Grisha Taroyan

Discrete differential geometry for high school (in Russian)

Sun, 22 Feb 2026 00:00:00 +0000

Дискретная дифференциальная геометрия для школьников

Презентация - обзор теоретического материала

В презентации даётся краткое описание основных теоретических понятий встречающихся в рамках практикума. В частности приведены определения многогранной поверхности, дискретной кривизны, геодезических. Приведены наброски доказательств основных теорем практикума: Гаусса–Бонне, существования геодезических на многогранной поверхности и др.

Задачи практикума

Материал представляет собой комбинацию теоретической части и задач дополняющих и раскрывающих теорию.

Warning: в некоторых задачах содержатся опечатки и даже неустранимые пробелы.

Expository notes

Sun, 22 Feb 2026 00:00:00 +0000

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 organized by Hiro Lee Tanaka and John Pardon.

Stable Moduli Spaces of Hermitian Forms. A review.

The purpose of this note is to explain the main results of the paper “Stable moduli spaces of hermitian forms” by Hebestreit–Steimle in an accessible to the general topological audience way. The notes were prepared for the seminar on Hermitian K-theory at University of Toronto.

Expository notes in Russian

Sun, 22 Feb 2026 00:00:00 +0000

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 характеристических классов, как двойственных по Пуанкаре локусам вырождений. За точное рассуждение в этом случае я обязан А. Рябичеву и форуму MathModern.

Почти весь материал основан на двух источниках: книге “3264 и всё такое: Введение в теорию пересечений” Айзенбада и Харриса, а также на “Принципах Алгебраической Геометрии” Гриффитса и Харриса.

MGSA 2025-2026

Sun, 22 Feb 2026 00:00:00 +0000

This page is preserved from the old site. No public content was present on the live Google Sites page at the time of migration.

Notes

Sun, 22 Feb 2026 00:00:00 +0000

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.
Stable Moduli Spaces of Hermitian Forms. A review.

Papers

Sun, 22 Feb 2026 00:00:00 +0000

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.

Personal

Sun, 22 Feb 2026 00:00:00 +0000

Personal life

I happen to be married to an incredible mathematician Alisa Chistopolskaya.

Our two cats Sheavetz (small sheaf) and Pafnuty Lvovich Chebyshev.

Since now it is prohibited in Russia to spread LGBTQIA+ “propaganda,” here is an official admission: I am an asexual. Fuck Vladimir Putin, Roskomnadzor, the Russian parliament, and all other Russian “authorities” responsible for this “law” and everything else that happened before, after, and during 2022.

Research

Sun, 22 Feb 2026 00:00:00 +0000

Papers

Derived geometry

De Rham Theory in Derived Differential Geometry arxiv:2505.03978
Equivalent models of derived stacks arXiv:2303.12699

Toric Geometry

Chern Classes of Toric Variety Bundles arXiv:2506.20848
Equivariant automorphisms of the Cox construction and applications arXiv:2403.02465
Infinite transitivity for automorphism groups of the affine plane (with Alisa Chistopolskaya) arXiv:2202.02214

Talks

2025

De Rham theory in derived differential geometry, Quantum Field Theory and Physical Mathematics Seminar, Harvard University, Center for Mathematical Sciences and Applications, Cambridge, MA
De Rham theory in derived differential geometry, flash talk, Summer Research Institute in Algebraic Geometry, Fort Collins, CO, slides
Why you should care about derived manifolds, flash talk, Summer School Physical Mathematics of Quantum Field Theory, UMass Amherst
De Rham theory in derived differential geometry, Geometric Structures Laboratory, Fields Institute, recording

2024

Equivalent models of derived stacks, Summer CMS/Thematic Program on Field Theory at Notre Dame, slides, poster
Unhinged Derived Mechanisms, Bird’s Eye Math Conference at UofT, slides

2023

Equivalent models of derived stacks, GROOT seminar, slides

Topology basics for high school (in Russian)

Sun, 22 Feb 2026 00:00:00 +0000

Основы топологии

Информационное сообщение

Курс проводится в СУНЦ МГУ в 2021–2022 учебном году. Начало занятий 8 октября. Место проведения Zoom. Пишите на почту tgv628@yahoo.com, если хотите ссылку.

Конспекты курса

Остались в недоделанном виде, но что-то там есть: конспекты курса.