Title: On the permanent of a random Bernoulli matrix

Abstract: The permanent of an n by n matrix is defined as a sum over permutations in the same way as the determinant, but without the alternating signs. We present recent work, joint with Van Vu, on understanding the permanent of a random matrix with each entry equal to +1 or -1 with equal probability. We show that with probability 1-o(1), the permanent has magnitude n^{(1/2+o(1)) n} (and in particular is non-zero with probability 1-o(1)). The proof is entirely combinatorial in nature.