Geometry and Complexity Theory

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.

• 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.

'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