Geometry and Complexity Theory
eBook - PDF

Geometry and Complexity Theory

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Geometry and Complexity Theory

About this book

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.

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Yes, you can access Geometry and Complexity Theory by J. M. Landsberg in PDF and/or ePUB format, as well as other popular books in Informatique & Sciences générales de l'informatique. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half title
  3. Series
  4. Title
  5. Copyright
  6. Contents
  7. Preface
  8. 1 Introduction
  9. 2 The Complexity of Matrix Multiplication I: First Lower Bounds
  10. 3 The Complexity of Matrix Multiplication II: Asymptotic Upper Bounds
  11. 4 The Complexity of Matrix Multiplication III: Explicit Decompositions via Geometry
  12. 5 The Complexity of Matrix Multiplication IV: The Complexity of Tensors and More Lower Bounds
  13. 6 Valiant's Hypothesis I: Permanent versus Determinant and the Complexity of Polynomials
  14. 7 Valiant's Hypothesis II: Restricted Models and Other Approaches
  15. 8 Representation Theory and Its Uses in Complexity Theory
  16. 9 The Chow Variety of Products of Linear Forms
  17. 10 Topics Using Additional Algebraic Geometry
  18. Hints and Answers to Selected Exercises
  19. Bibliography
  20. Index