We discuss algorithms for the private analysis of network data. Such algorithms work on data sets that contain sensitive relationship information (for example, romantic ties).
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).
Suppose we are given a list of numbers and we wish to determine whether it is sorted in increasing order. That problem obviously requires reading the entire list.
Abstract: An infinite graph may have the property that two independent random walks on the graph never meet each other, although each of them visits every vertex of the graph infinitely often.
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: Propp and Wilson showed how to generate a Markov chain which in a finite number of steps gives a sample from the stationary distribution supported by a countable set.
Arithmetic Complexity is a central topic of interest in theoretical computer science. The famous $P$ vs. $NP$ question that seeks to understand the limits of efficient computation has its natural arithmetic analogue.
