Related papers: The Maslov dequantization, idempotent and tropical…
We describe a mainstream "universalist" approach to the understanding of mathematics. We then conduct a systematic (but not exhaustive) review of the academic literature on the decolonisation of mathematics and identify how this challenges…
This short expository text is for readers who are confident in basic category theory but know little or nothing about toposes. It is based on some impromptu talks given to a small group of category theorists.
The aim of the paper is to provide a rather gentle introduction into Donaldson-Thomas theory using quivers with potential. The reader should be familiar with some basic knowledge in algebraic or complex geometry. The text contains many…
Encyclopedic article covering shallow water wave models used in oceanography and atmospheric science. Sections: Definition of the Subject; Introduction and Historical Perspective; Completely Integrable Shallow Water Wave Equations; Shallow…
In this article we introduce the concept of almost $\mathcal{P}$-numbers. We survey the existing results in literature for almost cyclic numbers and give characterizations for almost abelian and almost nilpotent numbers proving these two…
The article focuses on four aspects related to the descent algebras of type $A$. They are modular idempotents, higher Lie powers, higher Lie modules and the right ideals of the symmetric group algebras generated by the Solomon's descent…
We present a concise but complete conceptual treatment of quantum computing implemented with Cavity Quantum Electrodynamics (CQED. The paper is intended as a brief overview for professionals who are coming over to the field from other areas…
This essay provides a short introduction to the ideas and potential implications of quantum physics for scholars in the arts, humanities, and social sciences. Quantum-inspired ideas pepper current discourse in all of these fields, in ways…
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…
An algebraic investigation on bicomplex numbers is carried out here. Particularly matrices and linear maps defined on them are discussed. A new kind of cartesian product, referred to as an idempotent product, is introduced and studied. The…
This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins. It is intended to be accessible to…
A brief introduction is given to the topic of Smith normal forms of incidence matrices. A general discussion of techniques is illustrated by some classical examples. Some recent advances are described and the limits of our current…
The main aim of this paper is to show the interconnections between {\L}ukasiewicz logic and algebraic geometry using algebraic, geometric and logical instruments. We continue our investigation into a new algebraic geometry based on…
A simple, non-technical introduction to the pre-big bang scenario is given, emphasizing physical motivations, considerations, and consequences over formalism.
This document is an introduction to and review of two-dimensional mathematical physics. The reader is introduced to the subject matter primarily through problems, which are presented along with detailed worked solutions. For each chapter,…
This short article, which appeared in the MSRI Fall 2004 newletter, is intended for a general mathematical audience. It describes some mathematical themes from the Winter 2004 program at MSRI in topological aspects of real algebraic…
Informal collection of lecture notes introducing quantum mechanics in phase space and basic Gaussian quantum mechanics.
This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and…
Quantum Computing promises accelerated simulation of certain classes of problems, in particular in plasma physics. Given the nascent interest in applying quantum computing techniques to study plasma systems, a compendium of the relevant…
The aim of these lecture notes is, after having quickly described various compactifications of the Teichm\"{u}ller space of a compact connected oriented surface minus finitely many points, to give a construction, by the equivariant Gromov…