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Topological Recursion for the extended Ooguri–Vafa partition function of colored HOMFLY-PT polynomials of torus knots
Advances in Theoretical and Mathematical Physics. 2022. Vol. 26. No. 4. P. 793–833.
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).
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Springer, 2027.
The series Lecture Notes in Computer Science (LNCS), including its subseries Lecture Notes in Artificial Intelligence (LNAI) and Lecture Notes in Bioinformatics (LNBI), has established itself as a medium for the publication of new developments in computer science and information technology research, teaching, and education. LNCS enjoys close cooperation with the computer science R & ...
Added: July 8, 2026
Маликов М. А., Монахова Э. А., Rzaev E. et al., Ученые записки Казанского университета. Серия: Физико-математические науки 2026 Т. 168 № 2 С. 269–286
This article examines series of families of two-dimensional circulant networks with rectangular
L -shapes, optimal in diameter, as network-on-chip topologies with a minimal number of crossings
between the links and a bounded length of the maximum link that does not depend on the network
size. New network-on-chip routing algorithms, which use the coordinates of three adjacent zeros in
the ...
Added: July 8, 2026
Pilé I., Shchur L., Deng Y., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 Article 014101
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Swendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for models in different universality classes: Ising model, Potts model with three components, and four-state Potts model. The overlap of two ...
Added: July 6, 2026
Irkutsk: ISDCT SB RAS, 2026.
We study a model problem on the filtration of a conducting fluid through a
porous layer. A porous medium is presented as an assemblage of identical spherical
cells. Each cell consists of a porous core and liquid shell. We derive apriori estimates
for flow characteristics which show the specific behavior of the fluid. Our estimates
are validated numerically. ...
Added: July 5, 2026
М.: Наука и технологии, 2026.
«Телекоммуникации» ежемесячный рецензируемый производственный, информационно-аналитический и учебно-методический журнал выходит в свет с июля 2000 г.
Для руководителей и работников промышленности, научно-исследовательских и проектно-конструкторских институтов, высших учебных заведений, аспирантов и студентов, а также для специалистов, разрабатывающих, выпускающих и эксплуатирующих средства телекоммуникаций.
Новости разработок и производства, прогнозы развития, защита информации, Нормативные, справочные, аналитические и учебно-методические материалы.
Переход к глобальному информационному ...
Added: July 4, 2026
МФТИ, 2025.
абота редакции научного журнала «Труды Московского физико-технического института» (кратко «Труды МФТИ»), редакционной коллегии и редакционного совета осуществляется в соответствии с Положением, утвержденным ректором института. В состав редакционной коллегии входят руководители института, факультетов, институтских и факультетских кафедр. Главный редактор журнала —президент МФТИ, член-корр. РАН Кудрявцев Н.Н.
Журнал «Труды МФТИ» входит в базу данных РИНЦ (Российский Индекс Научного Цитирования) и доступен в электронной ...
Added: July 4, 2026
Springer, 2026.
This book presents established and new research on the close connections between graph games and systems of logic, particularly existing and newly designed modal logics. The volume utilizes two graph games – the sabotage game and the hide-and-seek game – to demonstrate the natural interplay between designing new graph games and exploring new kinds of ...
Added: June 30, 2026
Pochinka O., Barinova M., Journal of Geometry and Physics 2026 Vol. 228 P. 1–8
In the present paper we consider an Ω-stable 3-diffeomorphism with a solid or thickened surfaced non-trivial basic set. Such basic sets include, for instance, all one-dimensional expanding attractors and those two-dimensional basic sets that are not expanding. We prove that the chain recurrent set of every such a diffeomorphism necessarily contains at least two non-trivial ...
Added: June 30, 2026
German O., Illarionov A., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 3–18
Пусть симплекс с целочисленными вершинами - содержащий ровно одну целочисленную точку, отличную от своих вершин. В работе доказывается, что если точка находится во внутренности симплекса или в относительной внутренности некоторой гиперграни симплекса, то объем симплекса ограничен величиной, зависящей только от размерности, в противном случае объем симплекса может быть сколь угодно большим. Этот результат применяется для вывода асимптотической формулы для среднего числа вершин полиэдров ...
Added: June 29, 2026
Alexandrov A., Bychkov B., Dunin-Barkowski P. et al., Selecta Mathematica, New Series 2026 Vol. 32 Article 25
We revise the notion of the blobbed topological recursion by extending it to the setting of generalized topological recursion as well as allowing blobs which do not necessarily admit topological expansion. We show that the so-called non-perturbative differentials form a special case of this revisited version of blobbed topological recursion. Furthermore, we prove the KP ...
