Related papers: Quantum Spaces: Notes and Comments on a Lecture by…
This paper gives a representation of the most general positive operator valued measure in Minkowski space-time, covariant with respect to the Poincare' group. It provides the correct mathematical description of the space-time coordinates of…
This is a revised version of a tutorial lecture that I presented at the \`Ecole de Physique des Houches on July 26-31 2020. Topics include Non-parametric Information Geometry, the Statistical bundle, exponential Orlicz spaces, and Gaussian…
The present notes are based on a course on Cherednik algebras given by the first author at MIT in the Fall of 2009. Their goal is to give an introduction to Cherednik algebras, and to review the web of connections between them and other…
This brief set of notes presents a modest introduction to the basic features entering the construction of supersymmetric quantum field theories in four-dimensional Minkowski spacetime, building a bridge from similar lectures presented at a…
The Leuven workshop on the `Quantum Structure of Space-time and the Geometrical Nature of the Fundamental Interactions' had a special session dedicated to the memory of Sonia Stanciu. This is the summary of a talk delivered by the author on…
Lecture notes on selected topics in the theory of gravitation.
This is an introduction to Quantum Integrability and Quantum Groups, a special issue collection of articles published in Journal of Physics A in memory of Petr P. Kulish. A list of Kulish's publications is included.
These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.
Lecture notes for an introductory course in elementary particles.
Notes of five lectures given at the 2003 European School of High-Energy Physics, Tsakhkadzor, Armenia, September 2003
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…
These are lecture notes that are based on the lectures from a class I taught on the topic of Randomized Linear Algebra (RLA) at UC Berkeley during the Fall 2013 semester.
The well known ideal presentations of countably based domains were recently extended to (effective) quasi-Polish spaces. Continuing these investigations, we explore some classes of effective quasi-Polish spaces. In particular, we prove an…
Differential calculi are obtained for quantum homogeneous spaces by extending Woronowicz' approach to the present context. Representation theoretical properties of the differential calculi are investigated. Connections on quantum…
These are some basic notes concerning Holder and Lipschitz classes on metric spaces.
We give a short introduction to the theory of modular metric spaces. This is a corrected version of the paper [1], which had some errors. We are grateful to V. V. Chistyakov for bringing these to our attention.
The lecture notes contain three parts. The first part is Grover's Search Algorithm with modifications, generalizations, and applications. The second part is a discussion on the quantum fingerprinting technique. The third part is Quantum…
Introductory lectures notes on cosmology, aimed at master students in physics and based on a course held at Milano University (in Italian).
We discuss critical remarks raised by Horodecki towards our work on the connection between superluminal extension of special relativity and fundamental aspects of quantum theory.
We introduce the concept of quotient in PN spaces and give some examples. We prove some theorems with regard to the completeness of a quotient.