Seminars Sorted by Series

We discuss a family of ideas, algorithms, and results for analyzing various new and classical problems in the analysis of high-dimensional data sets. These methods we discuss perform well when data is (nearly) intrinsically low-dimensional. They...

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...

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...

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...

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...

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...

Motivated by thematic similarities between persistent homology and magnitude homology, we describe a simplicial construction associated to a metric space. This construction is determined by (apart from the metric space itself) a choice of two...

We first describe mathematical foundation of DSGRN (Dynamic Signatures Generated by Regulatory Networks), an approach that provides a queryable description of global dynamics of a network over its entire param- eter space. We describe a connection...

DNA rearrangement is observed at developmental and evolutionary scale. The recombination process can be directly modeled by 4-regular graphs and Gauss codes, also called double occurrence words. We discuss properties of these graphs, their spatial...

Polymers are macromolecules that cannot cross each other without breaking their bonds. This leads to polymer chain entanglement which determines bulk viscoelastic responses of the material. Understanding the relation between entanglement and...

I'll talk about two related projects, with two different groups, both aiming to see three-dimensional manifolds "from the inside". That is, we generate images assuming that light travels along geodesics in the geometry of the manifold. The first...