Expository notes
High-school courses
Notes of courses for high school I taught at AESC MSU.
This section contains my expository notes, high-school course materials, and links to more detailed legacy pages from the old site.
Expository notes in English
Derived Regularity Theorem for Moduli Spaces of ψ-holomorphic curves (after J. Pardon)
- The purpose of this note is to explain a proof of the derived regularity theorem following the notes of John Pardon. The notes were prepared for a talk at the moduli spaces ψ-holomorphic curves workshop.
Two approaches to homological stability of symmetric groups.
Expository notes in Russian
An informal note on a geometric definition of the Chern classes
- В тексте приводится два подхода к доказательству формулы Уитни для суммы расслоений. Один из них хорошо известен и основан на комбинаторике классов Шуберта в Грассманниане, другой менее известен и основан на интерпретации…
High-school courses
Notes of courses for high school I taught at AESC MSU in 2020–2021.
- Topology basics for high school web-page (in Russian)
- Geometry and groups web-page (in Russian)
- Discrete Differential geometry for high school web-page (in Russian)
Papers
Derived differential geometry
De Rham theory in derived differential geometry (arXiv:2505.03978)
The main question this text addresses is: What is the correct notion of de Rham cohomology for derived manifolds? We identify two natural answers to this question: one in terms of the cotangent complex and one in terms of the so-called C-infinity de Rham stack. It turns out that while the first version is very algebraically nice, it might not satisfy the Poincaré lemma for general derived manifolds. On the other hand, the second version is very hard to compute. Still, it gives a kind of de Rham isomorphism with the cohomology of the constant sheaf on the underlying topological space of a derived manifold. We also provide sufficient conditions for when the de Rham cohomology calculated using the cotangent complex is isomorphic to the constant sheaf cohomology.
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