Related papers: From analytical mechanical problems to rewriting t…
Term rewriting has a significant presence in various areas, not least in automated theorem proving where it is used as a proof technique. Many theorem provers employ specialised proof tactics for rewriting. This results in an interleaving…
In this invited talk, I will review five basic concepts of Axiomatic Rewriting Theory, an axiomatic and diagrammatic theory of rewriting started 25 years ago in a LICS paper with Georges Gonthier and Jean-Jacques L\'evy, and developed along…
A motivation to study Gr\"{o}bner theory for fields with valuations comes from tropical geometry, for example, they can be used to compute tropicalization of varieties \citep{maclagan2009introduction}. The computational aspect of this…
This is the first of two papers on partition functions and the index theory of transversally elliptic operators. In this paper we only discuss algebraic and combinatorial issues related to partition functions. The applications to index…
Motivated by Andrews' recent work related to Euler's partition theorem, we consider the set of partitions of an integer $n$ where the set of even parts has exactly $j$ elements, versus the set of partitions of $n$ where the set of repeated…
Motivated by the fundamental results of the geometric algebra we study quadrilateral lattices in projective spaces over division rings. After giving the noncommutative discrete Darboux equations we discuss differences and similarities with…
In this paper we make an overview of results relating the recent "discoveries" in differential geometry, such as higher structures and differential graded manifolds with some natural problems coming from mechanics. We explain that a lot of…
A fundamental theorem of linear algebra asserts that every basis for the vector space $\mathbb{R}^n$ has $n$ elements. In this expository note we present a theorem of W. G. Leavitt describing one way in which this invariant basis number…
In La G\'eom\'etrie, Descartes proposed a balance between geometric constructions and symbolic manipulation with the introduction of suitable ideal machines. In modern terms, that is a balance between analog and symbolic computation.…
Gr\"obner bases are a fundamental tool when studying ideals in multivariate polynomial rings. More recently there has been a growing interest in transferring techniques from the field case to other coefficient rings, most notably Euclidean…
We establish a natural translation from word rewriting systems to strictly positive polymodal logics. Thereby, the latter can be considered as a generalization of the former. As a corollary we obtain examples of undecidable strictly…
We present a general construction of the derived category of an algebra over an operad and establish its invariance properties. A central role is played by the enveloping operad of an algebra over an operad.
Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…
We generalize signature Gr\"obner bases, previously studied in the free algebra over a field or polynomial rings over a ring, to ideals in the mixed algebra $R[x_1,...,x_k]\langle y_1,\dots,y_n \rangle$ where $R$ is a principal ideal…
This paper presents an expository reverse-mathematical analysis of two fundamental theorems in commutative algebra: Hilbert's Nullstellensatz and Basis Theorem. In addition to its profound significance in commutative algebra and algebraic…
One approach to multivariate operator theory involves concepts and techniques from algebraic and complex geometry and is formulated in terms of Hilbert modules. In these notes we provide an introduction to this approach including many…
This is the second in a series of papers which give an explicit description of the reconstruction algebra as a quiver with relations; these algebras arise naturally as geometric generalizations of preprojective algebras of extended Dynkin…
The paper presents an interesting mathematical feedback between the formalism of coherent states and the field of integrals and integral representations involving special functions. This materializes through an easy and fast method to…
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…
In this note it is demonstrated how the Seiberg-Witten solutions and related integrable systems may arise from certain brane configurations in M-theory. Some subtleties of the formulation of the Seiberg-Witten theory via integrable systems…