Applications of FT-Mollification

Jelani Nelson
Institute for Advanced Study
March 6, 2012

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 over various distributions (Gaussian, Bernoulli, and p-stable).

This talk is based on various works by subsets of Ilias Diakonikolas, Daniel Kane, David Woodruff, and myself.

Various Approaches to Semiclassical Quantum Dynamics

George A. Hagedorn
Virginia Tech
March 6, 2012

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 "generalized squeezed states." The second is a time-dependent WKB approach that is related to the work of Maslov. I also plan briefly to describe the use of Bargmann transforms and Wigner.

Celebrating Modern Democracy’s Beginning: The “British Club” in Paris (1789–93)

Jonathan Israel
Institute for Advanced Study
March 7, 2012

Prior to the Terror (1793–94), the French Revolution was generally viewed very positively by progressive constitutional thinkers and law reformers. On November 18, 1792, more than a hundred distinguished Anglo-American democrats, including several founders of modern feminism, gathered at the British Club in Paris to celebrate liberty, human rights, and the spread of democracy across the world—what they viewed as the assured democratic future of mankind. In this lecture, Jonathan Israel, Professor in the School of Historical Studies, explores the vast significance of the toasts drunk at this banquet and of the public address that was afterward presented to the French National Assembly. They illuminate the relationship between the French Revolution and modernity, the history of our own time, and the many ironies of the values and propositions that the “British Club” in Paris proclaimed to the world.

Arnold Diffusion via Normally Hyperbolic Invariant Cylinders and Mather Variational Method, Part I

Vadim Kaloshin
Pennsylvania State University; Member, School of Mathematics
March 7, 2012

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 present a new approach to this problem. It is based on a construction of crumpled and flower Normally Hyperbolic Invariant Cylinders. Once existence of these cylinders is shown to construct diffusion we apply Mather variational mechanism. A part of the project is also joint with P. Bernard.