We give an algorithmic proof of Forster's Theorem, a fundamental result in communication complexity. Our proof is based on a geometric notion we call radial isotropic position which is related to the well-known isotropic position of a set of vectors. We point out an efficient algorithm to compute the radial isotropic position of a given set of vectors when it exists.

The question whether or not parallel repetition reduces the soundness error is a fundamental question in the theory of protocols. While parallel repetition reduces (at an exponential rate) the error in interactive proofs and (at a weak exponential rate) in special cases of interactive arguments (e.g., 3-message protocols - Bellare, Impagliazzo and Naor [FOCS '97], and public-coin protocols - Håstad, Pass, Pietrzak and WikstrÄm [Manuscript '08]), Bellare et. al gave example of interactive arguments for which parallel repetition does not reduce the soundness error at all.

Green and Tao used the existence of a dense subset indistinguishable from the primes under certain tests from a certain class to prove the existence of arbitrarily long prime arithmetic progressions. Reingold, Trevisan, Tulsiani and Vadhan, and independently, Gowers, give a quantitatively improved characterization of when such dense models exist. An equivalent formulation was obtained earlier by Barak, Shaltiel and Wigderson.

Renowned composer and pianist William Bolcom discusses his career as a composer and performer with Artist-in-Residence Derek Bermel.

In the aftermath of several great imperial expansions, especially those of the Arabs and the Europeans, one sees the phenomenon of the native who has accepted the religion and/or culture of the hegemonic foreigners, only to rediscover his native identity and proceed to take political action against them. In this lecture, Crone will explore what lies behind this reaction and why it was much less characteristic of Islamized natives than it has been of Westernized ones.

I will discuss the Green-Tao proof for existence of arbitrarily long arithmetic progressions in the primes. The focus will primarily be on the parts of the proof which are related to notions in complexity theory. In particular, I will try to describe in detail how the proof can be seen as applying Szemeredi's theorem to primes, by arguing that they are indistinguishable from dense subsets of integers, for a suitable family of distinguishers.

Research in the area of privacy of data analysis has been flourishing recently, with a rigorous notion such as differential privacy regarding the desired level of privacy and sanitizing algorithms matching the definition for many problems. Most of the work in the area assumes that the data to be sanitized is fixed.

The quest for understanding the origin of our universe has been dramatically transformed since the expansion of the universe was discovered by Edwin Hubble in 1929, thanks to impressive advances in astronomical observations and laboratory experiments. Cosmology is now widely regarded as a precision science. Although confidence in our models has increased, deep questions remain unanswered.

I will first give an overview of several constructions of graph sparsifiers and their properties. I will then present a method of sparsifying a subgraph W of a graph G with optimal number of edges and talk about the implications of subgraph sparsification in constructing nearly-optimal ultrasparsifiers and optimizing the algebraic connectivity of a graph by adding few edges.

The talk is based on joint work with Makarychev,Saberi,Teng.

I will survey some constructions of expander graphs using variants of Kazhdan property T . First, I describe an approach to property T using bounded generation and then I will describe a recent method based on the geometric properties of configurations of subspaces in a finite dimensional Euclidean space.