The Kakeya and restriction conjectures are two of the central
open problems in Euclidean Fourier analysis (with the second
logically implying the first, and progress on the first typically
implying progress on the second). Both of these have...
The Depth First Search (DFS) algorithm is one of the most
standard graph exploration algorithms, used normally to find the
connected components of an input graph. Though perhaps less popular
than its sister algorithm, Breadth First Search (BFS)...
Fluctuations of the current of one dimensional non equilibrium
diffusive systems are well understood. After a short review of the
one dimensional results, the talk will try to show that the
statistics of these fluctuations are exactly the same in...
Finding cliques in random graphs and the closely related
"planted" clique variant, where a clique of size k is planted in a
random G(n,1/2) graph, have been the focus of substantial study in
algorithm design. Despite much effort, the best known...
In this talk I will describe nondeterministic reductions which
yield new direct product theorems (DPTs) for Boolean circuits. In
our theorems one assumes that a function F is "mildly hard" against
*nondeterministic* circuits of some size s(n) , and...
In many distributed systems, the cost of computation is
dominated by the cost of communication between the machines
participating in the computation. Communication complexity is
therefore a very useful tool in understanding distributed
computation...
A continuous representation of a profinite group induces a
continuous pseudorepresentation, where a pseudorepresentation is
the data of the
characteristic polynomial coefficients. We discuss the geometry of
the resulting map from the moduli formal...