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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)

Modeling Core Parts of Zakeri Slices I

2022 · ARTICLE · en

The paper deals with cubic 1-variable polynomials whose Julia sets are connected. Fixing a bounded type rotation number, we obtain a slice of such polynomials with the origin being a fixed Siegel point of the specified rotation number. Such slices as parameter spaces were studied by S. Zakeri, so we call them Zakeri slices. We give a model of the central part of a slice (the subset of the slice that can be approximated by hyperbolic polynomials with Jordan curve Julia sets), and a continuous projection from the central part to the model. The projection is defined dynamically and agrees with the dynamical-analytic parameterization of the Principal Hyperbolic Domain by Petersen and Tan Lei.

PDF ↗

Slices of the Parameter Space of Cubic Polynomials

2022 · ARTICLE · en

In this paper, we study slices of the parameter space of cubic polynomials, up to affine conjugacy, given by a fixed value of the multiplier at a non-repelling fixed point. In particular, we study the location of the main cubioid in this parameter space. The main cubioid is the set of affine conjugacy classes of complex cubic polynomials that have certain dynamical properties generalizing those of polynomials z^2 + c for c in the filled main cardioid.

DOI ↗ PDF ↗

Cutpoints of Invariant Subcontinua of Polynomial Julia Sets

2022 · ARTICLE · en

We prove fixed point results for branched covering maps f of the plane. For complex polynomials P with Julia set J_P these imply that periodic cutpoints of some invariant subcontinua of J_P are also cutpoints of J_P. We deduce that, under certain assumptions on invariant subcontinua Q of J_P, every Riemann ray to Q landing at a periodic repelling/parabolic point x ∈ Q is isotopic to a Riemann ray to J_P relative to Q.

DOI ↗ PDF ↗

Location of Siegel capture polynomials in parameter spaces

2021 · ARTICLE · en

A cubic polynomial with a marked fixed point 0 is called an IS-capture polynomial if it has a Siegel disk D around 0 and if D contains an eventual image of a critical point. We show that any IS-capture polynomial is on the boundary of a unique bounded hyperbolic component of the polynomial parameter space determined by the rational lamination of the map and relate IS-capture polynomials to the cubic principal hyperbolic domain and its closure.

DOI ↗ PDF ↗

A model of the cubic connectedness locus

2021 · PREPRINT · en

We construct a model of the cubic connectedness locus.

On critical renormalization of complex polynomials

2021 · PREPRINT · en

Holomorphic renormalization plays an important role in complex polynomial dynamics. We consider certain conditions guaranteeing that a polynomial which does not admit a polynomial-like connected Julia set still admits an invariant continuum on which it is topologically conjugate to a lower degree polynomial. This invariant continuum may contain extra critical points of the original polynomial that are not visible in the dynamical plane of the conjugate polynomial. Thus, we extend the notions of holomorphic renormalization and polynomial-like maps and describe a setup where new generalized versions of these notions are applicable and yield useful topological conjugacies.

Cutpoints of invariant subcontinua of polynomial Julia sets

2021 · PREPRINT · en

We prove fixed point results for branched covering maps f of the plane. For complex polynomials P with Julia set J_P these imply that periodic cutpoints of some invariant subcontinua of J_P are also cutpoints of JP. We deduce that, under certain assumptions on invariant subcontinua Q of J_P, every Riemann ray to Q landing at a periodic repelling/parabolic point x∈Q is isotopic to a Riemann ray to J_P relative to Q.

Modeling core parts of Zakeri slices I

2021 · PREPRINT · en

The paper deals with cubic 1-variable polynomials whose Julia sets are connected. Fixing a bounded type rotation number, we obtain a slice of such polynomials with the origin being a fixed Siegel point of the specified rotation number. Such slices as parameter spaces were studied by S. Zakeri, so we call them \emph{Zakeri slices}. We give a model of the central part of a slice (the subset of the slice that can be approximated by hyperbolic polynomials with Jordan curve Julia sets), and a continuous projection from the central part to the model. The projection is defined dynamically and is coherent with the dynamical-analytic parameterization of the Principal Hyperbolic Domain by Petersen and Tan Lei.

Immediate renormalization of complex polynomials

2021 · PREPRINT · en

A cubic polynomial P with a non-repelling fixed point b is said to be immediately renormalizable if there exists a (connected) quadratic-like invariant filled Julia set K∗ such that b∈K∗. In that case exactly one critical point of Pdoes not belong to K∗. We show that if, in addition, the Julia set of P has no (pre)periodic cutpoints then this critical point is recurrent.

Laminational models for some spaces of polynomials of any degree

2020 · ARTICLE · en

The so-called “pinched disk” model of the Mandelbrot set is due to A. Douady, J. H. Hubbard and W. P. Thurston. It can be described in the language of geodesic laminations. The combinatorial model is the quotient space of the unit disk under an equivalence relation that, loosely speaking, “pinches” the disk in the plane (whence the name of the model). The significance of the model lies in particular in the fact that this quotient is planar and therefore can be easily visualized. The conjecture that the Mandelbrot set is actually homeomorphic to this model is equivalent to the celebrated MLC conjecture stating that the Mandelbrot set is locally connected.For parameter spaces of higher degree polynomials no combinatorial model is known. One possible reason may be that the higher degree analog of the MLC conjecture is known to be false. We investigate to which extent a geodesic lamination is determined by the location of its critical sets and when different choices of critical sets lead to essentially the same lamination. This yields models of various parameter spaces of laminations similar to the “pinched disk” model of the Mandelbrot set.

DOI ↗

Курсы (7)