Seminars Sorted by Series

Sparse recovery problems arise in many applications. Suppose v is an unknown N-dimensional signal with at most k nonzero components. We call such signals k-sparse. Suppose we are able to collect n \ll N linear measurements of v , and wish to...

An epsilon-biased set X in {0,1}^n is a set so that for every non-empty set T in [n] the following holds. The random bit B(T) obtained by selecting at random a vector x in X, and computing the mod-2 sum of its T-coordinates, has bias at most epsilon...

The small-set expansion conjecture introduced by Raghavendra and Steuerer is a natural hardness assumption concerning the problem of approximating edge expansion of small sets (of size $\delta n$) in graphs. It was shown to be intimately connected...

The Stepanov method is an elementary method for proving bounds on the number of roots of polynomials. At its core is the following idea. To upper bound the number of roots of a polynomial f(x) in a field, one sets up an auxiliary polynomial F(x)...

In this talk I will insult your intelligence by showing a non-original proof of the Central Limit Theorem, with not-particularly-good error bounds. However, the proof is very simple and flexible, allowing generalizations to multidimensional and...

Locally decodable codes are error-correcting codes that admit efficient decoding algorithms, that can recover any bit of the original message by looking at only a small number of locations of a corrupted codeword. The tradeoff between the rate of a...

We give a pseudorandom generator, with seed length O(log n), for CC0[p], the class of constant-depth circuits with unbounded fan-in MODp gates, for prime p. More accurately, the seed length of our generator is O(log n) for any constant error epsilon...

Finding the longest increasing subsequence (LIS) is a classic algorithmic problem. Simple O(n log n) algorithms, based on dynamic programming, are known for solving this problem exactly on arrays of length n. In this talk I'll discuss recent work of...

A (q,k,t)-design matrix is an m x n matrix whose pattern of zeros/non-zeros satisfies the following design-like condition: each row has at most q non-zeros, each column has at least k non-zeros and the supports of every two columns intersect in at...

Let f(x_1,...,x_n) be a low degree polynomial over F_p. I will prove that there always exists a small set S of variables, such that `most` Fourier coefficients of f contain some variable from the set S. As an application, we will get a derandomized...

The firefighter problem is a monotone dynamic process in graphs that can be viewed as modeling the use of a limited supply of vaccinations to stop the spread of an epidemic. In more detail, a fire spreads through a graph, from burning vertices to...

We give an elementary proof of a generalization of Bourgain and Tzafriri's Restricted Invertibility Theorem, which says roughly that any matrix with columns of unit length and bounded operator norm has a large coordinate subspace on which it is well...

Infinite continuous graphs emerge naturally in the geometric analysis of closed planar sets which cannot be presented as countable union of convex sets. The classification of such graphs leads in turn to properties of large classes of real functions...

A permutation pi=(pi_{1},...,pi_{n}) is consecutive 123-avoiding if there is no sequence of the form pi_i pi_{i+1} pi_{i+2}. More generally, for S a collection of permutations on m+1 elements, this definition extends to define consecutive S...

A hardness escalation method applies a simple transformation that increases the complexity of a computational problem. Using multiparty communication complexity we present a generic hardness escalation method that converts any family of...

Erdos conjectured that N points in the plane determine at least c N (log N)^{-1/2} different distances. Building on work of Elekes-Sharir, Nets Katz and I showed that the number of distances is at least c N (log N)^{-1} . (Previous estimates had...

Given data drawn from a mixture of multivariate Gaussians, a basic problem is to accurately estimate the mixture parameters. We provide a polynomial-time algorithm for this problem for any fixed number ($k$) of Gaussians in $n$ dimensions (even if...

Boolean Threshold Functions (BTF) arise in many contexts, ranging from computer science and learning theory to theoretical neurobiology. In this talk, I will present non-rigorous approaches developed in the statistical physics of disordered systems...

We study the complexity of computing some basic arithmetic operations over GF(2^n), namely computing q-th root and q-th residuosity, by constant depth arithmetic circuits over GF(2) (also known as AC^0(parity)). Our main result is that these...

The Unique Games conjecture (UGC) has emerged in recent years as the starting point for several optimal inapproximability results. While for none of these results a reverse reduction to Unique Games is known, the assumption of bijective projections...

The complexity of simple stochastic games (SSGs) has been open since they were defined by Condon in 1992. Such a game is played by two players, Min and Max, on a graph consisting of max nodes, min nodes, and average nodes. The goal of Max is to...

