Related papers: Quantum semigroups: A survey
I briefly review some of the recent progress in quantum field theory in curved spacetime and other aspects of semiclassical gravity, as reported at the D3 Workshop at GR15.
These notes were written as supplementary material for a five-hour lecture series presented at the Centre de Recerca Mathem\`atica at the Universitat Aut\`onoma de Barcelona from the 13th to the 17th of March 2017. The intention of these…
These lectures on supersymmetry and extra dimensions are aimed at finishing undergraduate and beginning postgraduate students with a background in quantum field theory and group theory. Basic knowledge in general relativity might be…
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…
These notes contain part of the lectures of an introductory course on orthogonal polynomials and special functions that I gave in the joint PhD Program in Mathematics UC|UP in the academic years 2015-2016 (at University of Porto) and…
These are informal lecture notes for a three-hour minicourse on Kac-Moody groups, given at the workshop "Kac-Moody geometry" in July 2023 in Kiel. They provide a concise overview of the book "An introduction to Kac-Moody groups over…
Survey article on loop groups and their representations, following a course of three lectures held at the summer school "algebraic groups" at the Georg-August-Universitaet zu Goettingen, June 27--July 13, 2005. We discuss loop groups, their…
Let $S$ be a subsemigroup of a second countable locally compact group $G$, such that $S^{-1}S=G$. We consider the $C^*$-algebra $C^*_\delta(S)$ generated by the operators of translation by all elements of $S$ in $L^2(S)$. We show that this…
This paper gives an overview from the perspective of Lie group theory of some of the recent advances in the rapidly expanding research area of quantum entanglement. This paper is a written version of the last of eight one hour lectures…
The past few years have produced major advances in our understanding of the quantum Hall effects---quantized and unquantized. Theories based on a mathematical transformation, where the electrons are replaced by a set of fermions interacting…
These notes grew out of two lectures I have given on CAT(0) cube complexes. I've tried to keep the material elementary and self-contained in order to keep the material easily accessible and to provide an elementary introduction on the topic…
These are lecture notes for a one semester introductory course I gave at Indiana University. The goal was to make this exposition as clear and elementary as possible. A particular emphasis is given on examples involving SU(1,1). These notes…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
This report presents a practical approach to teaching quantum computing to Electrical Engineering & Computer Science (EECS) students through dedicated hands-on programming labs. The labs cover a diverse range of topics, encompassing…
The purpose of this brief note is that of discussing the meaning of the uncertainty relations involving energy and time in quantum mechanics by means of a reading of the classical works on the subject. This was written for undergraduate…
We explore the difficulties that advanced undergraduate and graduate students have with non-relativistic quantum mechanics of a single particle in one spatial dimension. To investigate these difficulties we developed a conceptual survey and…
The unification of quantum mechanics and general relativity has long been elusive. Only recently have empirical predictions of various possible theories of quantum gravity been put to test, where a clear signal of quantum properties of…
This study targets quantum phases which are characterized by topological properties and no associated with the symmetry breaking. We concern ourselves primarily with the transitions among these quantum phases. This type of quantum phase…
We study C*-algebras associated with subsemigroups of groups. For a large class of such semigroups including positive cones in quasi-lattice ordered groups and left Ore semigroups, we describe the corresponding semigroup C*-algebras as…
This paper collects and extends the lectures I gave at the "XXIV International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain) August 31 - September 4, 2015. Within these lectures I review the formulation of Quantum…