Garth Warner
Professor, Department of Mathematics
University of Washington

E-mail: warner[at]
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.

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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.

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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.

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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.

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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.

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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.

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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.

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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."

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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.

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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.

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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.

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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.

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

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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.

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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.

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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.

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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.

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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)

Seminar Notes:

Quantum Field Theory Seminar:
(School of Wightman et al.)

Download as PDF (2.93MB, 158 pages)

Quantum Field Theory Seminar:
(School of Haag-Kastler et al.)

Download as PDF (5.35MB, 283 pages)

Quantum Gauge Theory Seminar

Download as PDF (2.92MB, 185 pages)

Trace Formula Papers:

The Selberg Trace Formula IX: Contribution from the Conjugacy Classes (The Regular Case):

Download as PDF (1MB, 37 pages)

On the Theory of c-Systems:

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Elementary Aspects of the Theory of Hecke Operators:

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Explicit Formulas from the Continuous Spectrum:

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G, Γ, G/Γ:

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Department of Mathematics University of Washington