We study the local testabilty of sparse linear codes. This problem is intimately connected to the problem of tolerant linearity testing of Boolean functions under nonuniform distributions. We give linearity tests for several natural and interesting...

Non-relativization of complexity issues can be interpreted as giving evidence that these issues cannot be resolved by “black-box” techniques. We show that the assumption $DistNP \subseteq AvgP$ does not imply that $NP\subseteq BPP$ by relativizing...

We define a polynomial threshold function to be a function of the form f(x) = sgn(p(x)) for p a polynomial. We discuss some recent techniques for dealing with polynomial threshold functions, particular when evaluated on random Gaussians. We show how...

In this talk, I will give new proofs for the hardness amplification of fficiently samplable predicates and of weakly verifiable puzzles. More oncretely, in the first part of the talk, I will give a new proof of Yao's XOR-Lemma as well as related...

Given a matrix $A$, it can be shown that there is a vector $z \in 0,1^n$ for which $|Az|/|Z| \geq |A|_2/C \log(n)$ (a0/1 sum of columns of $A$ which witnesses its large spectral norm) for instance by discretizing the top singular vector of $A$ and...

How to color $3$ colorable graphs with few colors is a problem of longstanding interest. The best polynomial-time algorithm uses $n^{0.2130}$ colors. We explore the possibility that more levels of Lasserre Hierarchy can give improvements over...

Decompositions in theorems in classical Fourier analysis which decompose a function into large Fourier coefficients and a part that is pseudorandom with respect to (has small correlation with) linear functions. The Goldreich-Levin theorem [GL89] can...

We show existence of rigid combinatorial objects that previously were not known to exist. Specifically, we consider two families of objects: 1. A family of permutations on n elements is t-wise independent if it acts uniformly on tuples of t elements...

A locally correctable code (LCC) is an error correcting code mapping d symbols to n symbols, such that for every codeword c and every received word r that is \delta-close to c, we can recover any coordinate of c (with high probability) by only...

We present a unified approach to various topics in mathematics including: Ergodic theory, graph limit theory, hypergraph regularity, and Higher order Fourier analysis. The main theme is that very large complicated structures can be treated as...

We present a unified approach to various topics in mathematics including: Ergodic theory, graph limit theory, hypergraph regularity, and Higher order Fourier analysis. The main theme is that very large complicated structures can be treated as...

We prove that a uniformly chosen proper coloring of Z_{2n}^d with 3 colors has a very rigid structure when the dimension d is sufficiently high. The coloring takes one color on almost all of either the even or the odd sub-lattice. In particular, one...

The notion of exactly (or approximately) representing certain combinatorial properties of a graph $G$ on a simpler graph is ubiquitous in combinatorial optimization. In this talk, I will introduce the notion of vertex sparsification. Here we are...

The notion of exactly (or approximately) representing certain combinatorial properties of a graph $G$ on a simpler graph is ubiquitous in combinatorial optimization. In this talk, I will introduce the notion of vertex sparsification. Here we are...

The long code is a central tool in hardness of approximation, especially in questions related to the unique games conjecture. Many hardness reductions and constructions of integrality gap instances use the long code as a core gadget. However, this...

The long code is a central tool in hardness of approximation, especially in questions related to the unique games conjecture. Many hardness reductions and constructions of integrality gap instances use the long code as a core gadget. However, this...

This is a survey talk about different attempts to deal with the very troubling phenomena of independence in Set Theory.

For modern SAT solvers based on DPLL with clause learning, the two major bottlenecks are the time and memory used by the algorithm. This raises the question of whether this memory bottleneck is inherent to Resolution based approaches, or an artifact...

The P vs. NP problem has sometimes been unofficially paraphrased as asking whether it is possible to improve on exhaustive search for such problems as Satisfiability, Clique, Graph Coloring, etc. However, known algorithms for each of these problems...

The Resolution proof system is among the most basic and popular for proving propositional tautologies, and underlies many of the automated theorem proving systems in use today. I'll start by defining the Resolution system, and its place in the proof...

A randomness extractor is an efficient algorithm which extracts high-quality randomness from a low-quality random source. Randomness extractors have important applications in a wide variety of areas, including pseudorandomness, cryptography...

In this talk I will present a colored version of Tverberg's theorem about partitioning finite point sets in R^d into rainbow groups whose convex hulls intersect. This settles the famous Bárány-Larman conjecture (1992) for primes minus one, and...