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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


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


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


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


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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