Abstract: We give an overview of zeros of random polynomials. Starting with results dating back to 1930s (Mark Kac, Offord etc), we intend to cover some of the many recent developments (due to various authors in the past ten years).

Abstract: Program invariants play an important useful role in understanding programs as well as verifying properties about them.

Abstract: Let B be standard Brownian motion. Fix an interval (a,b). Condition on B(t) to be in (a,b). Look at B(u) for u<.=t and B(u) u>.=t. We show that this converges weakly to a proper probability measure on C(R).

Abstract: We will start with the classical Albert - Barabasi model of preferential attachment random graphs.

Abstract: Differentiated service is typically provided to customers by offering different grades of service at different prices. We first consider a simple system with heterogeneous customers that are type indexed by $v$.