Two central problems in computer science are P vs NP and the complexity of matrix multiplication. The first is also a leading candidate for the greatest unsolved problem in mathematics. The second is of enormous practical and theoretical importance. Algebraic geometry and representation theory provide fertile ground for advancing work on these problems and others in complexity. This introduction to algebraic complexity theory for graduate students and researchers in computer science and mathematics features concrete examples that demonstrate the application of geometric techniques to real world problems. Written by a noted expert in the field, it offers numerous open questions to motivate future research. Complexity theory has rejuvenated classical geometric questions and brought different areas of mathematics together in new ways. This book will show the beautiful, interesting, and important questions that have arisen as a result.
Rezensionen / Stimmen
'The book under review provides an introduction accessible to graduate students and researchers either in computer science or in geometry and representation theory expanding a useful bridge between these disciplines and unifying recent trends.' Felipe Zaldivar, MAA Reviews 'Most of the book is self-contained, since it introduces the necessary concepts of algebraic geometry and representation theory when needed. Several exercises are provided (for some of which hints and answers are available at the end of the book), together with an assessment of their difficulty and importance, stimulating the reader to an active reading.' Matteo Gallet, MathSciNet 'We greatly encourage mathematicians interested in these subjects (algebraic geometers in particular, but not only!) to find many, many more interesting results in the Geometry and Complexity Theory by J. M. Landsberg.' Mateusz Michalek, Bulletin of the American Mathematical Society
Reihe
Sprache
Verlagsort
Zielgruppe
Produkt-Hinweis
Fadenheftung
Gewebe-Einband
Illustrationen
Worked examples or Exercises
Maße
Höhe: 286 mm
Breite: 221 mm
Dicke: 23 mm
Gewicht
ISBN-13
978-1-107-19923-1 (9781107199231)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
J. M. Landsberg is Professor of Mathematics at Texas A & M University. He is a leading geometer working in complexity theory, with research interests in differential geometry, algebraic geometry, representation theory, the geometry and application of tensors, and most recently, algebraic complexity theory. The author of over sixty research articles and four books, he has given numerous intensive research courses and lectures at international conferences. He co-organized the fall 2014 semester 'Algorithms and Complexity in Algebraic Geometry' program at the Simons Institute for the Theory of Computing, University of California, Berkeley and served as the UC Berkeley Chancellor's Professor during the program.
Autor*in
Texas A & M University
1. Introduction; 2. The complexity of matrix multiplication I; 3. The complexity of matrix multiplication II; 4. The complexity of matrix multiplication III; 5. The complexity of matrix multiplication IV; 6. Valiant's hypothesis I; 7. Valiant's hypothesis II; 8. Representation theory and its uses in complexity theory; 9. The Chow variety of products of linear forms; 10. Topics using additional algebraic geometry.
