Related papers: Five not-so-easy pieces:open problems about vertex…
The rings whose simple right modules are absolutely pure are called right $SAP$-rings. We give a new characterization of right $SAP$ rings, right $V$ rings, and von Neumann regular rings. We also obtain a new decomposition theory of right…
I review three different problems occuring in two dimensional field theory: 1) classification of conformal field theories; 2) construction of lattice integrable realizations of the latter; 3) solutions to the WDVV equations of topological…
New splitting theorems in a semi-Riemannian manifold which admits an irrotational vector field (not necessarily a gradient) with some suitable properties are obtained. According to the extras hypothesis assumed on the vector field, we can…
This is a non-standard paper, containing some problems, mainly in model theory, which I have, in various degrees, been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me,…
We review the open problems in the theory of deformations of zero-dimensional objects, such as algebras, modules or tensors. We list both the well-known ones and some new ones that emerge from applications. In view of many advances in…
We consider the $N$-vortex problem on the sphere assuming that all vorticities have equal strength. We investigate relative equilibria (RE) consisting of $n$ latitudinal rings which are uniformly rotating about the vertical axis with…
We consider two problems associated to the space of Riemann surfaces that are closely related to string theory. We first consider the problem of existence of heterotic-string and type-II-superstring field theory vertices in the product of…
In this paper, a theory of quandle rings is proposed for quandles analogous to the classical theory of group rings for groups, and interconnections between quandles and associated quandle rings are explored.
Deformation theory of complex manifolds is a classical subject with recent new advances in the noncompact case using both algebraic and analytic methods. In this note, we recall some concepts of the existing theory and introduce new notions…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
In this paper I present some open problems on Coxeter groups and unimodality, together with the main partial results, and computational evidence, that are known about them.
Unlike classical modular forms, there is currently no general way to implement the computation of Siegel modular forms of arbitrary weight, level and character, even in degree two. There is however, a way to do it in a unified way. After…
This paper investigates the relationship between multiplicities and the degree sequence of ideals in graded algebras, gives multiplicity equations of graded rings via the degree sequence of ideals, and characterizes mixed multiplicities and…
Twisted modules over vertex algebras formalize the relations among twisted vertex operators and have applications to conformal field theory and representation theory. A recent generalization, called twisted logarithmic module, involves the…
We describe recent work on the arithmetic properties of moduli spaces of stable vector bundles and stable parabolic bundles on a curve over a global field. In particular, we describe a connection between the period-index problem for Brauer…
We study the interplay between the notions of $n$-coherent rings and finitely $n$-presented modules, and also study the relative homological algebra associated to them. We show that the $n$-coherency of a ring is equivalent to the thickness…
Two observations in support of the thesis that trusses are inherent in ring theory are made. First, it is shown that every equivalence class of a congruence relation on a ring or, equivalently, any element of the quotient of a ring $R$ by…
We propose a list of open problems in pluripotential theory partially motivated by their applications to complex differential geometry. The list includes both local questions as well as issues related to the compact complex manifold…
We describe a method that allows, under some hypotheses, to compute all the rational points of some genus 5 curves defined over a number field. This method is used to solve some arithmetic problems that remained open.
An essay on Model Theory: Why am I interested in model theory? What are, in my opinion, the most challenging problems in model theory?