I shall describe several techniques for finding approximate
solutions to the time-dependent Schr\"odinger equation in the
semiclassical limit. The first of these involves expansions in
"semiclassical wave packets" that are also sometimes called...
In FT-mollification, one smooths a function while maintaining
good quantitative control on high-order derivatives. I will
describe this approach and show how it can be used to show that
bounded independence fools polynomial threshold functions...
A classical theorem in Euclidean geometry asserts that if a set
of points has the property that every line through two of them
contains a third point, then they must all be on the same line. We
prove several approximate versions of this theorem...
Complexity theory, with some notable exceptions, typically
studies the complexity of computing a function h(x) of a *given*
input x. We advocate the study of the complexity of generating --
or sampling -- the output distribution h(x) for random x...
