Seminars Sorted by Series

I will demonstrate how the Cocke-Kasami-Younger (CKY) algorithm, a standard dynamic programming technique that is normally used in natural language parsing, can be adapted to give us novel insights into the protein folding problem. If we assume that...

"I seemed to see the membraneous and cylindrical tubes tremble beneath the undulation of the waters." - Jules Verne (describing Captain Nemo's underwater garden in 20,000 Leagues Under the Sea) For over half a century, microscopists have seemed to...

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...

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...

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...

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...

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...

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...

Recent experimental advances have opened the door to laboratory realisations of a large range of complex textures with distinctive topological properties, including knots, skyrmions and “Hopf fibrations” in optics, fluids, helical magnets and liquid...

Our goal is to describe extensions of the main tools of signal processing, denoising feature extraction, prediction, regression, to deal with more general data sources such as heterogeneous nonlinearly correlated multisensor inputs, questionnaires...

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...