Seminars Sorted by Series

Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. I'll introduce the notions of a 'swatch' and a 'cloth', which provide a...

In two-dimensional grain structure, one observes that grains with a small number of sides tend to be surrounded by grains with a large number of sides, and vice-versa. The Law of Aboav--Weaire gives this observation a mathematical formulation, that...

We will discuss the notion of loops in linguistic structures, mainly in dictionaries. In a simplified view, a dictionary is a graph that links every word (vertex) to a set of alternative words (the definition) which in turn point to further...

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...

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...

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...

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"...

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...

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...

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...

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 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 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...

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...

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...

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 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...

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...