In 1964 Arnold constructed an example of instabilities for
nearly integrable systems and conjectured that generically this
phenomenon takes place.
There has been big progress attacking this conjecture in the past
decade. Jointly with Ke Zhang we...
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...