International Congress of Mathematicians: Geometry

ICM 2018 - Rio

GEOMETRY

Geometry

The Geometry and Physics of Knots Michael Atiyah Lezioni Lincee

The material presented rests primarily on the pioneering work of Vaughan Jones and Edward Witten – relating polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions.

August 1990 216 x 138 mm 108pp 978-0-521-39554-0 Paperback £24.99 / US$42.99

Noncommutative Algebraic Geometry Gwyn Bellamy, Daniel Rogalski Travis Schedler, J. Toby Stafford and Michael Wemyss

This book provides a comprehensive introduction to the interactions between noncommutative algebra and classical algebraic geometry.

Mathematical Sciences Research Institute Publications, 64

Moduli Spaces Edited by Leticia Brambila-Paz Peter Newstead Richard P. Thomas and Oscar García-Prada

A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.

London Mathematical Society Lecture Note Series, 411 March 2014 228 x 152 mm 346pp 978-1-107-63638-5 Paperback £54.99 / US$77.99

A First Course in Computational Algebraic Geometry

A First Course in Hurwitz Theory Renzo Cavalieri and Eric Miles

Wolfram Decker and Gerhard Pfister

Classroom-tested and featuring over 100 exercises, this text introduces the key algebraic geometry field of Hurwitz theory.

London Mathematical Society Student Texts, 87 September 2016 228 x 152 mm 194pp 50 b/w illus. 130 exercises 978-1-316-60352-9 Paperback £28.99 / US$44.99

A quick guide to computing in algebraic geometry with many explicit computational examples introducing the computer algebra system Singular.

AIMS Library of Mathematical Sciences February 2013 216 x 138 mm 126pp 40 b/w illus.

978-1-107-61253-2 Paperback £12.99 / US$21.99

Edited by Lucia Caporaso James McKernan Mircea Mustata and Mihnea Popa

This volume, based on a workshop by the MSRI, offers an overview of the state of the art in many areas of algebraic geometry.

Mathematical Sciences Research Institute Publications, 59 October 2014 234 x 156 mm 438pp 978-1-107-45946-5 Paperback £36.99 / US$51.99

June 2016 234 x 156 mm 358pp 978-1-107-57003-0 Paperback £30.99 / US$40.99

Riemann Surfaces and Algebraic Curves

Current Developments in Algebraic Geometry

3264 and All That A Second Course in Algebraic Geometry David Eisenbud and Joe Harris

Forming the basis of a second course in algebraic geometry, this book explains key ideas, each illustrated with abundant examples.

April 2016 253 x 177 mm 603pp 80 b/w illus. 360 exercises 978-1-107-60272-4 Paperback £30.99 / US$49.99

The Geometry of Physics An Introduction Third edition Theodore Frankel

Provides a working knowledge of tools that are of great value in geometry and physics and in engineering.

November 2011 247 x 174 mm 748pp 260 b/w illus. 205 exercises 978-1-107-60260-1 Paperback £55.99 / US$79.99

20% discount online at www.cambridge.org/ICM2018

Geometry

Lectures on K3 Surfaces

Geometries and Transformations

Daniel Huybrechts

Norman W. Johnson

Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.

A readable exposition of how Euclidean and other geometries can be distinguished using linear algebra and transformation groups.

Cambridge Studies in Advanced Mathematics, 158 October 2016 228 x 152 mm 496pp 21 b/w illus.

978-1-107-15304-2 Hardback £51.99 / US$74.99

June 2018 234 x 156 mm 452pp 978-1-107-10340-5 Hardback £59.99 / US$74.99

Optimal Control and Geometry: Integrable Systems Velimir Jurdjevic

Blending control theory, mechanics, geometry and the calculus of variations, this book is a vital resource for graduates and researchers in engineering, mathematics and physics.

Cambridge Studies in Advanced Mathematics, 154 July 2016 228 x 152 mm 423pp 4 tables 978-1-107-11388-6 Hardback £59.99 / US$84.99

Singularities of the Minimal Model Program

Geometry and Complexity Theory

Hyperbolic Manifolds

J. M. Landsberg

János Kollár In collaboration with Sándor Kovács

This comprehensive introduction to algebraic complexity theory presents new techniques for analyzing P vs NP and matrix multiplication.

An Introduction in 2 and 3 Dimensions Albert Marden

An authoritative reference and the first comprehensive treatment of the singularities of the minimal model program.

