Video Lectures

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...

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"...

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...

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...

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...

Hamiltonian spectral invariants have had many interesting and important applications in symplectic geometry. Inspired by Le Calvez's theory of transverse foliations for dynamical systems of surfaces, we introduce a new dynamical invariant, denoted...

Can one predict the future arrangements of planets over extremely large time periods? For centuries this issue has triggered dreams of curious people, and hot debates by specialists including Newton, Lagrange, Poincare, Kolmogorov, Laskar, and...

In the mid 1980s, Mark Green and I conjectured that one could read off the gonality of an algebraic curve $C$ from the syzygies among the equations defining any one sufficiently positive embedding of $C$. Ein and I recently noticed that a small...

Searching literature you will find the following statement (I'm paraphrasing): "If $X_1,X_2$ are nonsingular schemes proper over a complete DVR $R$ with residue characteristic 0, and $\phi: X_1 \to X_2$ is birational, then $\phi$ can be factored as...