Homepage of Professor Garth Warner

Garth Warner
Professor, Department of Mathematics
University of Washington

E-mail: warner[at]math.washington.edu

Address:
University of Washington
Department of Mathematics
Box 354350
Seattle, WA 98195-4350

Book Manuscripts Available for Download:

Topics in Topology and Homotopy Theory:
This book is addressed to those readers who have been through Rotman (or its equivalent), possess a wellthumbed copy of Spanier, and have a good background in algebra and general topology.

Download as PDF (43.5MB, 944 pages)

Mathematical Aspects of General Relativity:
This book can serve as a mathematical supplement to the standard graduate level texts on general relativity and is suitable for self-study. The exposition is detailed and includes accounts of several topics of current interest, e.g., Lovelock theory and Ashtekar's variables.

Download as PDF (9.4MB, 1188 pages)

Bosonic Quantum Field Theory:
The purpose of this book is to provide a systematic account of that part of Quantum Field Theory in which symplectic methods play a major role.

Download as PDF (14.1MB, 1007 pages)

Lagrangian Mechanics:
My original set of lectures on Mechanics was divided into three parts: Lagrangian Mechanics, Hamiltonian Mechanics, Equivariant Mechanics. The present text is an order of magnitude expansion of the first part and is differential geometric in character, the arena being the tangent bundle rather than the cotangent bundle. I have covered what I think are the basics. Points of detail are not swept under the rug but I have made an effort not to get bogged down in minutiae. Numerous examples have also been included.

Download as PDF (5.7MB, 440 pages)

Positivity:
This book provides a systematic account of certain aspects of the statistical structure of quantum theory. Here the all prevailing notion is that of a completely positive map and Stinespring's famous characterization thereof. I have also included a systematic treatment of "quantum dynamical semigroups," culminating in Linblad's celebrated description of their generators.

Download as PDF (6.37MB, 396 pages)

C*-Algebras:
This book is addressed to those readers who are already familiar with the elements of the theory but wish to go further. While some aspects, e.g. tensor products, are summarized without proof, others are dealt with in all detail. Numerous examples have been included and I have also appended an extensive list of references.

Download as PDF (7.48MB, 326 pages)

Reconstruction Theory:
Suppose that G is a compact group. Denote by Rep G the category whose objects are the continuous finite dimensional unitary representations of G and whose morphisms are the intertwining operators--then Rep G is a monoidal *-category with certain properties P₁,P₂, ... . Conversely, if C is a monoidal *-category possessing properties P₁,P₂, ..., can one find a compact group G, unique up to isomorphism, such that Rep G "is" C? The central conclusion of reconstruction theory is that the answer is affirmative.

Download as PDF (2.89MB, 159 pages)

Categorical Homotopy Theory:
This book is an account of certain developments in categorical homotopy theory that have taken place since the year 2000. Some aspects have been given the complete treatment (i.e., proofs in all detail), while others are merely surveyed. Therefore a lot of ground is covered in a relatively compact manner, thus giving the reader a feel for the "big picture" without getting bogged down in the "nitty-gritty."

Download as PDF (12.2MB, 537 pages)

Homotopical Topos Theory:
The purpose of this book is two-fold: (1) To give a systematic introduction to topos theory from a purely categorical point of view, thus ignoring all logical and algebraic issues. (2) To give an account of the homotopy theory of the simplicial objects in a Grothendieck topos.

Download as PDF (4.69MB, 213 pages)

Fibrations and Sheaves:
The purpose of this book is to give a systematic treatment of fibration theory and sheaf theory, the emphasis being on the foundational essentials.

Download as PDF (4.20MB, 216 pages)

Zeros:
The purpose of this book is two-fold: (1) To give a systematic account of classical "zero theory" as developed by Jensen, Pólya, Titchmarsh, Cartwright, Levinson and others. (2) To set forth developments of a more recent nature with a view toward their possible application to the Riemann Hypothesis.

Download as PDF (8.60 MB, 556 pages)

Abelian Theory:
These notes begin with a discussion of group schemes in general and the case of algebraic tori in particular. This done, we set up the "local Langlands correspondence" in the abelian setting and conclude with an introduction to Tamagawa measures.

Download as PDF (1.65 MB, 74 pages)

Sets and Classes: Operational Theory:
The purpose of this book is to lay out certain aspects of descriptive set theory.

Download as PDF (3.54 MB, 168 pages)

Local and Global Analysis:
The objective of this book is to give an introduction to p-adic analysis along the lines of Tate's thesis, as well as incorporating material of a more recent vintage, for example Weil groups.

Download as PDF (4.58 MB, 219 pages)

The Exponential World:
These notes are a systematic introduction to transcendental number theory, starting at the beginning and ending with Schanuel’s conjecture and some of its consequences, e.g., Schanuel implies Shapiro.

Download as PDF (9.74 MB, 575 pages)

Periods and Real Numbers:
The purpose of this book is to provide an introduction to period theory and then to place it within the matrix of recursive function theory.

Download as PDF (1.84 MB, 91 pages)

Functions of a Single Variable:
These notes are a chapter in Real Analysis. While primarily standard, the reader will find a discussion of certain topics that are ordinarily not covered in the standard accounts.

Download as PDF (2.39 MB, 113 pages)

Curves and Length:
In addition to providing a systematic account of the classical theorems of Jordan and Tonelli, I have also provided an introduction to the theory of the Weierstrass integral which in its definitive form is due to Cesari.

Download as PDF (1.37 MB, 72 pages)

Functions of Several Variables:
Apart from an account of classical preliminaries, these notes contain a systematic introduction to Sobolev spaces and functions of bounded variation, along with selected applications.

Download as PDF (4.93 MB, 220 pages)

Surfaces and Area:
Here one will find a rigorous treatment of the simplest situation in Surface Area Theory, viz. the nonparametric case with domain the unit square in the plane.

Download as PDF (1.3 MB, 64 pages)