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The Ambient Metric (AM-178)

The Ambient Metric (AM-178)

Charles Fefferman and C. Robin Graham

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153131
eISBN:
9781400840588
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153131.001.0001
Subject:
Mathematics, Geometry / Topology

This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient ... More

Arithmetic Compactifications of PEL-Type Shimura Varieties

Arithmetic Compactifications of PEL-Type Shimura Varieties

Kai-Wen Lan

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691156545
eISBN:
9781400846016
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691156545.001.0001
Subject:
Mathematics, Geometry / Topology

By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical ... More

Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

Claire Voisin

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691160504
eISBN:
9781400850532
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691160504.001.0001
Subject:
Mathematics, Geometry / Topology

This book provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. ... More

Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Paula Tretkoff

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691144771
eISBN:
9781400881253
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691144771.001.0001
Subject:
Mathematics, Geometry / Topology

This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. It emphasizes those finite coverings that ... More

The Decomposition of Global Conformal Invariants (AM-182)

The Decomposition of Global Conformal Invariants (AM-182)

Spyros Alexakis

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153476
eISBN:
9781400842728
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153476.001.0001
Subject:
Mathematics, Geometry / Topology

This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question ... More

Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

Isroil A. Ikromov and Detlef Müller

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691170541
eISBN:
9781400881246
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691170541.001.0001
Subject:
Mathematics, Geometry / Topology

This is the first book to present a complete characterization of Stein–Tomas-type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all ... More

Hodge Theory (MN-49)

Hodge Theory (MN-49)

Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dung Tráng

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161341
eISBN:
9781400851478
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161341.001.0001
Subject:
Mathematics, Geometry / Topology

This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics—from leading specialists on the subject. The ... More

Hypoelliptic Laplacian and Orbital Integrals (AM-177)

Hypoelliptic Laplacian and Orbital Integrals (AM-177)

Jean-Michel Bismut

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691151298
eISBN:
9781400840571
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691151298.001.0001
Subject:
Mathematics, Geometry / Topology

This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators ... More

Non-Archimedean Tame Topology and Stably Dominated Types (AM-192)

Non-Archimedean Tame Topology and Stably Dominated Types (AM-192)

Ehud Hrushovski and François Loeser

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691161686
eISBN:
9781400881222
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161686.001.0001
Subject:
Mathematics, Geometry / Topology

Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model ... More

Office Hours with a Geometric Group Theorist

Office Hours with a Geometric Group Theorist

Dan Margalit and Matt Clay (eds)

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691158662
eISBN:
9781400885398
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691158662.001.0001
Subject:
Mathematics, Geometry / Topology

Geometric group theory is the study of the interplay between groups and the spaces they act on, and has its roots in the works of Henri Poincaré, Felix Klein, J.H.C. Whitehead, and Max Dehn. This ... More

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