Previous Conferences & Workshops

Ruzsa asked whether there exist Fourier-uniform subsets of $\mathbb{Z}/N\mathbb{Z}$ with very few 4-term arithmetic progressions (4-AP). The standard pedagogical example of a Fourier uniform set with a "wrong" density of 4-APs actually has 4-AP...

In the last few years, expanders have been used in fast graph algorithms in different models, including static, dynamic, and distributed algorithms. I will survey these applications of expanders, explain the expander-related tools behind this...

In a vertex expanding graph, every small subset of vertices neighbors many different vertices. Random graphs are near-optimal vertex expanders; however, it has proven difficult to create families of deterministic near-optimal vertex expanders, as...

The quantum unique ergodicity conjecture of Rudnick and Sarnak concerns the mass equidistribution in the large eigenvalue limit of Laplacian eigenfunctions on negatively curved manifolds. This conjecture has been resolved by Lindenstrauss when this...

We discuss a one-phase degenerate free boundary problem which arises from the minimization of the so-called Alt-Phillips functional $$\int_\Omega (|\nabla u|^2 + u^\gamma \chi_{\{u>0\}}) dx$$ for $\gamma \in (-2,0).$ We establish partial regularity...

I will discuss pointwise ergodic theory as it developed out of Bourgain's work in the 80s, leading up to my work with Mirek and Tao on bilinear ergodic averages.