2011-2012 Seminars

A property of finite graphs is called nondeterministically testable if it has a "certificate'' such that once the certificate is specified, its correctness can be verified by random local testing. In this talk we consider certificates that consist...

The goal of the Balanced Separator problem is to find a balanced cut in a given graph G(V,E), while minimizing the number of edges that cross the cut. It is a fundamental problem with applications in clustering, image segmentation, community...

We study the list-decodability of multiplicity codes. These codes, which are based on evaluations of high-degree polynomials and their derivatives, have rate approaching 1 while simultaneously allowing for sublinear-time error-correction. In this...

Consider the problem when we want to construct some structure on a bounded degree graph, e.g. an almost maximum matching, and we want to decide about each edge depending only on its constant radius neighborhood. We show that the information about...

We present an iterative approach to constructing pseudorandom generators, based on the repeated application of mild pseudorandom restrictions. We use this template to construct pseudorandom generators for combinatorial rectangles and read-once CNFs...

We study a new type of proof system, where an unbounded prover and a polynomial time verifier interact, on inputs a string $x$ and a function $f$, so that the Verifier may learn $f(x)$. The novelty of our setting is that there no longer are ``good"...

A basic fact of algebraic graph theory is that the number of connected components in an undirected graph is equal to the multiplicity of the eigenvalue zero in the Laplacian matrix of the graph. In particular, the graph is disconnected if and only...

The problem of combinatorial auctions is one of the basic questions in algorithmic mechanism design: how can we allocate/sell m items to n agents with private valuations of different combinations of items, so that the agents are motivated to reveal...

I will talk about two natural notions of convergence for sequences of graphs of bounded degree and their connection to groups and group actions. The first is Benjamini-Schramm convergence, which is strongly related to parameter testing. The second...

The polynomial Freiman-Ruzsa conjecture is one of the important open problems in additive combinatorics. In computer science, it already has several diverse applications: explicit constructions of two-source extractors; improved bounds for the log...