Video Lectures

The Unique-Games Conjecture is a central open problem in the field of PCP’s (Probabilistically Checkable Proofs) and hardness of approximation, implying tight inapproximability results for wide class of optimization problems.

We will discuss PCPs...

Let X be the infinite graph partially pictured below, the "free product graph" C_4 * C_4 * C_4. Let FinQuo(X) be the set of all finite graphs G that covered by X (i.e., that 'locally resemble' X; i.e., that consist of C_4's joined 3-to-a-vertex). A...

The Zilber-Pink conjecture is a far reaching finiteness conjecture in diophantine geometry, unifying and extending Mordell-Lang and Andre-Oort. This lecture will state the conjecture, illustrate its varied faces, and indicate how the point-counting...

This lecture will describe the historical context and some key properties of o-minimality. It will then describe certain results in functional transcendence, generalizing the classical results on exponentiation due to Ax, and sketch how they can be...

We are living in a golden era for testing gravitational physics with precision experiments. This talk will present new results using a variety of tests with radio pulsars. These results will be placed in context of other experiments (including LIGO...

This introductory lecture will describe results about counting rational points on certain non-algebraic sets and sketch how they can be used to attack certain problems in diophantine geometry and functional transcendence.