Related papers: On the Calogero-Moser solution by root-type Lax pa…
We found a necessary and sufficient condition for the existence of the tensor product of modules over a vertex algebra. We defined the notion of vertex bilinear map and we provide two algebraic construction of the tensor product, where one…
Let $\mathbb F$ denote an algebraically closed field, and fix a nonzero $q \in \mathbb F$ that is not a root of unity. We consider the $q$-tetrahedron algebra $\boxtimes_q$ over $\mathbb F$. It is known that each finite-dimensional…
We give conditions for when two Euler products are the same given that they satisfy a functional equation and their coefficients are not too large and do not differ from each other by too much. Additionally, we prove a number of…
The method of fundamental solutions (MFS) is a numerical method for solving boundary value problems involving linear partial differential equations. It is well known that it can be very effective assuming regularity of the domain and…
It has been recently discovered in the context of the six vertex or XXZ model in the fundamental representation that new symmetries arise when the anisotropy parameter $(q+q^{-1})/2$ is evaluated at roots of unity $q^{N}=1$. These new…
In this paper, we continue to develop a general scheme to study a broad class of integrable systems naturally associated with the coboundary dynamical Lie algebroids. In particular, we present a factorization method for solving the…
Morse index theory provides an elegant and useful tool for describing several aspects of a Lagrangian system in terms of its variational properties. In the classical framework it provides an equality between the spectral properties of a…
Solutions to a class of differential systems that generalize the Halphen system are determined in terms of automorphic functions whose groups are commensurable with the modular group. These functions all uniformize Riemann surfaces of genus…
We study a class of overdetermined algebraic systems of equations. We prove that the number of distinct solutions equals to the maximal possible if and only if certain matrices are commuting and semisimple. This gives a characterization of…
We study a single matrix oscillator with the quadratic Hamiltonian and deformed commutation relations. It is equivalent to the multispecies Calogero model in one dimension, with inverse-square two-body and three-body interactions.…
We study the Born-Infeld equation from a Lagrangian point of view emphasizing the duality symmetry present in such systems. We obtain the Hamiltonian formulation directly from the Lagrangian. We also show that this system admits a…
We study multiple chordal SLE$(\kappa)$ systems in a simply connected domain $\Omega$, where $z_1, \ldots, z_n \in \partial \Omega$ are boundary starting points and $q \in \partial \Omega$ is an additional marked boundary point. As a…
We investigate the multiplicity of solutions for a generalized poly-Laplacian system on weighted finite graphs and a generalized poly-Laplacian system with Dirichlet boundary value on weighted locally finite graphs, respectively, via the…
The problem of inner vs outer conjugacy of subalgebras of certain graph C*-algebras is investigated. For a large class of finite graphs E, we show that whenever $\alpha$ is a vertex-fixing quasi-free automorphism of the corresponding graph…
Endowing the set of functional graphs (FGs) with the sum (disjoint union of graphs) and product (standard direct product on graphs) operations induces on FGs a structure of a commutative semiring R. The operations on R can be naturally…
We show that a set function $\nu$ satisfies the gross substitutes property if and only if its homogeneous generating polynomial $Z_{q,\nu}$ is a Lorentzian polynomial for all positive $q \le 1$, answering a question of Eur-Huh. We achieve…
For the Calabi-Yau threefolds $X$ constructed by C. Schoen as fiber products of generic rational elliptic surfaces, we show that the action of the automorphism group of $X$ on the K\"ahler cone of $X$ has a rationally polyhedral fundamental…
We study pairs of associative algebras and linear functionals. New results together with corrected proofs for previously published material are presented. In particular, we prove the identity ind Mat(n) (#) A=n * ind A$ for…
This is a footnote to earlier joint work with Yu. Berest, which constructed a bijection between the space of ideal classes of the Weyl algebra and a union of Calogero-Moser varieties. A key property of this bijection is that it is…
We consider polynomial maps described by so-called "(multivariate) linearized polynomials". These polynomials are defined using a fixed prime power, say q. Linearized polynomials have no mixed terms. Considering invertible polynomial maps…