Workshop on Topology: Identifying order in complex systems

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...

Nazarov and Sodin have shown that the zero set of a random real homogeneous polynomial in n+1 variables and of large degree has many components and the same is true for the random harmonic such polynomial ("mono-chromatic waves") .We show that for...