Related papers: Varieties
Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…
Diversities are a generalization of metric spaces, where instead of the non-negative function being defined on pairs of points, it is defined on arbitrary finite sets of points. Diversities have a well-developed theory. This includes the…
Choices in the semantics and the signature of a theory are integral in determining how the theory is used and how challenging it is to reason over it. Our interest in this paper lies in the SMT theory of sequences. Various versions of it…
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…
Taking an algebraic perspective on the basic structures of Rough Concept Analysis as the starting point, in this paper we introduce some varieties of lattices expanded with normal modal operators which can be regarded as the natural rough…
The point of view of these notes on the topic is to bring out the flavour that Representation Theory is an extension of the first course on Group Theory. We also emphasize the importance of the base field. These notes cover completely the…
ICM lecture on minimal models and moduli of varieties.
This is an introduction to linear algebra and group theory. We first review the linear algebra basics, namely the determinant, the diagonalization procedure and more, and with the determinant being constructed as it should, as a signed…
This paper is based on the first author's lectures at the 2012 University of Regina Workshop "Connections Between Algebra and Geometry". Its aim is to provide an introduction to the theory of higher secant varieties and their applications.…
Variational and divergence symmetries are studied in this paper for the whole class of linear and nonlinear equations of maximal symmetry, and the associated first integrals are given in explicit form. All the main results obtained are…
Given an algebra $A$ over a differential field $K$, we study derivations on $A$ that are compatible with the derivation on $K$. There is a universal object, which is a twisted version of the usual module of differentials, and we establish…
We show that for a large class of varieties of algebras, the equational theory of the congruence lattices of the members is not finitely based.
This paper treats the variation of sets. We attempt to formulate convergence and continuity of set-valued functions in a different way from the theories on sequences of sets and correspondence. In the final section, we also attempt to…
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…
The generality of a derivation is an equivalence relation on the set of occurrences of variables in its premises and conclusion such that two occurrences of the same variable are in this relation iff they must remain occurrences of the same…
We develop the usage of certain type theories as specification languages for algebraic theories and inductive types. We observe that the expressive power of dependent type theories proves useful in the specification of more complicated…
These lecture notes are intended to give a modest impulse to anyone willing to start or pursue a journey into the theory of Vertex Algebras by reading one of Kac's or Lepowsky-Li's books. Therefore, the primary goal is to provide required…
In this course we introduce the main notions relative to the classical theory of modular forms. A complete treatise in a similar style can be found in the author's book joint with F. Str{\"o}mberg [1].
Questions of set-theoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made…
The notion of a difference hierarchy, first introduced by Hausdorff, plays an important role in many areas of mathematics, logic and theoretical computer science such as descriptive set theory, complexity theory, and the theory of regular…