Related papers: Quantum Spaces: Notes and Comments on a Lecture by…
In this note we improve the parameter $q$ that appears in Theorem 1 obtained by the author in [Math. Ineq. \& appl., Vol 19 (3) (2016), 1013-1030].
A class of quantum analogues of compact symmetric spaces of classical type is introduced by means of constant solutions to the reflection equations. Their zonal spherical functions are discussed in connection with $q$-orthogonal…
This report is based on the talk given by the author in the concluding session of the workshop on Canonical Methods in Classical and Quantum General Relativity, held a Bad-Honef, Germany, in September 93. It contains an assessment of the…
We prove that the algebra of observables of a certain gauge model is generated by unbounded elements in the sense of Woronowicz. The generators are constructed from the classical generators of invariant polynomials by means of geometric…
A new characterization of conformal transformations is given. By use of this, the general form of conformal transformation on two-dimensional Minkowski space is given and its conformal structure is analyzed.
These are the lecture notes of a "Nachdiplomvorlesung" course taught at ETH Zurich in the Spring of 2013. They appeared in the EMS series Zurich Lectures in Advanced Mathematics.
In these lectures we discuss some elementary concepts in connection with the theory of symmetric spaces applied to ensembles of random matrices. We review how the relationship between random matrix theory and symmetric spaces can be used in…
The concept of a "space of quantum field theories" or "theory space" was set out in the 1970's in work of Wilson, Friedan and others. This structure should play an important role in organizing and classifying QFTs, and in the study of the…
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…
This is a written version of the review talk given at the meeting on "Interface of Gravitational and Quantum Realms" at IUCAA, Pune during December 2001. The talk reviewed the recent work of Martin Bojowald on Loop Quantum Cosmology.
This paper is an extended version of a series of lectures on polar spaces given during the workshop and conference 'Groups and Geometries', held at the Indian Statistical Institute in Bangalore in December 2012. The aim of this paper is to…
By popular request we post these old (from 2001) lecture notes of the Varenna Summer School Proceedings. The original was published as J. I. Cirac, L. M. Duan, and P. Zoller, in "Experimental Quantum Computation and Information" Proceedings…
This is the written version of a talk given in memory of Gunnar K\"{a}ll\'{e}n, at the Departments of Theoretical Physics, Physics, and Astronomy of Lund University on February 13, 2009. It will be published in a collection of the papers of…
These are author's recollections of informal discussions on foundations of quantum mechanics, which happened in his presence in 1970-80s
The purpose of this article is to introduce and motivate the notion of Minkowski (or box) dimension for measures. The definition is simple and fills a gap in the existing literature on the dimension theory of measures. As the terminology…
We review various combinatorial problems with underlying classical or quantum integrable structures. (Plenary talk given at the International Congress of Mathematical Physics, Aalborg, Denmark, August 10, 2012.)
This text contains lecture notes of the course taught to Ph.D. students of Jagiellonian University in Krakow on 25-28 November, 2013.
This is an extended abstract of my talk at the Oberwolfach-Workshop "Representation Theory of Finite-Dimensional Algebras" (February 6 - 12, 2005). It gives self-contained and simplified definitions of quantum cluster algebras introduced…
In joint work with Adam Black and Reuben Drogin, we develop a new approach to understanding the diffusive limit of the random Schrodinger equation based on ideas taken from random matrix theory. These lecture notes present the main ideas…
This course of lectures has been taught for several years at the Lomonosov Moscow State University; its modified version in 2021 is read in the Zhejiang University (Hangzhou), in the framework of summer school on quantum computing. The…