Landsberg Geometry and Complexity Theory

Erscheinungsjahr 2017
ISBN: 978-1-108-19621-5
Verlag: Cambridge University Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 169, 0 Seiten

Reihe: Cambridge Studies in Advanced Mathematics

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.

Autoren/Hrsg.

Landsberg, J. M.

Fachgebiete

• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen

Inhaltsverzeichnis

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.

Über Autor(innen)

Landsberg, J. M.
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.