Misha Kornev

Misha Kornev

Posts by Collection

music

poetry

под грецким орехом

Published:

Сидел я под грецким орехом
В бетонном бразильском лесу.
Мне пели цикады со смехом
Под речи соседей в бреду. И листья устало кряхтели,
В вечерней прохладе зевая.
Ежи за кустами хрустели,
Петуньи слегка задевая. Read more

ботанический сад

Published:

ботанический сад.
пепельный снег угасает.
на деревьях зеленые ленты висят,
движеньем своим укоряя. Read more

горький салат

Published:

горький салат,
тихий завод,
гнусный салют.
в чёрный квадрат
вас завернут. Read more

quattuor

Published:

Слова. Их тусклый образ смысла не достанет
Друзья. Помогут камень тот в тебе расплавить
Любовь. Не явится так просто без стараний
Душа. Воскреснет птицей красной из страданий Read more

элегия

Published:

кругом ходят дни
в одни борозды
водой не дышу
землёй не живу Read more

париж

Published:

Тепло.
Шагаю по пьяной брусчатке
по направлению к Монмартру.
Боюсь утонуть в ширине улиц,
поэтому опираюсь взглядом
на важные крыши. Read more

осень

Published:

Упругая плотва осенним днём играет,
Кругами зеркала собою возмущает,
И листьев шелуха сусально облетая,
Тот вальс из камыша устало повторяет. Read more

…

Published: 

...............проплывать в пластах сандалового эфира................
..................ловить звонкие вайбы осуществимости...................
....................скользить вдоль абсолюта мыслей.....................
.................глядеть на бесконечную улитку самости..................
......................зевать уверенно и символично......................
Read more

ноктюрн

Published: 

Хожу.
Блуждаю в пряной тишине.
Что написал сейчас тебе?
Какой-то вздор.
Жму кнопку «удалить-  
                                          -стереть-  
                                                               -забыть».  
Но тщетно — всё во мне.
Попытки возмутить эфир,
Так, чтобы звёзды осадить.
                         Однако
               Ты
Устал.
Ты-Вы меня смутили,
Вы-ты няме тилисму.
И вектора embedding’ов близки.
Казалось, вот и всё —
                              ура.
               Куда
там!
То лишь проекции
На подпространство разума.
Едва начавшись,
Чат совсем замолк.
               Стена.
               Замок.
Read more

беседа

Published:

Говорю ослеплённо, в себя,
Обратясь в глухоту своих глаз.
Вижу белки твоих уст
Слышу дугу их тепла. Read more

cogitare

Published:

Увидеть в линии торец,
Отбросить слой другой
И оказаться в эпохэ,
Сгорая холодом небес. Read more

факелы

Published:

Люди как факелы.
Кто-то теплом обжигает,
Кто-то потух и остыл.
Света держись и усиливай
Ясности глубь
И нежности ширь. Read more

στατική

Published:

Крути педали мыслей важных и разумных
В смирительном халате суеты.
Найдёт тебя с рождения уставшим Мойра,
Подымет вниз и вновь опустит вверх.
Твой ровен путь без бурь и бурелома:
Ну слава Богу, ну и пусть!
Обзавестись одним, приобрести другое,
Забыть себя, так и не узнавши суть. Read more

publications

talks

Dynamics and Multivalued Groups

Published:

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 The preprint and slides Read more

An Introduction To The ∞-Category Of Motivic Coarse Spaces. A Series Of Talks

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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 Read more

Principal ∞-Bundles

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We consider a generalization of principal bundles and gerbes following the paper by Thomas Nikolaus, Urs Schreiber and Danny Stevenson. Read more

Homology Spheres, Acyclic Groups and Kan-Thurston Theorem

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The theory of non-simply connected manifolds, the well-known area of algebraic topology, is closely related to combinatorial group theory and group cohomology. It is well known that for any finitely presented group $G$ and $n \geqslant 4$, there exists a smooth closed n-manifold whose fundamental group is isomorphic to $G$. This observation motivates the following question. Let us fix the class $\mathcal{C}$ of manifolds. What finitely presented groups can be fundamental groups of manifolds from that given class $\mathcal{C}$? The question is of interest in the case of $\mathcal{C}$ being the class of homology $n$-spheres, i.e., smooth closed $n$-manifolds with the homology of $n$-sphere. We review remarkable connections appearing in the study of homology spheres: we discuss applications of acyclic groups, the Kan-Thurston theorem, and smooth structures on spheres. We also present related author’s results. The page of the conference. Read more

An Introduction to Cartan Geometries

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Consider any geometry $(G,H)$ in the sense of F. Klein, consisting of a Lie group $G$ and its subgroup $H$. This setup provides the following data: the smooth manifold $G/H$, the principal $H$-bundle $H\to G\to G/H$, and the Maurer–Cartan form $\omega_G: TG→\mathfrak{g}$. Moreover, the form $\omega_G$ establishes a linear isomorphism on each fiber, respects the fundamental vector fields on $G$, and converts the tangent right action into the Ad-action. These properties, together with the Cartan development technique in Darboux contexts, play a crucial role in introducing the so-called Cartan geometries. In the talk, we will discuss this idea in greater detail. The page of the seminar. Read more

$n$-Valued Groups, Kronecker Sums, and Wendt Matrices

Published:

In 1971, V. M. Buchstaber and S. P. Novikov proposed a construction motivated by the theory of characteristic classes. This construction describes a multiplication in which the product of any pair of elements is a multiset of $n$ points. The axiomatic definition of $n$-valued groups and the first results of their algebraic theory were obtained in a subsequent series of works by V.,M. Buchstaber. At present, the theory of $n$-valued (formal, finite, discrete, topological, and algebro-geometric) groups and its applications in various areas of mathematics and mathematical physics is being developed by a number of authors. Read more

$n$-Valued Algebraic Monoids, Cubics, and Discriminants

Published:

In this talk, we introduce the notions of algebraic $n$-valued monoids and groups, obtain structural results about them, and present important examples. We solve the problem of explicitly describing and classifying coset $n$-valued addition laws constructed from cubic curves. As a consequence, we show that all such addition laws are given by polynomials, whereas the addition laws of formal groups on general cubic curves are given by formal power series. Read more

Buchstaber Genus and Formal Groups

Published:

We introduce a new class of formal groups for which the modulus square construction leads to a three-parameter family of Buchstaber polynomials $B_{\mathbf{a}}(z; x, y)$ with parameters $\mathbf{a} = (a_1, a_2, a_3)$. This class is related to the family of formal groups associated with the Krichever genus, but does not coincide with it. We compute the values of the corresponding Hirzebruch genus on theta divisors and complex projective spaces, describe its relation to the Ochanine, Krichever, and Witten genera, and show how this construction yields examples that do not arise from Hirzebruch elliptic genera of level $n$. We will discuss questions related to the construction of a generalized multiplicative complex-oriented cohomology theory $\mathrm{Bc}$, for which the map of spectra $\mathrm{MU} \longrightarrow \mathrm{Bc}$ induces on coefficient rings the Buchstaber genus $\Omega_{\mathrm{U}} \longrightarrow \mathbb{Z}[1/2, a_1, a_2, a_3]$. Read more

teaching

Little Mech-Math

Olympliad School Course, Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, 2022

During the period 2016-2022, I taught students not only olympiad mathematics but some interesting topics in Topology, Abstract Algebra, Differential Geometry, Probability in Combinatorics etc. In each case, I tried to simplify a language and gave some intuition of main ideas without loss of strictness as much as possible. Read more