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Тиморин Владлен Анатольевич

Факультет математики

Профиль на hse.ru ↗ тел.: +7 (495) 772-95-90 | 12736
Публикаций
77
Языков
1
Наград
15
Конференций
17
Профиль Публикации (77) Курсы (7)

Профессиональные интересы

выпуклые многогранникидинамика рациональных функцийинвариантные ламинацииклассические геометрии

Должности

  • Профессор — Факультет математики, Базовая кафедра Математического института им. В.А. Стеклова РАН
  • Научный сотрудник — Лаборатория алгебраической геометрии и ее приложений

Био

  • · Начал работать в НИУ ВШЭ в 2009 году.
  • · Научно-педагогический стаж: 22 года.

Образование

  • 2012 · Доктор физико-математических наук: Институт проблем передачи информации им. А.А.Харкевича РАН, специальность 01.01.02 «Дифференциальные уравнения, динамические системы и оптимальное управление», тема диссертации: Динамика и геометрия квадратичных отображений
  • 2004 · PhD: Университет Торонто, тема диссертации: Rectifiable families of conics
  • 2003 · Кандидат физико-математических наук: Математический институт им. В.А. Стеклова РАН, специальность 01.01.04 «Геометрия и топология», тема диссертации: Аналоги алгебр когомологий для выпуклых многогранников
  • 2000 · Специалитет: Московский государственный университет им. М.В. Ломоносова, факультет: механико-математический, специальность «Математика, прикладная математика», квалификация «Математик»

Опыт работы

  • · 2010: с Научный сотрудник Лаборатория алгебраической геометрии и ее приложений
  • · 2009: с Профессор Факультет математики

Награды и поощрения

  • · Благодарность факультета математики НИУ ВШЭ (декабрь 2025)
  • · Благодарность НИУ ВШЭ (март 2024)
  • · Благодарность факультета математики НИУ ВШЭ (октябрь 2021)
  • · Благодарственное письмо ректора НИУ ВШЭ (март 2021)
  • · Благодарность Высшей школы экономики (сентябрь 2020)
  • · Почетный знак II степени Высшей школы экономики (июнь 2020)
  • · Почетная грамота Высшей школы экономики (декабрь 2016)
  • · Благодарность Высшей школы экономики (ноябрь 2015)
  • · Надбавка за академические успехи и вклад в репутацию НИУ ВШЭ (2012–2014)
  • · Надбавка за публикации, вносящие особый вклад в международную научную репутацию НИУ ВШЭ (2021–2024)
  • · Надбавка за публикацию в журнале из Списка А (и приравненном к нему научном издании) (2025–2026, 2024–2025)
  • · Надбавка за публикацию в международном рецензируемом научном издании (2019–2021, 2017–2019)
  • · Надбавка за статью в зарубежном рецензируемом журнале (2015–2017, 2013–2015)
  • · Лучший преподаватель — 2023–2024, 2021, 2011–2013
  • · Победитель Конкурса лучших русскоязычных научных и научно-популярных работ работников НИУ ВШЭ – 2022

Гранты и проекты

  • — · Грант РНФ №14-21-00053 "Алгебраическая геометрия симплектических многообразий" (участник проекта)

Конференции (17)

Показать все
  • · 2022: Еженедельный семинар лаборатории алгебраической геометрии 2022 (Москва). Доклад: Вариации на тему неравенства Поммеренке-Левина-Йоккоза
  • · 2021: Dynamics in Siberia (Новосибирск). Доклад: A model for the cubic connectedness locus
  • · 2020: Dynamics in Siberia (Новосибирск). Доклад: Combinatorial models for spaces of dendritic polynomials
  • · 2019: Representation theory of Lie groups, mathematical physics, and combinatorics (Реймс). Доклад: Combinatorics of Gelfand-Zetlin polytopes
  • · 2019: Dynamics, Equations and Applications (DEA 2019) (Краков). Доклад: «Инвариантные остовные деревья для квадратичных рациональных отображений» (Invariant spanning trees for quadratic rational maps)
  • · 2018: Коллоквиум "Москва-Пиза" (Москва). Доклад: Slices of the parameter space of cubic polynomials
  • · 2015: Algebraic structures in convex geometry (Москва). Доклад: On the theory of coconvex bodies
  • · 2015: Conference of Complex Analysis in China 2015 (Пекин). Доклад: Slices of the parameter space of cubic polynomials
  • · 2015: The Fifth German-Russian Week of the Young Researcher on Discrete Geometry (Москва). Доклад: Maps that take lines to plane curves
  • · 2014: Convex Bodies and Representation Theory (Банфф). Доклад: On the theory of coconvex bodies
  • · 2014: International Conference "Attractors, Foliations and Limit Cycles" (Москва (Moscow)). Доклад: Smart criticality for cubic laminations
  • · 2014: Okounkov Bodies and Applications (Обервольфах). Доклад: Counting vertices in Gelfand-Zetlin polytopes
  • · 2014: Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва (Moscow)). Доклад: Топологические модели динамики рациональных функций
  • · 2014: Symposium on Differential Equations and Difference Equations 2014 (SDEDE 2014) (Хомбург (Homburg)). Доклад: Combinatorial Models for Spaces of cubic polynomials
  • · 2013: Российско-японская зимняя школа (Москва). Доклад: The Hurwitz sums of squares formulas
  • · 2013: Christmas meetings with Pierre Deligne, Рождественские встречи фонда «Династия» (Москва). Доклад: The number of vertices in Gelfand-Zetlin polytopes
  • · 2013: ICTP-SISSA-Mosсow School on Geometry and Dynamics (Триест). Доклад: Курс "Polynomial Dynamics and Thurston Laminations"

