Proving asymptotic upper bounds for matrix multiplication (Part 2)

We explain the different concepts and tools underlying the laser method, as invented by Strassen and Coppersmith-Winograd in 1987, for proving upper bounds on the exponent of matrix multiplication. Keywords are: tensor rank and restriction, border rank and degeneration, asymptotic sum inequality, tight sets. Details can be found in Chapter 15 of the book algebraic complexity.