Related papers: Quantum semigroups: A survey
These are lecture notes of a mini-course given by the first author in Moscow in July 2019, taken by the second author and then edited and expanded by the first author. They were also a basis of the lectures given by the first author at the…
These are partial lecture notes from the fifteen Ess\'en Lectures for graduate students at Uppsala University given (in four days!) in June 2013.
These are notes for lectures delivered at the NATO ASI on Dynamics in Leiden, The Netherlands, in July 1998. The main concepts relating to quantum phase transitions are explained, using the paramagnet-to-ferromagnet transition of itinerant…
I hesitated for a long time before giving shape to these notes, originally intended for preliminary reading by the attendees to the Summer School "New paths towards quantum gravity" (Holbaek Bay, Denmark, May 2008). At the end, I decide…
This is a write-up of the discussions during the meetings of the study group on representation theory of semirings which was organized at the Department of Mathematics, Uppsala University, during the academic year 2017-2018. The main…
These notes are based on a lecture course by L. Chekhov held at the University of Manchester in May 2006 and February-March 2007. They are divulgative in character, and instead of containing rigorous mathematical proofs, they illustrate…
These lecture notes were created for a graduate-level course on quantum simulation taught at Leibniz University Hannover in 2013. The first part of the course discusses various state of the art methods for the numerical description of…
This survey paper, written in spanish, is an extended version of lecture notes for a mini-course taught at the 2022 Summer School in Geometric Group Theory, which took place in the Centro de Ciencias Matem\'aticas in Morelia, Mexico in July…
These are the lecture notes of the master's course "Quantum Computing", taught at Chalmers University of Technology every fall since 2020, with participation of students from RWTH Aachen and Delft University of Technology. The aim of this…
The first ``Convegno Informale su Quantum Groups'' was held in Florence from February 3 to 6, 1993. This Convegno was conceived as an informal meeting to bring together all the italian people working in the field of quantum groups and…
We give an overview of some recent developments in semigroup C*-algebras.
This document presents the contents of three lectures delivered by the author at the Erd\H{o}s Center School ``Optimal Transport on Quantum Structures'', Septemer 19-23, 2022 in Budapest, Hungary. It presents a fairly self contained account…
This is a short survey paper, partly meant as a research announcement. Its purpose is to highlight some aspects of the interplay between quantales, inverse semigroups, and groupoids. Many of the results mentioned have not yet been presented…
We give a survey of techniques from quantum group theory which can be used to show that some quantum spaces (objects of the category dual to the category of $\mathrm{C}^*$-algebras) do not admit any quantum group structure. We also provide…
This is the extended version of a talk presented at the J.W.Goethe Universitaet Frankfurt a. M. and at the same time a preview at a forthcoming extensive publication on the same subject. It is shown that there is a common background…
These are notes accompanying lectures at 7th ILJU School of Mathematics "Banach Spaces and Related Topics" in Gyeongju, Koera. The lectures are devoted to exposition of the theory of quantum families of maps with emphasis on the study of…
The purpose of this text is to set up a few basic notions concerning quantum graphs, to indicate some areas addressed in the quantum graph research, and to provide some pointers to the literature. The pointers in many cases are secondary,…
This is a set of lecture notes used in a graduate topic class in applied mathematics called ``Quantum Algorithms for Scientific Computation'' at the Department of Mathematics, UC Berkeley during the fall semester of 2021. These lecture…
An introduction to quantum groups and non-commutative differential calculus (Lecture at the III Workshop on Differential Geometry, Granada, September 1994)
In this article we survey some of the recent goings-on in the classification programme of C$^*$-algebras, following the interesting link found between the Cuntz semigroup and the classical Elliott invariant and the fact that the Elliott…