Workshop on Topology: Identifying Order in Complex Systems

Imagine a 1D curve, then use it to fill a 2D manifold that covers an arbitrary 3D object – this computationally intensive materials challenge has been realized in the ancient technology known as knitting. This process for making functional materials...

What is the "right" topological invariant of a large point cloud XX? Prior research has focused on estimating the full persistence diagram of XX, a quantity that is very expensive to compute, unstable to outliers, and far from a sufficient statistic...

Links of strata in singular spaces are fundamental invariants which govern the topology of small neighbourhoods around points in those strata. This talk will focus on inferring links of strata from incomplete information in three completely...

Using the arithmetics of quantum numbers we construct some “approximations” of tilting modules for reductive algebraic groups that might be useful for understanding the generational patterns of tilting characters conjectured by Lusztig and...

We are surrounded by functional networks, from fluid transport in plants and animals to macroscopic elastic scaffoldings and microscopic crystals and materials, and engineered power grids. Often, such networks can be seen as optimized for their...

In this talk, I will give an overview of some recent results motivated by the computation and applications of persistent homology, a theory that creates a bridge between the continuous world of topology and the discrete world of data, and assigns...

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...

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...

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...