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Преобразования Дарбу для дискретных версий иерархии КП и строгой иерархии КП
Теоретическая и математическая физика. 2024. Т. 221. № 3. С. 503–522.
We introduce the notion of Darboux transformations for the discrete KP hierarchy and its strict version,
and present an explicit form of these transformations for the solutions of discrete KP and discrete strict
KP hierarchies constructed in our previous work.
Basalaev A., Rarovskii A., Journal of Singularities 2026 Vol. 30 P. 61–80
Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau-Ginzburg orbifolds. Namely, for the pairs (f,G), where f defines an isolated singularity of A and D type and G is a group of symmetries of ...
Added: September 1, 2026
Rybakov M., Shkatov D., Journal of Logic and Computation 2026 Vol. 36 No. 6 Article exag026
We prove Pi-1-1-hardness, and thus lack of recursive axiomatizability, of constant-domain modal predicate logics defined by a class of Dedekind complete linear Kripke frames containing a frame with an infinitely increasing chain of worlds. The result holds even for the language with one unary predicate letter, one propositional letter, and two individual variables. ...
Added: September 1, 2026
Селянин Ф. И., Moscow Mathematical Journal 2026 Vol. 26 No. 2 P. 167–187
Minkowski mixed volume of n subpolytopes D1,…,Dn of a polytope P⊂Rn clearly does not exceed the normalized volume n!Vol(P). Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face F⊊P intersects at least dim(F)+1 of the polytopes Di. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems.
Motivated by relaxing the bound dim(F)+1 to dim(F), we ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., International Mathematics Research Notices 2026 Vol. 14 Article rnag146
We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov–Witten theory of the projective line and is dictated by Z 2 -equivariant ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Communications in Mathematical Physics 2026 Vol. 407 No. 69
We prove that for any initial data on a genus zero spectral curve the cor responding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r-th roots of the twisted powers of the log canonical bundles ...
Added: August 31, 2026
Gromov V., Переслегин С. Б., Переслегина Е. Б. et al., СПб.: Полакс, 2026.
Механизм происходящих в мире изменений носит эволюционный, а не экологический характер. Иначе говоря, Человечество столкнулось с кризисом развития, который имеет три независимые составляющие: кризис индустриального общества (фазовый кризис), кризис научного мышления (эпистемный кризис) и кризис формата существования разума (социосистемный кризис). Доклад посвящён аспектам этого триединого кризиса и возможным путям его преодоления, не сводящимся к первичному ...
Added: August 31, 2026
Devyatov R. A., Mathematical notes 2026 Vol. 119 No. 3 P. 782–786
Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Journal fuer die reine und angewandte Mathematik 2026 Vol. 2026 No. 836 P. 111–162
We give a self-contained and simplified proof of Mukai’s classification of prime Fano threefolds of index 1 and genus g ≥ 6 with at most factorial terminal singularities, and of its extension to higher dimension. ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Compositio Mathematica 2026 Vol. 162 No. 1 P. 59–99
We give a proof of Mukai’s theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature. The result is essential for Mukai’s biregular classification of prime Fano threefolds, and for the existence of semiorthogonal decompositions in their derived categories. Our ...
Added: August 30, 2026
Guseva L., Novikov A., Advances in Mathematics 2026 Vol. 503 Article 111211
We prove that the Kuznetsov–Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups Sp(2n,C) are full and consist of vector bundles. To achieve this, we construct several classes of complexes, which we call generalized staircase complexes, symplectic staircase complexes and secondary staircase complexes — each of which may be of independent interest. ...
Added: August 30, 2026
Polishchuk A., Rains E., Journal of the Institute of Mathematics of Jussieu 2026 Vol. 25 No. 1 P. 339–373
We prove that for every relatively prime pair of integers (d,r) with r>0, there exists an exceptional pair (O,V) on any del Pezzo surface of degree 4, such that V is a bundle of rank r and degree d. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be ...
Added: August 30, 2026
Kazhdan D., Polishchuk A., Pure and Applied Mathematics Quarterly 2026 Vol. 22 No. 3 P. 1115–1166
We continue the study of automorphic functions associated with a curve C over the ring k[ε]/(ε²), where k is a finite field, begun in arXiv:2303.16259. Namely, we study an example of theta-lifting in this framework and show that it can be understood in terms of the orbit decomposition of the space of automorphic functions S(SL₂(F)\SL₂(A_C)) ...
