Related papers: The Hydra-k partial fields
We report on various results, conjectures, and open problems related to Kazhdan-Lusztig polynomials of matroids. We focus on conjectures about the roots of these polynomials, all of which appear here for the first time.
This paper presents analogous results of Hua [7][8] on numbers of representations of quivers over finite fields which respect nilpotent relations under certain assumptions. A closed formula which counts isomorphism classes of absolutely…
In this paper we introduce valuated $\Delta$-matroids, a natural generalization of two objects of study in matroid theory: valuated matroids and $\Delta$-matroids. We show that these objects exhibit nice properties analogous to ordinary…
This is a presentation of recent work on quantum permutation groups, complex Hadamard matrices, and the connections between them. A long list of problems is included. We include as well some conjectural statements, about matrix models.
We provide a systematic approach to describing the Ramond-Ramond (RR) fields as elements in twisted differential K-theory. This builds on a series of constructions by the authors on geometric and computational aspects of twisted…
Dirac delta function of matrix argument is employed frequently in the development of diverse fields such as Random Matrix Theory, Quantum Information Theory, etc. The purpose of the article is pedagogical, it begins by recalling detailed…
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…
The first problem we investigate is the following: given $k\in \mathbb{R}_{\ge 0}$ and a vector $v$ of Pl\"ucker coordinates of a point in the real Grassmannian, is the vector obtained by taking the $k$th power of each entry of $v$ again a…
We give new explicit formulas for the representations of the mapping class group of a genus one surface with one boundary component which arise from Integral TQFT. Our formulas allow one to compute the h-adic expansion of the TQFT-matrix…
Let k be a field of characteristic zero. We consider graded subalgebras A of k[x_1,...,x_m]/(x_1^2,...,x_m^2) generated by d linearly independant linear forms. Representations of matroids over k provide a natural description of the…
We obtain new integral representations, expressed as contour integrals in the complex Fourier plane, for the solution of fully nonhomogeneous interface problems for the linearized Cahn-Hilliard equation with arbitrary initial data on the…
An informal introduction to some new geometric partial differential equations motivated by string theories is provided. Some of these equations are also interesting from the point of view of non-K\"ahler geometry and the theory of…
We present a quantum-field-theoretic treatment of massive chiral fields in which particles possess well-defined chirality and helicity. This framework reproduces the chiral oscillation formula previously obtained in first-quantized…
We present some new families of quadratic vector fields, not necessarily integrable, for which their Kahan-Hirota-Kimura discretization exhibits the preservation of some of the characterizing features of the underlying continuous systems…
We define and study q-delta-matroids, and q-g-matroids. These objects are analogues, for finite-dimensional vector spaces over finite fields, of delta-matroids and g-matroids arising from finite sets. We compare axiomatic descriptions with…
Quark-hadron duality and its potential applications are discussed. We focus on theoretical efforts to model duality.
Rough sets were proposed to deal with the vagueness and incompleteness of knowledge in information systems. There are may optimization issues in this field such as attribute reduction. Matroids generalized from matrices are widely used in…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
We define partial differential (PD in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, PD Poisson…
Using parafermionic field theoretical methods, the fundamentals of 2d fractional supersymmetry ${\bf Q}^{K} =P$ are set up. Known difficulties induced by methods based on the $U_{q}(sl(2))$ quantum group representations and non commutative…