Geometry and Complexity Theory

ISBN-13: 9781107199231 / Angielski / Twarda / 2017 / 350 str.

J. M. Landsberg

Opis

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

Recenzje

'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

Spis treści

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.