The question of measuring "handedness" is of some significance in both mathematics and in the real world. Propellors and screws, proteins and DNA, in fact *almost everything* is chiral.  Can we quantify chirality?  Or can we perhaps answer the question:  "Are your shoes more left-or-right handed than a potato?" We can begin with the hydrodynamic…

One approach to studying symplectic manifolds with contact boundary is to consider Lagrangian submanifolds with Legendrian boundary; in particular, one can study exact Lagrangian fillings of Legendrian links. There are still many open questions on the spaces of exact Lagrangian fillings of Legendrian links in the standard contact 3-sphere, and one can use Floer theoretic…

Consider the geometric inverse problem: There is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct the space, a Riemannian manifold with boundary? With a finite set of sources we can only hope to…