Идентификаторы исследователя

Публикации (77)

The combinatorial Mandelbrot set as the quotient of the space of geolaminations

2015 · PREPRINT · en

We interpret the combinatorial Mandelbrot set in terms of quadratic laminations (equivalence relations ∼ on the unit circle invariant under σ2). To each lamination we associate a particular geolamination (the collection L∼ of points of the circle and edges of convex hulls of ∼-equivalence classes) so that the closure of the set of all of them is a compact metric space with the Hausdorff metric. Two such geolaminations are said to be minor equivalent if their minors (images of their longest chords) intersect. We show that the corresponding quotient space of this topological space is homeomorphic to the boundary of the combinatorial Mandelbrot set. To each equivalence class of these geolaminations we associate a unique lamination and its topological polynomial so that this interpretation can be viewed as a way to endow the space of all quadratic topological polynomials with a suitable topology

Reasons for the Success of the Soviet Mathematical School

2015 · ARTICLE · en

It is widely known that Soviet school of exact sciences, was among the strongest in the world, particularly in terms of physics and mathematics. Why? This is the question we would like to address in this paper by collecting and sum￾marizing different viewpoints on this issue expressed by prominent mathematicians. Many of them witnessed the most fruitful period, the “golden years” of Soviet science and played a major role in the subsequent development of Soviet/Russian mathematics. There is little controversy in the explanations provided by different people; the only es￾sential differences are in the emphases. Thus the list of fac￾tors may be regarded as precisely determined. This paper simply aims at communicating them to a non-mathematical community interested in issues of science and education.

A Metric View on Russian Mathematics and Russian Mathematical Diaspora (A Study Based on Frequent Russian Surnames)

2015 · ARTICLE · en

What happens with Russian mathematics in terms of metric parameters? Where do Russian mathematicians work, where do they publish, how well are they cited?

Changing Traditions of Mathematical Education: BSc Program in Mathematics at the National Research University Higher School of Economics

2015 · ARTICLE · en

HSE Faculty of Mathematics invited its first bachelor students in 2008. The program aims at providing a funda￾mental mathematical background as well as wide oppor￾tunities for its application: from physics, economics and computer science to actuary and financial analysis. Below we describe the problems encountered by the Faculty of Mathematics while building a new mathematical curric￾ulum, and the solutions found. To this end, we first need to recap the principles of mathematical education in tradi￾tional Russian universities.

The main cubioid

2014 · ARTICLE · en

The connectedness locus in the parameter space of quadratic polynomials is called the Mandelbrot set. A good combinatorial model of this set is due to Thurston. By definition, the principal hyperbolic domain of the Mandelbrot set consists of parameter values, for which the corresponding quadratic polynomials have an attracting fixed point. The closure of the principal hyperbolic domain of the Mandelbrot set is called the main cardioid. Its topology is completely described by Thurston's model. Less is known about the connectedness locus in the parameter space of cubic polynomials. In this paper, we discuss cubic analogues of the main cardioid and establish relationships between them.

DOI ↗ PDF ↗

On maps taking lines to plane curves

2014 · PREPRINT · en

We study cubic rational maps that take lines to plane curves. A complete description of such cubic rational maps concludes the classification of all planarizations, i.e., maps taking lines to plane curves.

