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Geometric and Topological Methods for Quantum Field Theory
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Geometric and Topological Methods for Quantum Field TheoryGeometric and Topological Methods for Quantum Field Theory

Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics at the interface between algebra, geometry, topology and quantum field theory. The first part of the book begins with an account of important results in geometric topology.
 
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Tags: topology, begins, account, first, theory, Geometric, Field, Theory, Topological
Fourier Analysis on Number Fields
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Fourier Analysis on Number FieldsFourier Analysis on Number Fields

The general aim of this book is to provide a modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasizing harmonic analysis on topological groups. The more particular goal is to cover John Tate's visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries--technical prerequisites that are often foreign to the typical, more algebraically inclined number theorist.
 
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Tags: number, analytic, thesis, topological, While, Fourier, Analysis
Topological Strings and Quantum Curves
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Topological Strings and Quantum CurvesTopological Strings and Quantum Curves

This thesis presents several new insights on the interface between mathematics and theoretical physics, with a central role for Riemann surfaces. First of all, the duality between Vafa-Witten theory and WZW models is embedded in string theory. Secondly, this model is generalized to a web of dualities connecting topological string theory and N=2 supersymmetric gauge theories to a configuration of D-branes that intersect over a Riemann surface.
 
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Tags: theory, string, between, Riemann, topological, Topological