Effective potential and warp factor dynamics

We define an effective potential describing all massless and massive modes in the supergravity limit of string/M theory compactification which is valid off-shell, i.e. without imposing the equations of motion. If we neglect the warp factor, it is unbounded below, as is the case for the action in Euclidean quantum gravity. By study of the constraint which determines the warp factor, we solve this problem, obtaining a physically satisfying and tractable description of the dynamics of the warp factor.Comment: 32 pages, JHEP3.cls. v4: added reference to hep-th/050715

Basic results in Vacuum Statistics

A review of recent work on constructing and finding statistics of string theory vacua, done in collaboration with Frederik Denef, Bogdan Florea, Bernard Shiffman and Steve Zelditch.Comment: 11 pages, 5 figures (Latex elsart.cls, included

Enhanced Gauge Symmetry in M(atrix) Theory

We discuss the origin of enhanced gauge symmetry in ALE (and K3) compactification of M theory, either defined as the strong coupling limit of the type IIa superstring, or as defined by Banks et al. In the D-brane formalism, wrapped membranes are D0 branes with twisted string boundary conditions, and appear on the same footing with the Kaluza-Klein excitations of the gauge bosons. In M(atrix) theory, the construction appears to work for arbitrary ALE metric.Comment: 10 pp, harvma

A Brief Retrospective Look at the Cayley-Purser Public-key Cryptosystem, 19 Years Later

The purpose of this paper is to describe and analyze the Cayley-Purser algorithm, which is a public-key cryptosystem proposed by Flannery in 1999. I will present two attacks on it, one of which is apparently new. I will also examine a variant of the Cayley-Purser algorithm that was patented by Slavin in 2008, and show that it is also insecure.Comment: submitted for publicatio