Related papers: Ken Kunen: Algebraist
We argue that computation is an abstract algebraic concept, and a computer is a result of a morphism (a structure preserving map) from a finite universal semigroup.
In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.
This is an expository article discussing some of the work of Uhlenbeck, focusing mainly on work concerning harmonic maps and Yang-Mills fields.
Work in progress concerning alternative formalizations of arithmetic.
We study Kleene iteration in the categorical context. A celebrated completeness result by Kozen introduced Kleene algebra (with tests) as a ubiquitous tool for lightweight reasoning about program equivalence, and yet, numerous variants of…
We give a brief introduction to (upper) cluster algebras and their quantization using examples. Then we present several important families of bases for these algebras using topological models. We also discuss tropical properties of these…
In the literature on Kleene algebra (KA), a number of variants have been proposed such as Kleene algebra with tests, commutative KA, bi-KA, and concurrent KA. The equational theories of some of these structures have then been studied in the…
This article is an expanded version of my talk at the Gathering for Gardner, 2012.
The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…
We study a physically motivated representation of an algebra of operators in gravitational and non gravitational theories called the covariant representation of an algebra. This is a representation where the symmetries of the operator…
Algebraic effects and handlers are a powerful abstraction to build non-local control-flow mechanisms such as resumable exceptions, lightweight threads, co-routines, generators, and asynchronous I/O. All of such features have very evolved…
An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut
This paper develops techniques for producing presentations of upper cluster algebras. These techniques are suited to computer implementation, and will always succeed when the upper cluster algebra is totally coprime and finitely generated.…
This chapter surveys the advances of the past decade arising from the contributions of Indian mathematicians in the broad areas of operator algebras and operator theory. It brings together the work of twenty mathematicians and their…
A personal and informal account of what a pure mathematician might expect when using tools from deep learning in their research.
We describe an algebra for composing automata which includes both classical and quantum entities and their communications. We illustrate by describing in detail a quantum protocol.
In this contribution to the proceedings of the 68eme Rencontre entre Physiciens Theoriciens et Mathematiciens on Deformation Quantization I shall report on some recent joint work with Henrique Bursztyn on the representation theory of…
Kleene Algebra with Tests (KAT) provides an elegant algebraic framework for describing non-deterministic finite-state computations. Using a small finite set of non-deterministic programming constructs (sequencing, non-deterministic choice,…
This is a brief introduction to the quiver Hecke algebras of Khovanov, Lauda and Rouquier, emphasizing their application to the categorification of quantum groups. The text is based on lectures given by the author at the ICRA workshop in…