Previous Special Year Seminar

The Schmidt subspace theorem is a deep generalization of Roth's theorem in Diophantine approximation to the setting of hyperplanes in projective space. Another well-known generalization of Roth's theorem is the theorem of Wirsing, which extends Roth...

I will discuss several results on mean-values of multiplicative functions, notably Halasz's method for estimating such averages. In the second lecture I will show how this circle of ideas can be used to derive "weak subconvexity" bounds for L...

I will discuss several results on mean-values of multiplicative functions, notably Halasz's method for estimating such averages. In the second lecture I will show how this circle of ideas can be used to derive "weak subconvexity" bounds for L...

In this talk, I will discuss several topics related to transverse knots in contact 3-manifolds. I will introduce a conjecture on the maximal self-linking number of a topological knot in the standard contact 3-sphere. I will show how to apply braid...

We formulate several new boundary value problems for the 2D Navier-Stokes system. In all cases, we obtain quantitative decay estimates of the Fourier modes for both the vorticity and the velocity. In some special cases we found that the Fourier...

In this talk, I will first give an overview of recent progress on the scattering conjecture and rigidity conjecture for mass critical NLS. Then I will describe our recent results concerning both conjectures for L_2 initial data. I will also discuss...

We construct new solutions to the $\sigma_k$-Yamabe problem on compact manifolds by considering the connected sum of two nondegenerate solutions $(M^n_1,g_1)$ and $(M^n_2,g_2)$, for any $2 \leq 2k < n$.