相关论文: Calcul Moulien
In this paper, we give precise mathematical form to the idea of a structure whose data and axioms are faithfully represented by a graphical calculus; some prominent examples are operads, polycategories, properads, and PROPs. Building on the…
This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…
For matrix analogues of embedded surfaces we define discrete curvatures and Euler characteristics, and a non-commutative Gauss--Bonnet theorem is shown to follow. We derive simple expressions for the discrete Gauss curvature in terms of…
This article is devoted to rational equivalence for non-commutative polynomial algebras in a context including both the classical Gelfand-Kirillov problem and its quantum version. We introduce in this ``mixed'' context some reference…
The Gauss-Bonnet theorem for a polyhedron (a union of finitely many compact convex polytopes) in $n$-dimensional Euclidean space expresses the Euler characteristic of the polyhedron as a sum of certain curvatures, which are different from…
Many different types of fractional calculus have been defined, which may be categorised into broad classes according to their properties and behaviours. Two types that have been much studied in the literature are the Hadamard-type…
A quandle is an algebraic system whose axioms generalize the algebraic structure of the point symmetries of symmetric spaces. In this paper, we give a definition of Euler characteristics for quandles. In particular, the quandle Euler…
We derive analytic solutions for the potential and field in a one-dimensional system of masses or charges with periodic boundary conditions, in other words Ewald sums for one dimension. We also provide a set of tools for exploring the…
This contribution is the first in a series of three: it reports on the construction of (a fine sheaf of) diffeomorphism invariant Colombeau algebras on open sets of Eucildean space, which completes earlier approaches. Part II and III will…
This is the first paper in a series (of four) designed to show how to use geometric algebras of multivectors and extensors to a novel presentation of some topics of differential geometry which are important for a deeper understanding of…
We present an extension of the methods of classical Lie group analysis of differential equations to equations involving generalized functions (in particular: distributions). A suitable framework for such a generalization is provided by…
The link between modular functions and algebraic functions was a driving force behind the 19th century study of both. Examples include the solutions by Hermite and Klein of the quintic via elliptic modular functions and the general sextic…
Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…
In this expository article, we present a brief introduction to the theory of Hilbert modular forms and Galois representations, and describe what it means to attach a compatible system of Galois representations to a Hilbert modular form.
Polyfold theory was developed by Hofer-Wysocki-Zehnder by finding commonalities in the analytic framework for a variety of geometric elliptic PDEs, in particular moduli spaces of pseudoholomorphic curves. It aims to systematically address…
We discuss various aspects concerning transformations of local analytic, or formal, vector fields to Poincare-Dulac normal form, and the convergence of such transformations. We first review A.D. Bruno's approach to formal normalization, as…
We study polymorphic type assignment systems for untyped lambda-calculi with effects, based on Moggi's monadic approach. Moving from the abstract definition of monads, we introduce a version of the call-by-value computational…
It is a classical result in matrix algebra that any square matrix over a field can be conjugated to its transpose by a symmetric matrix. For $F$ a non-Archimedean local field, Tupan used this to give an elementary proof that transpose…
We give arithmetical proofs of the strong normalization of two symmetric $\lambda$-calculi corresponding to classical logic. The first one is the $\bar{\lambda}\mu\tilde{\mu}$-calculus introduced by Curien & Herbelin. It is derived via the…
We write out some sequences of linear maps of vector spaces with fixed bases. Each term of a sequence is a linear space of differentials of metric values ascribed to the elements of a simplicial complex - a triangulation of a manifold. If…