## 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

*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)

*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)

*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)

*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)

*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)

*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)

*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)

*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

## A Primer on Mapping Class Groups (PMS-49)

*Benson Farb and Dan Margalit*

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691147949
- eISBN:
- 9781400839049
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691147949.001.0001
- Subject:
- Mathematics, Geometry / Topology

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many ... More