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Дунин-Барковский Петр Игоревич

Факультет математики

Профиль на hse.ru ↗ тел.: +7 (495) 772-95-90 | 12742
Публикаций
37
Языков
2
Наград
2
Конференций
13
Профиль Публикации (37) Курсы (12)

Профессиональные интересы

алгебраическая геометрияматематическая физикаинварианты узловкомбинаторика

Должности

  • Доцент — Факультет математики
  • Ведущий научный сотрудник — Факультет математики, Международная лаборатория кластерной геометрии
  • Заместитель заведующего лабораторией — Факультет математики, Международная лаборатория кластерной геометрии

Био

  • · Начал работать в НИУ ВШЭ в 2014 году.
  • · Научно-педагогический стаж: 11 лет.

Образование

  • 2015 · PhD: Амстердамский университет
  • 2014 · Кандидат физико-математических наук: Национальный исследовательский центр "Курчатовский институт"
  • 2011 · Магистратура: Московский физико-технический институт, специальность «Прикладные математика и физика», квалификация «Магистр прикладной математики и физики»
  • 2009 · Бакалавриат: Московский физико-технический институт, специальность «Прикладные математика и физика», квалификация «Бакалавр прикладных математики и физики»
  • — · Образование:Московский физико-технический институт, Москва, 2011. PhD

Опыт работы

  • · 2014: Работает в НИУ ВШЭ с года
  • · 2025: Проведение научных исследований по проекту «Геометрия и комбинаторика интегрируемых систем» (код проекта ФИ-2025-62) в лаборатории согласно техническому заданию под руководством С.К. Ландо год

Награды и поощрения

  • · Лучший преподаватель — 2019, 2017
  • · Группа высокого профессионального потенциала (кадровый резерв НИУ ВШЭ)Категория "Новые исследователи" (2015–2016)

Гранты и проекты

  • 2022 · 2020-2022 грант РНФ № 20-61-46005 «Алгебра и геометрия интегрируемых статистических моделей в старших размерностях» (участник проекта)
  • 2020 · 2019-2020 грант РНФ № 16-11-10316-П «Характеристические классы и теория представлений» (участник проекта)

Конференции (13)

Показать все
  • · 2024: Международная конференция "Инвариантность и интегрируемость 2" (г.Пушкин, Санкт-Петербург). Доклад: Symplectic duality and logarithmic topological recursion
  • · 2023: Инвариантность и интегрируемость (Репино). Доклад: Симплектическая двойственность в топологической рекурсии
  • · 2022: George Shabat 70 Conference (Москва). Доклад: Double Hurwitz numbers, maps, topological recursion, and dualities
  • · 2021: 7th Workshop on Combinatorics of Moduli Spaces, Cluster Algebras and Topological Recursion (Москва). Доклад: Explicit closed algebraic formulas for hypergeometric KP/generalized Hurwitz n-point functions
  • · 2019: Dynamics, Equations and Applications (DEA 2019) (Краков). Доклад: Loop equations and a proof of Zvonkine's qr-ELSV formula
  • · 2018: Workshop and School «Topological Field Theories, String theory and Matrix Models – 2018» (Москва). Доклад: On cut-and-join equation for monotone Hurwitz numbers
  • · 2017: Quantum information and topological recursion (Москва). Доклад: Proving topological recursion combinatorially for Hurwitz-type problems
  • · 2016: 5th Workshop on Combinatorics of Moduli Spaces, Hurwitz numbers, and cohomological field theories (Москва). Доклад: Dubrovin's superpotential as a global spectral curve
  • · 2016: 2016 American Mathematical Society von Neumann Symposium (Шарлотт, Северная Каролина). Доклад: Topological Recursion and Givental's Formalism: Spectral Curves for Gromov-Witten Theories
  • · 2015: Geometric Invariants and Spectral Curves (Leiden). Доклад: Superpotential as a global spectral curve
  • · 2015: Workshop and School "Quantum Geometry, Duality and Matrix Models" (Москва). Доклад: Dubrovin's superpotential as a global spectral curve
  • · 2014: "Group Theory and Knots" (Натал). Доклад: "Bi-colored and 4-colored maps, chains of matrices and spectral curve topological recursion".
  • · 2014: Symposium about Mathematics (Цюрих). Доклад: "Gromov-Witten theory and spectral curve topological recursion"

Идентификаторы исследователя

Публикации (37)

Generalised Ordinary vs Fully Simple Duality for n-Point Functions and a Proof of the Borot–Garcia-Failde Conjecture.

2023 · ARTICLE · en

We study a duality for the n-point functions in VEV formalism that we call the ordinary vs fully simple duality. It provides an ultimate generalisation and a proper context for the duality between maps and fully simple maps observed by Borot and Garcia-Failde. Our approach allows to transfer the algebraicity properties between the systems of n-point functions related by this duality, and gives direct tools for the analysis of singularities. As an application, we give a proof of a recent conjecture of Borot and Garcia-Failde on topological recursion for fully simple maps.

DOI ↗

Loop equations and a proof of Zvonkine's qr-ELSV formula

2023 · ARTICLE · en

We prove the 2006 Zvonkine conjecture that expresses Hurwitz numbers with completed cycles in terms of intersection numbers with the Chiodo classes via the so-called r-ELSV formula, as well as its orbifold generalization, the so-called qr-ELSV formula.

