We consider the problem of counting the number of spanning trees in planar graphs. We prove tight bounds on the complexity of the problem, both in general and especially in the modular setting. We exhibit the problem to be complete for Logspace when the modulus is 2^k, for constant k. ... more >>>

A construction of Bourgain gave the first 2-source
extractor to break the min-entropy rate 1/2 barrier. In this note,
we write an exposition of his result, giving a high level way to view
his extractor construction.

We also include a proof of a generalization of Vazirani's XOR lemma
that seems ... more >>>

We recover the first linear programming bound of McEliece, Rodemich, Rumsey, and Welch for binary error-correcting codes and designs via a covering argument. It is possible to show, interpreting the following notions appropriately, that if a code has a large distance, then its dual has a small covering radius and, ... more >>>