Workshop on Topology: Identifying order in complex systems

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...

The notion of complexity appears in many different contexts, including in the theory of computation, but also in topology and geometry. In the context of computational complexity there are also famous open questions about separations of complexity...

A standard question in contemporary proteomics asks which properties of proteins may be directly inferred from their molecular structure. Using only X-Ray crystallography data (of the type which is cataloged in the Protein Data Bank), I will outline...

The problem of comparing shapes turns up in different guises in numerous fields. I will discuss a new metric on the space of smooth Riemannian 2-spheres that is well suited for comparing geometric similarity. The metric is based on a distortion...

Experimental and computational model systems composed of frictionless particles in a fixed geometry have a finite number of distinct mechanically stable (MS) packings. The frequency of occurrence for each MS packing is highly variable and depends...