DOI ↗ PDF ↗

Explicit closed algebraic formulas for Orlov–Scherbin n-point functions

2022 · ARTICLE · en

We derive a new explicit formula in terms of sums over graphs for the n-point correlation functions of general formal weighted double Hurwitz numbers coming from the Kadomtsev–Petviashvili tau functions of hypergeometric type (also known as Orlov–Scherbin partition functions). Notably, we use the change of variables suggested by the associated spectral curve, and our formula turns out to be a polynomial expression in a certain small set of formal functions defined on the spectral curve.

DOI ↗

Topological Recursion for the extended Ooguri–Vafa partition function of colored HOMFLY-PT polynomials of torus knots

2022 · ARTICLE · en

We prove that topological recursion applied to the spectral curve of colored HOMFLY-PT polynomials of torus knots reproduces the n-point functions of a particular partition function called the extended Ooguri-Vafa partition function. This generalizes and refines the results of Brini-Eynard-Marino and Borot-Eynard-Orantin. We also discuss how the statement of spectral curve topological recursion in this case fits into the program of Alexandrov-Chapuy-Eynard-Harnad of establishing the topological recursion for general weighted double Hurwitz numbers partition functions (a.k.a. KP tau-functions of hypergeometric type).

DOI ↗

Evolution for Khovanov polynomials for figure-eight-like family of knots

2022 · ARTICLE · en

We look at how evolution method deforms, when one considers Khovanov polynomials instead of Jones polynomials. We do this for the figure-eight-like knots (also known as 'double braid' knots, see arXiv:1306.3197) -- a two-parametric family of knots which "grows" from the figure-eight knot and contains both two-strand torus knots and twist knots. We prove that parameter space splits into four chambers, each with its own evolution, and two isolated points. Remarkably, the evolution in the Khovanov case features an extra eigenvalue, which drops out in the Jones (t -> -1) limit.

DOI ↗

Integrable hierarchies associated to infinite families of Frobenius manifolds

2021 · ARTICLE · en

We propose a new construction of an integrable hierarchy associated to any infinite series of Frobenius manifolds satisfying a certain stabilization condition. We study these hierarchies for Frobenius manifolds associated to AN, DN and BN singularities. In the case of AN Frobenius manifolds our hierarchy turns out to coincide with the KP hierarchy; for BN Frobenius manifolds it coincides with the BKP hierarchy; and for DN hierarchy it is a certain reduction of the 2-component BKP hierarchy. As a side product to these results we illustrate the enumerative meaning of certain coefficients of AN, DN and BN Frobenius potentials.

DOI ↗

Combinatorics of Bousquet-Mélou-Schaeffer numbers in the light of topological recursion

2020 · ARTICLE · en

In this paper we prove, in a purely combinatorial-algebraic way, a structural quasi-polynomiality property for the Bousquet-Mélou–Schaeffer numbers. Conjecturally, this property should follow from the Chekhov–Eynard–Orantin topological recursion for these numbers (or, to be more precise, the Bouchard–Eynard version of the topological recursion for higher order critical points), which we derive in this paper from the recent result of Alexandrov–Chapuy–Eynard–Harnad. To this end, the missing ingredient is a generalization to the case of higher order critical points on the underlying spectral curve of the existing correspondence between the topological recursion and Givental’s theory for cohomological field theories.

DOI ↗

Dubrovin's superpotential as a global spectral curve

2019 · ARTICLE · en

В работе применена процедура топологической рекурсии к суперпотенциалу Дубровина, соответствующему полупростой точке конформного фробениусова многообразия. Показано, что при определенных условиях разложения мультидифференциалов, получаемых в результате применения топологической рекурсии, воспроизводят когомологическую теорию поля, соответствующую данной точке фробениусова многообразия.

DOI ↗

Cut-and-join equation for monotone Hurwitz numbers revisited

2019 · ARTICLE · en

We give a new proof of the cut-and-join equation for the monotone Hurwitz numbers, derived first by Goulden, Guay-Paquet, and Novak. The main interest in this particular equation is its close relation to the quadratic loop equation in the theory of spectral curve topological recursion, and we recall this motivation giving a new proof of the topological recursion for monotone Hurwitz numbers, obtained first by Do, Dyer, and Mathews.

DOI ↗

Combinatorial structure of colored HOMFLY-PT polynomials for torus knots.

2019 · ARTICLE · en

We rewrite the (extended) Ooguri–Vafa partition function for colored HOMFLY-PT polynomials for torus knots in terms of the free-fermion (semi-infinite wedge) formalism, making it very similar to the generating function for double Hurwitz numbers. This allows us to conjecture the combinatorial meaning of full expansion of the correlation differentials obtained via the topological recursion on the Brini–Eynard–Mariño spectral curve for the colored HOMFLY-PT polynomials of torus knots. This correspondence suggests a structural combinatorial result for the extended Ooguri–Vafa partition function. Namely, its coefficients should have a quasi-polynomial behavior, where nonpolynomial factors are given by the Jacobi polynomials (treated as functions of their parameters in which they are indeed nonpolynomial). We prove this quasi-polynomiality in a purely combinatorial way. In addition to that, we show that the (0,1)(0,1)- and (0,2)(0,2)-functions on the corresponding spectral curve are in agreement with the extension of the colored HOMFLY-PT polynomials data, and we prove the quantum spectral curve equation for a natural wave function obtained from the extended Ooguri–Vafa partition function.

DOI ↗ PDF ↗

Курсы (12)