相关论文: Notes on Free Probability Theory

Free entropy is the analogue of entropy in free probability theory. The paper is a survey of free entropy, its applications to von Neumann algebras, connections to random matrix theory and a discussion of open problems.

These are lecture notes for a 4h mini-course held in Toulouse, May 9-12th, at the thematic school on "Quantum topology and geometry". The goal of these lectures is to (a) explain some incarnations, in the last ten years, of the idea of…

Lecture given Thursday 22 October 1992 at a Mathematics-Computer Science Colloquium at the University of New Mexico. The lecture was videotaped; this is an edited transcript.

These notes represent a much expanded and updated version of the \textquotedblleft mini course\textquotedblright that the author gave at the ETH (Z\"{u}rich) and the University of Z\"{u}rich in February of 1995. The purpose of these notes…

Notes from 11 October 2004 lecture presented at the Joint Institute for Nuclear Astrophysics R-Matrix School at Notre Dame University.

This text is an introduction to a few selected areas of Alain Connes' noncommutative geometry written for the volume of the school/conference "Noncommutative Geometry 2005" held at IPM Tehran. It is an expanded version of my lectures which…

These are lecture notes of a course on Calogero-Moser systems and their connections with representation theory and geometry, given by the author in Zurich in May-June 2005.

Various connections between the theory of permutation groups and the theory of topological groups are described. These connections are applied in permutation group theory and in the structure theory of topological groups. The first draft of…

The present overview and gentle introduction to Grassmannian calculus and some of its applications to probability collects the notes of a mini-course given by the authors at the Brazilian School of Probability, August 5-9, 2024, in…

This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incomplete, but due to recent requests from…

This is a slightly edited version of the transparencies for a seminar at UCL, May 7, 2003. It is intended to give a quick view of background, ideas, and some calculations, in the applicatioon of some non commutative methods to algebraic…

Brief lecture notes for a course about random matrices given at the University of Cambridge.

These lecture notes are an expanded write-up of my short lecture series "Noncommutative Resolutions" given to the MSRI Graduate Student Workshop "Noncommutative Algebraic Geometry" during June 2012. The notes include five chapters, an…

Two lectures given at the UK-Japan Winter School on 'Geometry and Analysis Towards Quantum Theory', Durham, January 2004.

This is the introduction and bibliography for lecture notes of a course given at the Summer School on Noncommutative Geometry and Applications, sponsored by the European Mathematical Society, at Monsaraz and Lisboa, Portugal, September…

These are the notes from Asger T\"ornquist's Appalachian Set Theory lectures at Carnegie Mellon University. They form a chapter in the LMS lecture notes series 406.

We characterize semicircular distribution by the freeness of linear and quadratic forms in noncommutative random variables from a tracial $W^*$-probability space with relaxed moment conditions.

This is a redacted transcript of a course given by the author at Harvard in spring semester 2016. It contains a pedagogical overview of recent developments connecting the subjects of soft theorems, the memory effect and asymptotic…

This is the text of the lecture given by the author in Naples at "Giornata IndAM", June 7, 2005. The lecture is addressed at the general mathematical audience and reviews several topics in deformation theory of associative algebras.

This article is an elaboration of a talk given at an international conference on Operator Theory, Quantum Probability, and Noncommutative Geometry held during December~20--23, 2004, at the Indian Statistical Institute, Kolkata. The lecture…