Added: April 23, 2026
Alexandrov A., Bychkov B., Dunin-Barkowski P. et al., Selecta Mathematica, New Series 2025 Vol. 31 Article 42
We discuss a universal relation that we call the x-y swap relation, which plays a prominent role in the theory of topological recursion, Hurwitz theory, and free probability theory. We describe in a very precise and detailed way the interaction of the x-y swap relation and KP integrability. As an application, we prove a recent conjecture ...
Added: May 27, 2025
Alexandrov A., Bychkov B., Dunin-Barkowski P. et al., Communications in Mathematical Physics 2025 Vol. 406 Article 94
We use the theory of x-y duality to propose a new definition/construction for the correlation differentials of topological recursion; we call it generalized topological recursion. This new definition coincides with the original topological recursion of Chekhov–Eynard–Orantin in the regular case and allows, in particular, to get meaningful answers in a variety of irregular and degenerate ...
Added: May 27, 2025
Alexandrov A., Bychkov B., Dunin-Barkowski P. et al., Journal of the European Mathematical Society 2025 P. 1–62
We prove a recent conjecture of Borot et al. that a particular universal closed algebraic formula recovers the correlation differentials of topological recursion after the swap of x and y in the input data. We also show that this universal formula can be drastically simplified (as it was already done by Hock). As an application ...
Added: May 27, 2025
Alexandrov A., Bychkov B., Dunin-Barkowski P. et al., Communications in Number Theory and Physics 2024 Vol. 18 No. 4 P. 795–841
We review the notion of symplectic duality earlier introduced in the context of topological recursion. We show that the transformation of symplectic duality can be expressed as a composition of x-y dualities in a broader context of log topological recursion. As a corollary, we establish nice properties of symplectic duality: various convenient explicit formulas, invertibility, ...
Added: March 11, 2025
Alexandrov A., Bychkov Boris, Dunin-Barkowski Petr et al., International Mathematics Research Notices 2024 Vol. 2024 No. 21 P. 13461–13487
We introduce a new concept of logarithmic topological recursion that provides a patch to topological recursion in the presence of logarithmic singularities and prove that this new definition satisfies the universal x-y swap relation. This result provides a vast generalization and a proof of a very recent conjecture of Hock. It also uniformly explains (and ...
Added: March 11, 2025
Bychkov B., Dunin-Barkowski P., Kazaryan M. et al., Transactions of the American Mathematical Society 2025 Vol. 378 No. 2 P. 1001–1054
We consider weighted double Hurwitz numbers, with the weight given by arbitrary rational function times an exponent of the completed cycles. Both special singularities are arbitrary, with the lengths of cycles controlled by formal parameters (up to some maximal length on both sides), and on one side there are also distinguished cycles controlled by degrees ...
Added: March 11, 2025
Bychkov B., Dunin-Barkowski P., Maxim Kazarian et al., Journal of London Mathematical Society 2024 Vol. 109 No. 6 Article e12946
We study the n-point differentials corresponding to Kadomtsev–Petviashvili (KP) tau functions of hypergeometric type (also known as Orlov–Scherbin partition functions), with an emphasis on their ℏ2-deformations and expansions. Under the naturally required analytic assumptions, we prove certain higher loop equations that, in particular, contain the standard linear and quadratic loop equations, and thus imply the blobbed topological recursion. ...
Added: October 29, 2024
Alexandrov A., B. Bychkov, P. Dunin-Barkowski et al., Journal of Geometry and Physics 2024 Vol. 206 Article 105329
For a given spectral curve, we construct a family of symplectic dual spectral curves for which we prove an explicit formula expressing the n-point functions produced by the topological recursion on these curves via the n-point functions on the original curve. As a corollary, we prove topological recursion for the generalized fully simple maps generating functions. ...
Added: October 25, 2024
Dunin-Barkowski P., Kramer R., Popolitov A. et al., Annales Scientifiques de l'Ecole Normale Superieure 2023 Vol. 56 No. 4 P. 1199–1229
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. ...
Added: October 5, 2023
Bychkov B., Dunin-Barkowski P., Kazaryan M. et al., Communications in Mathematical Physics 2023 Vol. 402 P. 665–694
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 ...
Added: June 29, 2023