research Intern in the Department of Geometry and Topology of the Steklov Mathematical Institute of the Russian Academy of Sciences (since 2023) and a doctoral student there in geometry and topology (since 2024), and a Research Intern of the Laboratory of Topology and Complex Networks at the Faculty of Mathematics of HSE University.

He graduated from the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University (2024) in Fundamental Mathematics and Mechanics. In 2022–2025 he worked in the International Laboratory of Algebraic Topology and its Applications at HSE University.

At HSE he taught in "Mathematical Analysis 2" (2025/26); at the Independent University of Moscow he teaches "Topology 2" in autumn 2026.

Personal Information
Researcher Info

Web of Science ResearcherID

FGW-6259-2022
Contact Information

Links

Math-Net.Ru: https://www.mathnet.ru/person179305

НИУ ВШЭ: https://www.hse.ru/staff/vylegf

Most popular works
All works

Topology 2. Lecture 3

Sep 22, 2026LectureФёдор Вылегжанин

Singular homology — standard simplices and the inclusions of facets, singular simplices and chains, the differential; zeroth homology and path components, the homology of a point, reduced homology; chain maps and maps of homology, functoriality, the chain map induced by a continuous map; chain homotopies and the prism; the homotopy invariance theorem with a full proof via the prism operator; subcomplexes, quotient complexes and the homology of a pair.
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560

Topology 2. Lecture 2

Sep 22, 2026LectureФёдор Вылегжанин

Where simplicial homology shows up in real life — topological data analysis. The union of balls around a point cloud, persistence modules and their decomposition into a sum of interval modules over a field (the structure theorem and the algorithm), the barcode; the Vietoris–Rips and Čech complexes; the stability theorem for barcodes, the Hausdorff, Gromov–Hausdorff and Wasserstein distances; open covers and their nerves, Leray covers and the nerve theorem, the category of covers, paracompactness, Lebesgue covering dimension, Čech homology and cohomology.
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520

Topology 2. Lecture 1

Sep 22, 2026LectureФёдор Вылегжанин

Why homology is needed — the fundamental group as a functor, homotopy groups, bordism and its combinatorial approximation; chain complexes and their homology; abstract simplicial complexes, geometric realisation and triangulations; the complex of simplicial chains, the proof of d2=0d^2 = 0, the simplicial homology of a segment, of two points and of the boundary of a triangle; reduced homology.

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Recent works

Topology 2. Problem sheet 2

Sep 22, 2026Problem sheetФёдор Вылегжанин

Problems for the course "Topology 2" (F. E. Vylegzhanin, Independent University of Moscow, autumn 2026), sheet 2 of 16 September 2026 — singular homology and chain homotopies. A chain map from simplicial to singular chains; retractions and direct summands; the Hurewicz homomorphism from the fundamental group to the first homology; finite CW complexes and homology classes; homology of a union of a chain of spaces; homology of a simplex and of its skeleton; simplicial maps; the chain homotopy equivalence between a complex and its homology; chain homotopy as an equivalence relation; the five lemma.
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Topology 2. Problem sheet 1

Sep 22, 2026Problem sheetФёдор Вылегжанин

Problems for the course "Topology 2" (F. E. Vylegzhanin, Independent University of Moscow, autumn 2026), sheet 1 of 9 September 2026 — simplicial homology and chain complexes. Zeroth homology and connected components; homology of a disjoint union and of a wedge; triangulations of the circle, the sphere and the Möbius band; the join and the product of simplicial complexes; the Euler characteristic and the Morse inequalities; the number of vertices of a triangulated surface; operations on chain complexes; exact sequences; the Smith normal form and the splitting of a complex.
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Fedor Vylegzhanin (@fedor-vylegzhanin) - LibreTimes