Workshop on Topology: Identifying order in complex systems

The scaling symmetries of both static and dynamic critical phenomena naturally yield associated power laws and scaling functions. Going beyond simple scalings, we reveal how general emergent symmetries control the coarsening statistics of non...

Cellular structures are compact domains joined along codimension 1 interfaces to fill space. Such cellular microstructures are ubiquitous in materials science and biology. I will briefly review the basic theory of cellular structure evolution via...

Persistent homology is a central object of study in applied topology. It offers a flexible framework for defining invariants, called barcodes, of point cloud data and of real valued functions. Many of the key results of the last several years in the...

In this talk we introduce a discrete and computable version of a mathematical technique known as sheaf theory. This tool provides a method for extracting qualitative topological features of data over a space, rather than of the space itself. We...

Networks arise pervasively in biology, physics, technology, social science, and myriad other areas. They consist of a collection of entities (called nodes) connected via ties, and they typically exhibit a complicated mixture of random and structured...

The rapid improvements in computational power have enabled researchers to produce large amounts of molecular simulation data. Hence there is a pressing need to be able to analyze such data to enhance our understanding of molecular dynamics. However...