Related papers: In the beginning: Langlands' doctoral thesis
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
PhD thesis (University of York). The thesis covers in a unified way the material presented in quant-ph/0403073, quant-ph/0502040, quant-ph/0504160, quant-ph/0510035, quant-ph/0512012 and quant-ph/0603283. It includes two large review…
This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…
The aim of these notes is to give an overview of several aspects of what has come to be called the relative Langlands program, a theme that takes its origin in the study of automorphic periods and their relations to particular cases of…
This is an appendix to the Handbook of Tilting Theory, edited by Angeleri-Huegel, Happel and Krause, to be published soon. Part 1 of the appendix provides an outline of the core of tilting theory. Part 2 is devoted to topics where tilting…
The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups. The trace formula is a powerful tool in the study of this connection and the Langlands Functoriality Conjecture. After…
This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.
These are expended notes of my talk at the summer institute in algebraic geometry (Seattle, July-August 2005), whose main purpose is to present a global overview on the theory of higher and derived stacks. This text is far from being…
This is is a copy of dissertation that I have submitted in defense of my ph.d. thesis, with some minor changes that I have made since then. The goal of the project is to generalize matter fields and their Lagrangians from regular space time…
An outline of recent work on complex networks is given from the point of view of a physicist. Motivation, achievements and goals are discussed with some of the typical applications from a wide range of academic fields. An introduction to…
The paper is withdrawn by the author. This was an embryon of the book which has now been published with World Scientific under the title "Lectures on Quantum Chromodynamics". See http://www.wspc.com.sg/books/physics/4443.html, where the…
This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability…
This book is the final version of a course on algorithmic information theory and the epistemology of mathematics and physics. This is camera-ready copy prepared for publication as a book, but at the last minute I decided to publish it…
Brief lecture notes for a course about random matrices given at the University of Cambridge.
Just a survey on I0: The basics, some things known but never published, some things published but not known.
Since the subject of noncommutative geometry is now entering maturity, we felt there is need for presentation of the material at an undergraduate course level. Our review is a zero order approximation to this project. Thus, the present…
These are the notes for the lecture given by the author at the "Current Events" Special Session of the AMS meeting in Baltimore on January 17, 2003. Topics reviewed include the Langlands correspondence for GL(n) in the function field case…
This paper has been withdrawn by the author; a revised version is part of the author's phd-thesis "Quasi-logarithmic structures" (Zurich, 2007).
In this preprint we present an outline of the multidimensional version of topological Galois theory. The theory studies topological obstruction to solvability of equations "in finite terms" (i.e. to their solvability by radicals, by…
I developed the lecture notes based on my ``Linear Model'' course at the University of California, Berkeley over the past ten years. This book provides an intermediate-level introduction to the linear model. It balances rigorous proofs and…