Seminars Sorted by Series

Can we use computational algorithms to make accurate predictions of physical phenomena? In this talk, intended for non-experts, I will give examples where complicated space-time phenomena can be exquisitely captured with simple computational...

DNA copy number abnormalities (CNAs) play an important role in cancer, and are associated with tumor progression as well as clinical outcome. Using microarray based comparative genomic hybridization (CGH), analysis of CNAs across large cohorts of...

High-dimensional data sets often carry meaningful low-dimensional structures. There are different ways of extracting such structural information. The classic (circa 2000, with some anticipation in the 1990s) strategy of nonlinear dimensionality...

How do things hold up? What are the geometric ideas that are involved? One of the principles can be seen with simple models, where sticks are suspended in mid-air with inextendable cables. These were called tensegrities by Buckminster Fuller...

In this talk we discuss the recent area of topological data analysis (TDA) from a probabilistic perspective. The talk falls under two parts. The first part of the talk considers a classic object in topology and geometry, a (Whitney) stratified space...

Topological defects pervade a wide range of physical systems, from superconductors to smectic liquid crystals. The behavior and interactions of such singularities impart many materials with a wealth of rich behavior. Just as flux vortices in the...

This will be a survey talk on equivariant topology methods and how to use them in discrete geometry and combinatorics, based on examples.

Computation of cycles representing classes of homology groups is a fundamental problem arising in applications such as parameterization, feature identification, topology simplification, and data analysis. Variations of the classical Smith Normal...

Suppose a large number of voters have each rated or compared a small subset of a large number of alternatives, how could we rank the alternatives based on these data? The rank aggregation problem is fraught with famous difficulties --- Arrow's...

The number of energetically stable structures that a system of N particles can form grows exponentially with N. Stabilizing any one structure over all others is thus a challenging problem. We consider a system of N spherical colloidal particles that...

I derive a new set of bounds on the percolation threshold of a class of continuum percolation models consisting overlapping convex hyperparticles in d-dimensional Euclidean space. The bounds converge to one another as the space dimension increases...

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...