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...
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...
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...
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...
An XOR game is a very simple model of evaluating a distributed
function f(x,y) . With probability p(x,y) a Verifier sends
questions x, y to Alice and Bob, respectively. Without
communicating, Alice and Bob then output a, b in {-1,+1} in the
hope...
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...
A PCP is a proof system in which the proofs that can be verified
by a verifier that reads only a very small part of the proof. One
line of research concerning PCPs is trying to reduce their
soundness error (i.e., the probability of accepting false...
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...
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...
We present a gap theorem regarding the complexity of the circuit
satisfiability problem.
We prove that the success probability of deciding Circuit
Satisfiability for deterministic
circuits with n variables and size m is either
2−n or 2−o(n) when...