PDF ↗

On the Theory of Coconvex Bodies

2014 · ARTICLE · en

If the complement of a closed convex set in a closed convex cone is bounded, then this complement minus the apex of the cone is called a coconvex set. Coconvex sets appear in singularity theory (they are closely related to Newton diagrams) and in commutative algebra. Such invariants of coconvex sets as volumes, mixed volumes, number of integer points, etc., play an important role. This paper aims at extending various results from the theory of convex bodies to the coconvex setting. These include the Aleksandrov–Fenchel inequality and the Ehrhart duality.

DOI ↗ PDF ↗

Complementary components to the cubic Principal Hyperbolic Domain

2014 · PREPRINT · en

We study the closure of the cubic Principal Hyperbolic Domain and its intersection $\mathcal{P}_\lambda$ with the slice $\mathcal{F}_\lambda$ of the space of all cubic polynomials with fixed point $0$ defined by the multiplier $\lambda$ at $0$. We show that any bounded domain $\mathcal{W}$ of $\mathcal{F}_\lambda\setminus\mathcal{P}_\lambda$ consists of $J$-stable polynomials $f$ with connected Julia sets $J(f)$ and is either of \emph{Siegel capture} type (then $f\in \mathcal{W}$ has an invariant Siegel domain $U$ around $0$ and another Fatou domain $V$ such that $f|_V$ is two-to-one and $f^k(V)=U$ for some $k>0$) or of \emph{queer} type (then at least one critical point of $f\in \mathcal{W}$ belongs to $J(f)$, the set $J(f)$ has positive Lebesgue measure, and carries an invariant line field).

Combinatorial models for spaces of cubic polynomials

2014 · PREPRINT · en

To construct a model for a connectedness locus of polynomials of degree $d\ge 3$ (cf with Thurston's model of the Mandelbrot set), we define \emph{linked} geolaminations $\mathcal{L}_1$ and $\mathcal{L}_2$. An \emph{accordion} is defined as the union of a leaf $\ell$ of $\mathcal{L}_1$ and leaves of $\mathcal{L}_2$ crossing $\ell$. We show that any accordion behaves like a gap of one lamination and prove that the maximal \emph{perfect} (without isolated leaves) sublaminations of $\mathcal{L}_1$ and $\mathcal{L}_2$ coincide. In the cubic case let $\mathcal{D}_3\subset \mathcal{M}_3$ be the set of all \emph{dendritic} (with only repelling cycles) polynomials. Let $\mathcal{MD}_3$ be the space of all \emph{marked} polynomials $(P, c, w)$, where $P\in \mathcal{D}_3$ and $c$, $w$ are critical points of $P$ (perhaps, $c=w$). Let $c^*$ be the \emph{co-critical point} of $c$ (i.e., $P(c^*)=P(c)$ and, if possible, $c^*\ne c$). By Kiwi, to $P\in \mathcal{D}_3$ one associates its lamination $\sim_P$ so that each $x\in J(P)$ corresponds to a convex polygon $G_x$ with vertices in $\mathbb{S}$. We relate to $(P, c, w)\in \mathcal{MD}_3$ its \emph{mixed tag} $\mathrm{Tag}(P, c, w)=G_{c^*}\times G_{P(w)}$ and show that mixed tags of distinct marked polynomials from $\mathcal{MD}_3$ are disjoint or coincide. Let $\mathrm{Tag}(\mathcal{MD}_3)^+ = \bigcup_{\mathcal{D}_3}\mathrm{Tag}(P,c,w)$. The sets $\mathrm{Tag}(P, c, w)$ partition $\mathrm{Tag}(\mathcal{MD}_3)^+$ and generate the corresponding quotient space $\mathrm{MT}_3$ of $\mathrm{Tag}(\mathcal{MD}_3)^+$. We prove that $\mathrm{Tag}:\mathcal{MD}_3\to \mathrm{MT}_3$ is continuous so that $\mathrm{MT}_3$ serves as a model space for $\mathcal{MD}_3$.

Smart criticality

2014 · PREPRINT · en

A crucial fact established by Thurston in his 1985 preprint is that distinct \emph{minors} of quadratic laminations do not cross inside the unit disk; this led to his construction of a combinatorial model of the Mandelbrot set. Thurston's argument is based upon the fact that \emph{majors} of a quadratic lamination never enter the region between them, a result that fails in the cubic case. In this paper, devoted to laminations of any degree, we use an alternative approach in which the fate of sets of intersecting leaves of two distinct laminations is studied. It turns out that, under some natural assumptions, these sets of intersecting leaves behave like gaps of a lamination. Relying upon this, we rule out certain types of mutual location of critical sets of distinct laminations (this can be viewed as a partial generalization of the theorem that quadratic minors do not cross inside the unit disk). The main application is to the cubic case.

Курсы (7)