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Faltings Heights and L-functions: Minicourse Given by Shou-Wu Zhang

Ziyang Gao, Rafael von Känel, and Lucia Mocz

in Arithmetic and Geometry: Ten Years in Alpbach (AMS-202)

Published in print:
2019
Published Online:
May 2020
ISBN:
9780691193779
eISBN:
9780691197548
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691193779.003.0004
Subject:
Mathematics, Geometry / Topology

This chapter explores Shou-Wu Zhang's minicourse on Faltings heights and L-functions. It essentially consists of three parts. The first part discusses conjectures and results in the literature which ... More


Open Quantum Electrodynamics

Heinz-Peter Breuer and Francesco Petruccione

in The Theory of Open Quantum Systems

Published in print:
2007
Published Online:
February 2010
ISBN:
9780199213900
eISBN:
9780191706349
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213900.003.12
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In quantum electrodynamics, the matter degrees of freedom are coupled to the radiation field through a local, gauge-invariant interaction density. Due to the linear structure of this coupling, the ... More


Introduction

Dennis Gaitsgory and Jacob Lurie

in Weil's Conjecture for Function Fields: Volume I (AMS-199)

Published in print:
2019
Published Online:
September 2019
ISBN:
9780691182148
eISBN:
9780691184432
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691182148.003.0001
Subject:
Mathematics, Mathematical Finance

This introductory chapter sets out the book's purpose, which is to study Weil's conjecture over function fields: that is, fields K which arise as rational functions on an algebraic curve X over a ... More


Random matrices and number theory: some recent themes

Jon P. Keating

in Stochastic Processes and Random Matrices: Lecture Notes of the Les Houches Summer School: Volume 104, July 2015

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198797319
eISBN:
9780191838774
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198797319.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The aim of this chapter is to motivate and describe some recent developments concerning the applications of random matrix theory to problems in number theory. The first section provides a brief and ... More


Interacting Electron–Hole–Phonon System

Norman J. Morgenstern Horing

in Quantum Statistical Field Theory: An Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198791942
eISBN:
9780191834165
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198791942.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 11 employs variational differential techniques and the Schwinger Action Principle to derive coupled-field Green’s function equations for a multi-component system, modeled as an interacting ... More


Graphene

Norman J. Morgenstern Horing

in Quantum Statistical Field Theory: An Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198791942
eISBN:
9780191834165
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198791942.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 12 introduces Graphene, which is a two-dimensional “Dirac-like” material in the sense that its energy spectrum resembles that of a relativistic electron/positron (hole) described by the Dirac ... More


Introduction

Peter Scholze and Jared Weinstein

in Berkeley Lectures on p-adic Geometry

Published in print:
2020
Published Online:
January 2021
ISBN:
9780691202082
eISBN:
9780691202150
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202082.003.0001
Subject:
Mathematics, Geometry / Topology

This introductory chapter provides an overview of Drinfeld's work on the global Langlands correspondence over function fields. Whereas the global Langlands correspondence is largely open in the case ... More


The Formalism of l-adic Sheaves

Dennis Gaitsgory and Jacob Lurie

in Weil's Conjecture for Function Fields: Volume I (AMS-199)

Published in print:
2019
Published Online:
September 2019
ISBN:
9780691182148
eISBN:
9780691184432
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691182148.003.0002
Subject:
Mathematics, Mathematical Finance

The ℓ-adic product formula discussed in Chapter 4 will need to make use of analogous structures, which are simply not visible at the level of the triangulated category Dℓ(X). This chapter attempts to ... More


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