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## K-Contact and Sasakian Structures

*Charles P. Boyer and Krzysztof Galicki*

### in Sasakian Geometry

- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198564959
- eISBN:
- 9780191713712
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198564959.003.0008
- Subject:
- Mathematics, Geometry / Topology

This chapter begins the study of Sasakian geometry, where all important structure theorems are presented. It then gathers all the results concerning the geometry, topology, and curvature properties ... More

## Algebraic Surfaces and the Miyaoka-Yau Inequality

*Paula Tretkoff*

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

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691144771
- eISBN:
- 9781400881253
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144771.003.0005
- Subject:
- Mathematics, Geometry / Topology

This chapter discusses complex algebraic surfaces, with particular emphasis on the Miyaoka-Yau inequality and the rough classification of surfaces. Every complex algebraic surface is birationally ... More

## Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

*Mark Green, Phillip A. Griffiths, and Matt Kerr*

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691154244
- eISBN:
- 9781400842735
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691154244.001.0001
- Subject:
- Mathematics, Analysis

Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive ... More

## On non-parametric statistical methods

*Peter Hall*

### in Celebrating Statistics: Papers in honour of Sir David Cox on his 80th birthday

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566540
- eISBN:
- 9780191718038
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566540.003.0007
- Subject:
- Mathematics, Probability / Statistics

This chapter describes some contemporary topics in non-parametric statistics and outlines their relation to computation, particularly some topics on pure mathematics. It opens with a brief comparison ... More

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

*Gisbert Wüstholz and Clemens Fuchs (eds)*

- Published in print:
- 2019
- Published Online:
- May 2020
- ISBN:
- 9780691193779
- eISBN:
- 9780691197548
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691193779.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures—which were delivered in celebration of the ... More

## Riemann Surfaces

*Simon Donaldson*

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780198526391
- eISBN:
- 9780191774874
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526391.001.0001
- Subject:
- Mathematics, Geometry / Topology, Analysis

The theory of Riemann surfaces occupies a very special place in mathematics. It is a culmination of much of traditional calculus, making surprising connections with geometry and arithmetic. It is an ... 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

##
E*∞*-Structures on *l*-Adic Cohomology

*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/9780691182148.003.0003
- Subject:
- Mathematics, Mathematical Finance

For applications to Weil's conjecture, a version of (3.1) is formulated in the setting of algebraic geometry, where M is replaced by an algebraic curve X (defined over an algebraically closed field ... More

## Dynamics of automorphisms of compact complex surfaces

*Serge Cantat*

*Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland (eds)*

### in Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691159294
- eISBN:
- 9781400851317
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159294.003.0018
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter describes the dynamics of automorphisms of compact complex surfaces when it is rich. In particular, the chapter carries to this general setting the interplay between ideas from ergodic ... More

## Geometry and Physics: Volume II: A Festschrift in honour of Nigel Hitchin

*Andrew Dancer, Jørgen Ellegaard Andersen, and Oscar García-Prada (eds)*

- Published in print:
- 2018
- Published Online:
- December 2018
- ISBN:
- 9780198802020
- eISBN:
- 9780191869068
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198802020.001.0001
- Subject:
- Mathematics, Geometry / Topology

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and ... More

## Geometry and Physics: Volume I: A Festschrift in honour of Nigel Hitchin

*Andrew Dancer, Jørgen Ellegaard Andersen, and Oscar García-Prada (eds)*

- Published in print:
- 2018
- Published Online:
- December 2018
- ISBN:
- 9780198802013
- eISBN:
- 9780191840500
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198802013.001.0001
- Subject:
- Mathematics, Geometry / Topology

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and ... More

## Classification of Pseudo-reductive Groups (AM-191)

*Brian Conrad and Gopal Prasad*

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691167923
- eISBN:
- 9781400874026
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691167923.001.0001
- Subject:
- Mathematics, Numerical Analysis

This book goes further than the exploration of the general structure of pseudo-reductive groups to study the classification over an arbitrary field. An Isomorphism Theorem proved here determines the ... More

## The Norm Residue Theorem in Motivic Cohomology

*Christian Haesemeyer and Charles A. Weibel*

- Published in print:
- 2019
- Published Online:
- January 2020
- ISBN:
- 9780691191041
- eISBN:
- 9780691189635
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691191041.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book presents the complete proof of the Bloch–Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these ... More

## Proving P ≠ NP

*Lance Fortnow*

### in The Golden Ticket: P, NP, and the Search for the Impossible

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175782
- eISBN:
- 9781400846610
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175782.003.0007
- Subject:
- Computer Science, Programming

This chapter focuses on a few of the ideas that people have tried to solve the P versus NP problem. These have not panned out to anything close to a solution to the problem. To prove P ≠ NP one needs ... More

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