Cambridge Tracts in Mathematics, 200 February 2013 228 x 152 mm 382pp 978-1-107-03534-8 Hardback £65.00 / US$99.99

Cambridge Studies in Advanced Mathematics, 169 September 2017 228 x 152 mm 350pp 978-1-107-19923-1 Hardback £49.99 / US$64.99

Recent Advances in Hodge Theory Period Domains, Algebraic Cycles, and Arithmetic Edited by Matt Kerr and Gregory Pearlstein

Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.

London Mathematical Society Lecture Note Series, 427 February 2016 228 x 152 mm 521pp 10 b/w illus. 7 tables 978-1-107-54629-5 Paperback £65.99 / US$91.99

This study of hyperbolic geometry has both pedagogy and research in mind, and includes exercises and further reading for each chapter.

February 2016 247 x 174 mm 529pp 55 b/w illus. 21 colour illus. 250 exercises 978-1-107-11674-0 Hardback £51.99 / US$79.99

Algebraic Groups The Theory of Group Schemes of Finite Type over a Field J. S. Milne

Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.

Cambridge Studies in Advanced Mathematics, 170 September 2017 228 x 152 mm 660pp 5 b/w illus. 95 exercises 978-1-107-16748-3 Hardback £79.99 / US$99.99

20% discount online at www.cambridge.org/ICM2018

Geometry

Indra’s Pearls

How to Fold It

The Vision of Felix Klein David Mumford Caroline Series and David Wright

The Mathematics of Linkages, Origami, and Polyhedra Joseph O’Rourke

This book tells the story of the first computer exploration of Klein’s vision of infinitely repeated reflections, featuring extraordinary images.

Discover and understand mathematical theorems through paper folding, starting with high school algebra and geometry through to more advanced concepts.

November 2015 246 x 189 mm 414pp 55 b/w illus. 150 colour illus. 75 exercises 978-1-107-56474-9 Paperback £38.00 / US$59.99

Spaces of Kleinian Groups Edited by Yair N. Minsky Makoto Sakuma and Caroline Series

Important and original research in the fast-developing subject of Kleinian groups and hyperbolic 3-manifolds.

London Mathematical Society Lecture Note Series, 329 July 2006 228 x 152 mm 398pp 68 b/w illus. 4 colour illus. 10 tables 978-0-521-61797-0 Paperback £70.00 / US$129.99

June 2011 228 x 152 mm 190pp 171 b/w illus. 1 table 48 exercises 978-0-521-14547-3 Paperback £24.99 / US$36.99

Differential Geometry of Singular Spaces and Reduction of Symmetry J. Śniatycki

A complete presentation of the theory of differential spaces, with applications to the study of singularities in systems with symmetry.

New Mathematical Monographs, 23 June 2013 228 x 152 mm 247pp 978-1-107-02271-3 Hardback £60.00 / US$94.99

Recent Advances in Algebraic Geometry A Volume in Honor of Rob Lazarsfeld’s 60th Birthday Edited by Christopher D. Hacon Mircea Mustaţă and Mihnea Popa

A comprehensive collection of expository articles on cutting-edge topics at the forefront of research in algebraic geometry.

London Mathematical Society Lecture Note Series, 417

Conformal Fractals Ergodic Theory Methods Feliks Przytycki and Mariusz Urbański

A one-stop introduction to the methods of ergodic theory applied to holomorphic iteration that is ideal for graduate courses.

London Mathematical Society Lecture Note Series, 371 May 2010 228 x 152 mm 366pp 26 b/w illus. 90 exercises 978-0-521-43800-1 Paperback £59.99 / US$94.99

January 2015 228 x 152 mm 447pp 12 b/w illus. 9 tables 978-1-107-64755-8 Paperback £67.00 / US$102.00

The Banach– Tarski Paradox Second edition Grzegorz Tomkowicz and Stan Wagon

The Banach–Tarski Paradox seems patently false. The authors explain it and its implications in terms appropriate for an undergraduate.

Encyclopedia of Mathematics and its Applications, 163 October 2016 234 x 156 mm 360pp 47 b/w illus. 6 colour illus.

978-1-107-04259-9 Hardback £74.99 / US$110.00

Group Cohomology and Algebraic Cycles Burt Totaro

This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.

Cambridge Tracts in Mathematics, 204 June 2014 228 x 152 mm 246pp 2 b/w illus.

978-1-107-01577-7 Hardback £60.00 / US$91.99

20% discount online at www.cambridge.org/ICM2018