# Past Events

If X is a Riemannian manifold, the Laplacian is a second order elliptic operator on X. The hypoelliptic Laplacian bL is an operator acting on the total space of the tangent bundle of X, that is supposed to interpolate between the elliptic Laplacian (when 0b→) and the geodesic flow (when b…

I will discuss some applications of approximate groups including, hopefully, (i) the construction of expander graphs and the affine sieve and (ii) Dirac's problem on the minimal number of ordinary lines (lines with exactly two points) determined by n points in R2, not all collinear.

I will introduce the Gowers norms, which are a way of measuring how close a function f : [N] → C is to a polynomial phase function. I will survey some work in this area and its applications, for example, to counting certain configurations of prime numbers. I will end with a discussion of…

What does it mean for A to be an approximate group? What can one say about approximate groups? What applications does this have? I will try to answer some aspects of the first two of these questions in this talk.

Gromov's work on the nonsqueezing problem showed that embedding questions lie at the heart of symplectic geometry. This talk will discuss a variety of these questions, mostly in four dimensions. It is aimed at a general audience, and will not assume prior knowledge of symplectic geometry.

…Beginning with some simple principles that go back to the ancient Greeks for solving some low-degree equations, we will then turn to some basic questions raised by Euler and Fermat, whose answers have led to surprising applications (secure Internet commerce) as well as to the solution of famous…

The way that a magic trick works can be just as amazing as the trick itself. I will illustrate with performance-level magic whose workings involve a look at combinatorics, number theory, and higher algebra. This talk is aimed at a broad public audience; no prior “mathemagical” knowledge required…

Professor Bhargava’s work on composition laws revolutionized algebraic number theory, and earned him the Cole Prize in number theory, the SASTRA Ramanujan Prize, and a Clay Research Award, as well as a full professorship at Princeton at the age of 29—just two years after earning his PhD. …

String theory and the geometry of the universe's hidden Dimensions.

You can learn more about Professor Shing-Tung Tau https://www.physics.harvard.edu/people/facpages/yau

You can learn more about Professor Tao at https://www.math.ucla.edu/~tao/