Added: August 30, 2026
Kuznetsov A. P., Sataev I. R., Stankevich N., Chaos 2026 Vol. 36 No. 8 Article 083131
A radio-physical system, namely, a two-mode van der Pol generator, is considered. It is shown that this system demonstrates two types of chaos: with one and two zero Lyapunov exponents. The regions of the second type of chaos are surrounded by bifurcation lines of invariant tori doubling. Quasi-periodic structures of various shapes are embedded within ...
Added: August 30, 2026
Shirokov N. A., Rozenblum G., Israel Journal of Mathematics 2026 P. 1–30
We establish that a generalized H\¨older continuous function on an (m−2)-Ahlfors regular compact set in Rm can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity modulus of the function ...
Added: August 29, 2026
Takebe T., A. V. Zabrodin, Russian Mathematical Surveys 2025 Vol. 80 No. 4(484) P. 47–120
We give a detailed account of the N -component Toda lattice hierarchy,
which can be regarded as a generalization of the well-known Toda chain model
and its non-abelian version. This hierarchy is an extension of the one introduced earlier by Ueno and Takasaki. Our version contains N discrete variables rather than one. We start from the Lax ...
Added: September 16, 2025
Zabrodin A., Mathematical Physics Analysis and Geometry 2024 Vol. 27 Article 1
We consider multi-component Kadomtsev-Petviashvili hierarchy of type C (the multi-component CKP hierarchy) originally defined with the help of matrix pseudo-differential operators via the Lax-Sato formalism. Starting from the bilinear relation for the wave functions, we prove existence of the tau-function for the multi-component CKP hierarchy and provide a formula which expresses the wave functions through ...
Added: November 28, 2024
Helminck G. F., Poberezhny V. A., Polenkova S. V., Theoretical and Mathematical Physics 2022 Vol. 213 No. 1 P. 1348–1361
The discrete KP hierarchy and its strict version are both deformations of the commutative algebra k[Λ]k[Λ] inside the algebra PsΔPsΔ of pseudo-difference operators, where ΛΛ is the Z×ZZ×Z-matrix corresponding to the shift operator and k=Rk=R or k=Ck=C. Under these deformations, the matrix coefficients of the elements of PsΔPsΔ come from a commutative kk-algebra RR. We discuss both deformations from a wider perspective and consider them in a presetting instead ...
Added: December 6, 2022
Buryak A., Rossi P., Advances in Mathematics 2021 Vol. 386 No. 6 Article 107794
In this paper we construct a family of cohomology classes on the moduli space of stable curves generalizing Witten's r-spin classes. They are parameterized by a phase space which has one extra dimension and in genus 0 they correspond to the extended r-spin classes appearing in the computation of intersection numbers on the moduli space of open Riemann surfaces, while ...
Added: October 29, 2021
Helminck G. F., Poberezhny V. A., Polenkova S. V., Theoretical and Mathematical Physics 2020 Vol. 204 No. 3 P. 1140–1153
We show that both the dKP hierarchy and its strict version can be extended to a wider class of deformations satisfying a larger set of Lax equations. We prove that both extended hierarchies have appropriate linearizations allowing a geometric construction of their solutions. ...
Added: October 28, 2020
Terekhovich V., Метафизика 2019 Т. 31 № 1 С. 155–165
В статье рассматривается проблема реальности волновой функции квантовой теории. Перечислены основные точки зрения на реальность ненаблюдаемых объектов теорий вообще и волновой функции в частности. Особое внимание уделено манипулятивному аргументу, предложенному Я. Хакингом и Н. Картрайт в рамках экспериментального реализма. Сильные и слабые стороны этого аргумента рассматриваются на примере технологий квантовой криптографии и квантового компьютера, а ...
Added: March 4, 2020
Хельминк Г. Ф., Poberezhny V. A., Поленкова С. В., Theoretical and Mathematical Physics 2019 Vol. 198 No. 2 P. 197–214
In this paper we consider inside the algebra PsΔ of pseudo di erence
operators, two deformations of the Lie subalgebra spanned by the positive powers
of an invertible constant pseudo difference operator 0 of degree one. The rst
deformation is by the group in PsΔ corresponding to the Lie subalgebra PsΔ<0
of elements of negative degree and the second by the group ...
Added: March 20, 2019