Category Videos

Videos from the Workshop on Morphometrics, Morphogenesis and Mathematics

In Fall 2018, the CMSA will host a Program on Mathematical Biology, which aims to describe recent mathematical advances in using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems.

The plethora of natural shapes that surround us at every scale is both bewildering and astounding – from the electron micrograph of a polyhedral virus, to the branching pattern of a gnarled tree to the convolutions in the brain. Even at the human scale, the   shapes seen in a garden at the scale of a pollen grain, a seed, a sapling, a root, a flower or leaf are so numerous that “it is enough to drive the sanest man mad,” wrote Darwin. Can we classify these shapes and understand their origins quantitatively?

In biology, there is growing interest in and ability to quantify growth and form in the context of the size and shape of bacteria and other protists, to understand how polymeric assemblies grow and shrink (in the cytoskeleton), and how cells divide, change size and shape, and move to organize tissues, change their topology and geometry, and link multiple scales and connect biochemical to mechanical aspects of these problems, all in a self-regulated setting.

To understand these questions, we need to describe shape (biomathematics), predict shape (biophysics), and design shape (bioengineering).

For example, in mathematics there are some beautiful links to Nash’s embedding theorem,  connections to quasi-conformal geometry, Ricci flows and geometric PDE, to Gromov’s h principle, to geometrical singularities and singular geometries, discrete and computational differential geometry, to stochastic geometry and shape characterization (a la Grenander, Mumford etc.). A nice question here is to use the large datasets (in 4D) and analyze them using ideas from statistical geometry (a la Taylor, Adler) to look for similarities and differences across species during development, and across evolution.

In physics, there are questions of generalizing classical theories to include activity, break the usual Galilean invariance, as well as isotropy, frame indifference, homogeneity, and create both agent (cell)-based and continuum theories for ordered, active machines, linking statistical to continuum mechanics, and understanding the instabilities and patterns that arise. Active generalizations of liquid crystals, polar materials, polymers etc. are only just beginning to be explored and there are some nice physical analogs of biological growth/form that are yet to be studied.

The CMSA hosted a Workshop on Morphometrics, Morphogenesis and Mathematics from October 22-24.

 

The videos of the talks are contained in the youtube playlist below.

 

Big Data 2018 Videos

On August 23-24, 2018 the CMSA hosted our fourth annual Conference on Big Data. The Conference featured many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. Videos of the talks are contained in the youtube playlist below.

You can visit the event page for more information.

 

Videos of the Kickoff Workshop on Topology and Quantum Phases of Matter

On August 27-28, 2018, the CMSA hosted a Kickoff workshop on Topology and Quantum Phases of Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program is to deepen these connections by fostering discussion and seeding new collaborations within and across disciplines.

This workshop is a part of the CMSA’s program on Program on Topological Aspects of Condensed Matter,  and is the first of two workshops, in addition to a visitor program and seminars.

The videos of the talks are contained in the youtube playlist below.
Continue reading

Interview with Dan Spielman

Dan Spielman (Yale University) discusses expander graphs, laplacians matrices, and his CMSA public talk as part of the Special Program on Combinatorics and Complexity.

 


Title: The Laplacian Matrices of Graphs: Algorithms and Applications

Abstract: The Laplacian matrices of graphs arise in many fields, including Machine Learning, Computer Vision, Optimization, Computational Science, and of course Network Analysis. We will explain what these matrices are and why they appear in so many applications.

We then survey recent ideas that allow us to solve systems of linear equations in Laplacian matrices in nearly linear time, emphasizing the utility of graph sparsification—the approximation of a graph by a sparser one—and a recent algorithm of Kyng and Sachdeva that uses random sampling to accelerate Gaussian Elimination.

Symplectic Geometry and Mirror Symmetry with Hansol Hong

Hansol Hong (CMSA Postdoc) describes his current research at the Center of Mathematical Sciences and Applications.

Check out the program page for the Simons Collaboration on Homological Symmetry here: https://cmsa.fas.harvard.edu/simons-collaboration-on-homological-mirror-symmetry/