Seminars Sorted by Series

We consider several natural problems related to the design of approximation algorithms and the analysis of their error bounds. We define a set of sufficient conditions on a function $f:D --> R^+$ and its domain $D$ , so that we can construct good...

Abstract: Studying dynamical systems is key to understanding a wide range of phenomena ranging from planets' movement to climate patterns to market dynamics. Various numerical tools have been developed to address specific questions about dynamical...

Pseudo-random generators that are secure against constant depth polynomial size circuits have been known since the seminal paper by Ajtai and Wigderson (1985). All available constructions of such generators, however, appear to be somewhat special...

Nisan and Wigderson defined the model of multilinear circuits as a natural model for computing multilinear polynomials (such as matrix product and the Permanent). We will go over several results regarding such circuits -- a few structural results...

Nisan and Wigderson defined the model of multilinear circuits as a natural model for computing multilinear polynomials (such as matrix product and the Permanent). We will go over several results regarding such circuits -- a few structural results...

One natural strategy for proving a time lower bound for a problem is proof-by-contradiction: assume that there is a great algorithm for the problem, and apply this algorithm as a subroutine to solve other problems until the algorithms get so great...

A celebrated theorem of Razborov/Smolensky says that constant depth circuits comprising AND/OR/MOD_{p^k} gates of unbounded fan-in, require exponential size to compute the MAJORITY function if p is a fixed prime and k is a fixed integer. Extending...

A celebrated theorem of Razborov/Smolensky says that constant depth circuits comprising AND/OR/MOD_{p^k} gates of unbounded fan-in, require exponential size to compute the MAJORITY function if p is a fixed prime and k is a fixed integer. Extending...

In the lecture we will explain how various fundamental structures from group representation theory appear naturally in the context of discrete harmonic analysis and can be applied to solve concrete problems from digital signal processing. We will...

The dichotomy conjecture asks if every Constraint Satisfaction Problem is either in P or NP-complete. We will study the basic algorithms and reductions for such problems. We will see many (equivalent) stronger versions of this conjecture actually...

The dichotomy conjecture asks if every Constraint Satisfaction Problem is either in P or NP-complete. We will study the basic algorithms and reductions for such problems. We will see many (equivalent) stronger versions of this conjecture actually...

I will outline the general area of proof complexity, and its traditional problems. I will focus on less traditional ones, namely the complexity of proving identities over certain algebraic structures. The paradigmatic example is a system intended to...

I will outline the general area of proof complexity, and its traditional problems. I will focus on less traditional ones, namely the complexity of proving identities over certain algebraic structures. The paradigmatic example is a system intended to...

Combinatorial arguments have played a crucial role in the investigation of several surprising phenomena in Information Theory. After a brief discussion of some of these results I will describe a recent example, based on joint work with Hassidim...

In this work we study the task of randomness extraction from sources which are distributed uniformly on an unknown algebraic variety. In other words, we are interested in constructing a function (an extractor) whose output is close to uniform even...

In this work we study the task of randomness extraction from sources which are distributed uniformly on an unknown algebraic variety. In other words, we are interested in constructing a function (an extractor) whose output is close to uniform even...

Mechanism design is not robust. It traditionally guarantees a desired property "at equilibrium", but an equilibrium is by definition very fragile: it only guarantees that no INDIVIDUAL player can profitably deviate from his envisaged strategy. Two...

Amplifying the difficulty of a somewhat hard function is a central technique in complexity, cryptography and pseudorandomness. By far the most common method of amplification is by repetition - asking to compute the original function in many...

We will describe the recent proof of the 1990 Linial-Nisan conjecture. The conjecture states that bounded-depth boolean circuits cannot distinguish poly-logarithmically independent distributions from the uniform one. The talk will be almost...

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. Tao and Ziegler showed some general conditions...

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. Tao and Ziegler showed some general conditions...

Affine extractors are maps over F^n that are balanced on every affine subspace of large enough dimension. A random map is, with high probability, a good affine extractor. However so far we do not know how to build explicit affine extractors that are...

Does computing n copies of a function require n times the computational effort? In this work, we give the first non-trivial answer to this question for the model of randomized communication complexity. We show that: 1. Computing n copies of a...

The Parallel Repetition Theorem by Raz is used to amplify the soundness of PCP's, and is one of the ingredients to prove strong inapproximability results. Unfortunately, Raz's proof was very complicated. In these two talks, I will present the...

Planarity is a central theme in graph theory and combinatorial geometry, dating back to Euler. There are many beautiful characterizations of planar graphs such as Kuratowski's forbidden minor theorem and Koebe's circle packing theorem from the 1930s...

The list decoding problem consists of finding the list of all codewords that differ from an input string (the received word) in at most a certain fraction of positions (equal to the target error-correction radius). Informally, the list decoding...

In this talk, we will discuss how the circle method can be used to count solutions to Diophantine problems. After a brief overview of the circle method's history and applications, we will sketch how to prove an asymptotic for the number of integer...

It has been checked, for zillions of even numbers, that they can all be expressed as a sum of two primes. It has also been checked for zillions of (non-trivial) zeros of Zeta(s), that their real parts are all equal to one half. Alas, these checks do...

In their seminal paper Feder and Vardi proved that every problem in the class Monotone Monadic Strict NP (MMSNP) is random polynomial-time equivalent to a finite union of Constraint Satisfaction Problems (CSP). The class MMSNP is the "largest...

We study solution sets to systems of 'generalized' linear equations of the form ell_i (x_1, x_2,...,x_n) \in A_i (mod m) where ell_1,...,ell_t are linear forms in n Boolean variables, each A_i is an arbitrary subset of Z_m, and m is a composite...

The 'method of multiplicities' (which is a variant of the polynomial method in combinatorics) is a very effective method to derive combinatorial bounds on the size of certain sets in vector spaces over finite fields. In this work we extend this...

An affine disperser over F_2^n for sources of dimension d is a function f: F_2^n --> F_2 such that for any affine subspace S in F_2^n of dimension at least d, we have {f(s) : s in S} = F_2 . Affine dispersers have been considered in the context of...

In his seminal work, Valiant defined algebraic analogs for the classes P and NP, which are known today as VP and VNP. He also showed that the permanent is VNP-complete (that is, the permanent is in VNP and any problem in VNP is reducible to it). We...

The general adversary bound is a lower bound on the number of input queries required for a quantum algorithm to evaluate a boolean function. We show that this lower bound is in fact tight, up to a logarithmic factor. The proof is based on span...

In his seminal work, Valiant defined algebraic analogs for the classes P and NP, which are known today as VP and VNP. He also showed that the permanent is VNP-complete (that is, the permanent is in VNP and any problem in VNP is reducible to it). We...

We present two new approximation algorithms for Unique Games. The first generalizes the results of Arora et al. who give polynomial time approximation algorithms for graphs with high conductance. We give a polynomial time algorithm assuming only...

The PCP Theorem shows that any mathematical proof can be efficiently converted into a form that can be checked probabilistically by making only *two* queries to the proof, and performing a "projection test" on the answers. This means that the answer...

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...