Mathematics, Department of
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The Department of Mathematics at the University of Washington is one of the major research mathematics departments in the United States. It has an excellent research reputation, a strong, demanding program of graduate study in mathematics, and a full range of excellent undergraduate course offerings. The department has approximately 60 faculty with research interests in virtually every area of mathematics, from algebra to string theory.
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Affine Partitions and Affine Grassmannians
(2008)We give a bijection between certain colored partitions and the elements in the quotient of an aﬃne Weyl group modulo its Weyl group. By Bott’s formula these colored partitions give rise to some partition identities. In ... 
Fibrations and Sheaves
(20121213)The purpose of this book is to give a systematic treatment of fibration theory and sheaf theory, the emphasis being on the foundational essentials. 
Homotopical Topos Theory
(201205)The purpose of this book is twofold: (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 ... 
Categorical Homotopy Theory
(201201)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 ... 
Reconstruction Theory
(201101)Suppose that G is a compact group. Denote by \underline{Rep} G the category whose objects are the continuous finite dimensional unitary representations of G and whose morphisms are the intertwining operatorsthen ... 
C*Algebras
(20101115)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 ... 
Lectures on Lost Mathematics
(2010) 
Lectures on Arrangements
(1974) 
The Bilinski dodecahedron, and assorted parallelohedra, zonohedra, monohedra, isozonohedra and otherhedra.
(2010)Fifty years ago Stanko Bilinski showed that Fedorov's enumeration of convex polyhedra having congruent rhombi as faces is incomplete, although it had been accepted as valid for the previous 75 years. The dodecahedron he ... 
Positivity
(20091223)These notes provide 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 ... 
Shocks and Business Cycles
(2005)A popular theory of business cycles is that they are driven by animal spirits: shifts in expectations brought on by sunspots. A prominent example is Howitt and McAfee (AER, 1992). We show that this model has a unique ... 
Lagrangian Mechanics
(20090112)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 ... 
{4,5} cubic lattice sponges
(20090106)Isogonal polyhedra are those polyhedra having the property of being vertextransitive. By this is meant that every vertex can be mapped to any other vertex via a symmetry of the whole polyhedron; in a sense, every vertex ... 
Can Every Face of a Polyhedron Have Many Sides?
(200811)The simple question of the title has many different answers, depending on the kinds of faces we are willing to consider, on the types of polyhedra we admit, and on the symmetries we require. Known results and open problems ... 
An enduring error
(20080605) 
Bosonic Quantum Field Theory
(20080331)The purpose of these notes is to provide a systematic account of that part of Quantum Field Theory in which symplectic methods play a major role. 
Topics in Topology and Homotopy Theory
(Hopf Topology Archive, 200501)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. Granted these prerequisites, ... 
Mathematical Aspects of General Relativity
(20060908)These notes can serve as a mathematical supplement to the standard graduate level texts on general relativity and are suitable for selfstudy. The exposition is detailed and includes accounts of several topics of current ...