DLCQ strings and branched covers of torii

In this lecture I will review some results about the discrete light-cone quantization (DLCQ) of strings and some connections of the results with matrix string theory. I will review arguments which show that, in the path integral representation of the thermal free energy of a string, the compactifications which are necessary to obtain discrete light-cone quantization constrains the integral over all Riemann surfaces of a given genus to the set of those Riemann surfaces which are branched covers of a particular torus. I then review an explicit check of this result at genus 1. I discuss the intriguing suggestion that these branched covers of a torus are related to those which are found in a certain limit of the matrix string model