Video Lectures

U.S. presidential elections often drive many citizens to vote strategically—to vote for a candidate they do not like in hope of preventing someone they dislike even more from winning. Many who favored Ralph Nader in the 2000 election ended up voting...

JOINT IAS/PU NUMBER THEORY SEMINAR

We give a survey of recent results on conjectures of Heath-Brown and Serre on the asymptotic density of rational points of bounded height. The main tool in the proofs is a new global determinant method inspired...

GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR

We shall recall the spectral terms from the trace formula for G and its stabilaization, as well as corresponding terms from the twisted trace formula for GL(N). We shall then discuss aspects of...

GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR

Suppose that G is a connected, quasisplit, orthogonal or symplectic group over a field F of characteristic 0. We shall describe a classification of the irreducible representations of G(F) if F is...

Decompositions in theorems in classical Fourier analysis which decompose a function into large Fourier coefficients and a part that is pseudorandom
with respect to (has small correlation with) linear functions. The Goldreich-Levin theorem [GL89]...

A k-modal probability distribution over the domain {1,...,N} is one whose histogram has at most k "peaks" and "valleys". Such distributions are a natural generalization of the well-studied class of monotone increasing (or monotone decreasing)...