相关论文: Geometric Complexity Theory: Introduction

This is an expanded version of the notes to a course taught by the first author at the 1995 Les Houches Summer School. Constraints on a tentative reconciliation of quantum theory and general relativity are reviewed. It is explained what…

This paper is based on the first author's lectures at the 2012 University of Regina Workshop "Connections Between Algebra and Geometry". Its aim is to provide an introduction to the theory of higher secant varieties and their applications.…

General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…

These notes are loosely based on an introductory course in algebraic geometry given at Rutgers University in Spring of 2024. We introduce some relatively advanced topics at the expense of the technical details.

This is a philosophical paper. It claims that there is a gap to be filled in the relationship between complexity theory (CT) and quantum theory (QT). This gap concerns two very distinct understandings of time. The paper provides the ground…

This survey paper is divided into two parts. In the first (section 2), I give a brief account of the structure of classical relativity theory. In the second (section 3), I discuss three special topics: (i) the status of the relative…

This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel…

These are lectures presented at the Les Houches Summer School ``Topology and Geometry in Physics'', July 1998. They provide a simple introduction to non perturbative methods of field theory in 1+1 dimensions, and their application to the…

Mostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author. The focus is on derived algebraic geometry, mainly…

These lecture notes provide a basic introduction to the framework of generalized probabilistic theories (GPTs) and a sketch of a reconstruction of quantum theory (QT) from simple operational principles. To build some intuition for how…

We discuss the use of projects in first-year graduate complexity theory courses.

This document contains notes from the graduate lecture course, "Symmetries in QFT" given by J.F.Wheater at Oxford University in Hilary term. The course gives an informal introduction to QFT.

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 paper is an elaboration of an introductory talk given by the author at a workshop on Clifford algebras at Tennessee Technical University, in May 2002. We give an introduction to the basic concepts of Clifford analysis, including links…

These lecture notes are intended for starting PhD students in theoretical physics who have a working knowledge of General Relativity. The 4 topics covered are (1) Surface charges as conserved quantities in theories of gravity; (2) Classical…

Mulmuley and Sohoni (GCT1 in SICOMP 2001, GCT2 in SICOMP 2008) proposed to view the permanent versus determinant problem as a specific orbit closure problem and to attack it by methods from geometric invariant and representation theory. We…

Divided into three parts, the first marks out enormous geometric issues with the notion of quasi-freenss of an algebra and seeks to replace this notion of formal smoothness with an approximation by means of a minimal unital commutative…

This is the preliminary manuscript of a book on symplectic field theory based on a lecture course for PhD students given in 2015-16. It covers the essentials of the analytical theory of punctured pseudoholomorphic curves, taking the…

This is a slightly updated version of lectures notes for a course on analytic geometry taught in the winter term 2019/20 at the University of Bonn. The material presented is part of joint work with Dustin Clausen. This is intended as a…

The goal of this article is to present an introduction to loop quantum gravity -a background independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of…