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Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2012. Vol. 8. No. 095.
We describe new families of the Knizhnik-Zamolodchikov-Bernard (KZB) equations related to the WZW-theory corresponding to the adjoint G-bundles of different topological types over complex curves Sigma(g,n) of genus g with n marked points. The bundles are defined by their characteristic classes - elements of H-2 (Sigma(g,n), Z(G)), where Z (G) is a center of the simple complex Lie group G. The KZB equations are the horizontality condition for the projectively flat connection (the KZB connection) defined on the bundle of conformal blocks over the moduli space of curves. The space of conformal blocks has been known to be decomposed into a few sectors corresponding to the characteristic classes of the underlying bundles. The KZB connection preserves these sectors. In this paper we construct the connection explicitly for elliptic curves with marked points and prove its flatness.
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
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
Piontkovski D., / Series arXiv "math". 2026.
A noncommutative projective variety is defined, following Artin and Zhang, by a graded coherent algebra 𝐴. The category of coherent sheaves is then the quotient qgr(𝐴) of the category of finitely presented graded modules by the subcategory of torsion modules. We consider the categorical and polynomial entropies of the Serre twist, that is, of the ...
Added: June 23, 2026
Piontkovski D., / Series arXiv "math". 2025.
If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed ...
Added: June 23, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Derkacheva A., Sakirkina M., Kraev G. et al., /. 2026.
Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
Added: April 28, 2026
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
Added: April 20, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Buryak A., Rossi P., International Mathematics Research Notices 2025 Vol. 2025 No. 20 Article rnaf315
The Riemann hierarchy is the simplest example of rank one, (+)-dimensional integrable system of nonlinear evolutionary PDEs. It corresponds to the dispersionless limit of the Korteweg–de Vries hierarchy. In the language of formal variational calculus, we address the classification problem for deformations of the Riemann hierarchy satisfiying different extra requirements (general deformations, deformations as systems ...
Added: November 27, 2025
Vassiliev V., Pacific Journal of Mathematics 2023 Vol. 326 No. 1 P. 135–160
The topology of the space of subalgebras of the function space specified by collections of equality conditins f(x)=f(y) is studied and applied to the problems of interpolation theory and knot theory ...
Added: October 31, 2025
Huang G., Kuksin S., Piatnitski A., Journal of Dynamics and Differential Equations 2024
We are concerned with averaging theorems for ε-small stochastic perturbations of integrable equations in Rd×Tn={(I,φ)} (Formula presented.) and in R2n={v=(v1,⋯,vn),vj∈R2}, (Formula presented.) where I=(I1,⋯,In) is the vector of actions, Ij=12‖vj‖2. The vector-functions θ and W are locally Lipschitz and non-degenerate. Perturbations of these equations are assumed to be locally Lipschitz and such that some few ...
Added: March 20, 2025
Basalaev A., Letters in Mathematical Physics 2024 Vol. 114 Article 120
According to Zuo and an unpublished work of Bertola, there is a two-index series of Dubrovin–Frobenius manifold structures associated to a B-type Coxeter group. We study the relations between these structures for the different values of these indices. We show that part of the data of such Dubrovin–Frobenius manifold indexed by (k, l) can be recovered ...
Added: December 4, 2024
Zabrodin A., Успехи математических наук 2023 Т. 78 № 2(470) С. 149–188
We find integrals of motion for the recently introduced
deformed Ruijsenaars–Schneider many-body system, which is the dynamical system for poles of elliptic solutions to the Toda lattice with constraint
of type B. Our method is based on the fact that the equations of motion
for this system coincide with those for pairs of Ruijsenaars–Schneider particles which stick together ...
Added: December 1, 2023
Krichever I., A. Zabrodin, Physica D: Nonlinear Phenomena 2023 Vol. 453 Article 133827
We introduce a new integrable hierarchy of nonlinear differential-difference equations which is a subhierarchy of the 2D Toda lattice defined by imposing a constraint to the Lax operators of the latter. The 2D Toda lattice with the constraint can be regarded as a discretization of the BKP hierarchy. We construct its algebraic-geometrical solutions in terms ...
Added: November 30, 2023
Springer, 2016.
This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "Lie Theory and Its Applications in Physics", held near Varna, Bulgaria, in June 2015. Traditionally, Lie theory is a tool to build mathematical models for physical systems.
Recently, the trend has been towards geometrization of the mathematical ...
Added: October 18, 2023
Basalaev A., Journal of Physics A: Mathematical and Theoretical 2022 Vol. 55 No. 29 Article 295202
We investigate the solutions to open WDVV equation, associated to type A and D Dubrovin–Frobenius manifolds. We show that these solutions satisfy some stabilization condition and associate to both of them the systems of commuting PDEs. In the type A we show that the system of PDEs constructed coincides with the dispersionless modified KP hierarchy ...
Added: December 4, 2022
Sarkissian G., Spiridonov V., Journal of Physics A: Mathematical and Theoretical 2022 Vol. 55 No. 38 Article 385203
General reduction of the elliptic hypergeometric equation to the level of complex hypergeometric functions is described. The derived equation is generalized to the Hamiltonian eigenvalue problem for new rational integrable N-body systems emerging from particular degenerations of the elliptic Ruijsenaars and van Diejen models. ...
Added: August 30, 2022
Spiridonov V., Sarkissian G. A., / Series arXiv "math". 2021. No. arXiv:2105.15031.
General reduction of the elliptic hypergeometric equation to the level of complex hypergeometric functions is described. Derived equation is generalized to the Hamiltonian eigenvalue problem for new rational integrable N-body systems emerging from particular degenerations of the elliptic Ruijsenaars and van Diejen models. ...
Added: November 9, 2021
Cham: Birkhäuser, 2020.
The book consists of articles based on the XXXVIII Białowieża Workshop on Geometric Methods in Physics, 2019. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, ...
Added: November 3, 2021