The green sea turtle Chelonia midas travels for thousands of miles from the coast of Brazil to a small island in the Atlantic Ocean, Ascension Island. There the turtles lay their eggs into the warm sand on the beach. It is a classic scientific challenge to understand the navigational skills of the turtles and several orienteering mechanisms are discussed, such as geomagnetic information, chemotaxis, atlantic flow patterns etc.
In this talk I will present a mathematical model for the homing of sea turtles and discuss how it can be used to identify the navigational mechanisms of sea turtles. (joint work with K.J. Painter)

Sparsity and compressive sensing have had a tremendous impact in science, technology, medicine, imaging, machine learning and now, in solving multiscale problems in applied partial differential equations, developing sparse bases for Elliptic eigenspaces and connections with viscosity solutions to Hamilton-Jacobi equations. ℓ1 and related optimization solvers are a key tool in this area. The special nature of this functional allows for very fast solvers: ℓ1 actually forgives and forgets errors in Bregman iterative methods.
I will describe simple, fast algorithms and new applications ranging from image processing, machine learning to sparse dynamics for PDE.