Previous Conferences & Workshops

There is a canonical pairing on the Brauer group of a surface over a finite field, which is the analogue of the Cassels-Tate pairing on the Tate-Shafarevich group of a Jacobian variety. An old conjecture of Tate predicts that this pairing is...

Consider a Calabi-Yau manifold which arises as a member of a Lefschetz pencil of anticanonical hypersurfaces in a Fano variety. The Fukaya categories of such manifolds have particularly nice properties. I will review this (partly still conjectural)...

Abstract: We first examine the existence, uniqueness, regularity, twist and symplectic properties of compact invariant cylinders with boundary, located near simple or double resonances in perturbations of action-angle systems on the annulus $A^3$...

What is the probability that the number of triangles in the Erd\H{o}s-R\'enyi random graph with edge density $p$, is at least twice its mean? What is the typical structure of the graph conditioned on this rare event? For instance, when $p=o(1)$...

Abstract: We prove that for any non-trivial perturbation depending on any two independent harmonics of a pendulum and a rotor there is global instability. The proof is based on the geometrical method and relies on the concrete computation of several...

We use persistent homology to analyze predictions of protein folding by trying to identify global geometric structures that contribute to the error when the protein is misfolded. The goal is to find correlations between global geometric structures...

We will showcase persistent homology as a promising new tool for use in the study of complicated fluid flows. Through a collection of examples spanning 2D Kolmogorov and Rayleigh-Bénard convection flows to fully-developed 3D turbulence and...

The problems come in two flavors.

Extrinsic Flavor: Given a point cloud in R^N sampled from an unknown probability density, how can we decide whether that probability density is concentrated near a low-dimensional manifold M with reasonable...

Using the geometry of sheaves as the common language, this talk will bridge three separate areas: dynamical systems, signal processing, and data fusion. Because sheaves model consistency relationships between local data, they are easily assembled...