## Edward T. Cone Concert Talk

Tommasini discusses his role as a music critic.

Anthony Tommasini, Chief Music Critic

New York Times

October 17, 2009

Tommasini discusses his role as a music critic.

William Matthews

University of California at San Diego

October 13, 2009

William Matthews

University of California at San Diego

October 13, 2009

Ramamohan Paturi

University of California at San Diego

October 12, 2009

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

circuit families

Amir Yehudayoff

Institute for Advanced Study

October 6, 2009

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 will describe the ideas behind the proof of this completeness of the permanent.

Itai Arad

Hebrew University of Jerusalem

October 5, 2009

Ben Reichardt

University of Waterloo

September 29, 2009

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 programs. It implies that span programs are an (almost) equivalent computational model to quantum query algorithms.

Amir Yehudayoff

Institute for Advanced Study

September 22, 2009

Nikhil Srivastava

Yake University

September 21, 2009

We prove that every graph has a spectral sparsifier with a number of edges linear in its

number of vertices. As linear-sized spectral sparsifiers of complete graphs are expanders, our

sparsifiers of arbitrary graphs can be viewed as generalizations of expander graphs.

In particular, we prove that for every d > 1 and every undirected, weighted graph G =

(V,E,w) on n vertices, there exists a weighted graph H = (V, F, ~w) with at most dn edges

such that for every x ∈ ℜ^{V} ,

Swastik Kopparty

Massachusetts Institute of Technology

September 15, 2009