Progress on Polynomial Identity Testing - II

We survey the area of algebraic complexity theory; with the focus being on the problem of polynomial identity testing (PIT). We discuss the key ideas that have gone into the results of the last few years.Comment: 17 pages, 1 figure, surve

Foundations of the AdS_5 x S^5 Superstring. Part I

We review the recent advances towards finding the spectrum of the AdS_5 x S^5 superstring. We thoroughly explain the theoretical techniques which should be useful for the ultimate solution of the spectral problem. In certain cases our exposition is original and cannot be found in the existing literature. The present Part I deals with foundations of classical string theory in AdS_5 x S^5, light-cone perturbative quantization and derivation of the exact light-cone world-sheet scattering matrix.Comment: 161 page