Past Events

 Unique continuation property is a fundamental property of harmonic functions, as well as solutions to a large class of elliptic and parabolic PDEs. It says that if a harmonic function vanishes to infinite order at a point, it must be zero everywhere. In the same spirit, we can use the…

I will explain how to construct a rational elliptic
surface out of every non-Euclidean tetrahedra. This surface
"remembers" the trigonometry of the tetrahedron: the length of edges,
dihedral angles and the volume can be naturally computed in terms…

Abstract: Magic angles are a hot topic in condensed matter physics: when two sheets of graphene are twisted by those angles the resulting material is superconducting. I will present a very simple operator whose spectral properties are thought to determine which angles are magical. It comes from…

We will define ribbon concordance of knots, and show that ribbon concordance forms a partial order, answering a conjecture of Cameron Gordon. The result makes use of a bit of real algebraic geometry of representation varieties to compact connected Lie…

Many random networks arising in statistical physics are stochastically homogeneous and can be modeled as stationary random graphs. Often in these models, certain asymptotic geometric and spectral properties are known (or conjectured) to have scaling exponents. These include the fractal dimension…

Direct sum of subspaces defines a map on Grassmannians, which, after taking an appropriate limit, leads to a product-like structure on the infinite Grassmannian.  The corresponding cohomology pullback coincides with a famous co-product on the ring of symmetric functions.  I’ll describe…

Kahn and Kalai conjectured that the threshold of an increasing property is always within a logarithmic factor of the expectation threshold, a quantity often much easier to compute. The Kahn-Kalai conjecture directly implies a number of difficult results in probabilistic combinatorics. I will…

Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is an outstanding open problem. In 2014, Hou-Luo obtained strong numerical evidence that the 3D axisymmetric Euler equations with a boundary can develop a potential finite-time…