Workshop on Topology: Identifying order in complex systems

In topological data analysis, we often study data by associating to the data a filtered topological space, whose structure we can then examine using persistent homology. However, in many settings, a single filtered space is not a rich enough...

The problem of determining clusters in a data set admits different interpretations depending on whether the data is metric, symmetric but not necessarily metric, or asymmetric. Whereas there is a good degree of understanding of what are the natural...

In the first half of the talk I will give a very compressed introduction into parts of Theoretical Distributed Computing from the point of view of mathematician. I will describe how to construct simplicial models whose combinatorics contains...

The recent advances in our understanding of topological states of free-fermion insulators give some valuable concepts and tools for the analysis of metals. The first part of this talk focuses on low-energy electrodynamic responses of simple metals...

Critical mechanical structures are structures at the verge of mechanical instability. These structures are characterized by their floppy modes, which are deformations costing little energy. On the one hand, numerous interesting phenomena in soft...

In their seminal work on homological sensor networks, de Silva and Ghrist showed the surprising fact that its possible to certify the coverage of a coordinate free sensor network even with very minimal knowledge of the space to be covered. We give a...

Experimental neuroscience is achieving rapid progress in the ability to collect neural activity and connectivity data. Detecting meaningful structure in this data is challenging because the measured quantities are related to more "fundamental"...

Existing formulations of Maxwell's equations encounter numerical difficulties in geometries with sub-wavelength features and/or non-trivial genus. We will describe a new system of boundary value problems for the electromagnetic vector and scalar...

Even simple graphs can be embedded in space ($\mathbb E^3$ or $\mathbb S^3$) in a topologically complex way. If there is a cycle in the graph then there can be knots in the embedding, if there are disjoint cycles then there can be links. However...

Force chains form heterogeneous physical structures that can constrain the mechanical stability and acoustic transmission of granular media. However, despite their relevance for predicting bulk properties of materials, there is no agreement on a...