Workshop on Topology: Identifying order in complex systems

For a planar domain, a finite point configuration is said to be caging, if the set of Euclidean motions of the domain not hitting the point configuration is bounded. Caging configurations are important in robotics and are a popular topic in...

We discuss some geometric and topological methods that are applied to overcome the large gap problem in Arnold diffusion for a priori unstable Hamiltonian systems. The geometric methods rely on the theory of normally hyperbolic invariant manifolds...

Proteins with knots in their native state were discovered few years ago. Analysis of the entire protein data base indicates that there are quite a few proteins with knots, particularly with slip knots, but still the fraction of proteins with knots...

My collaborators and I have spent a the better part of two decades seeking to develop formally and apply empirically methods of programming work: that is, we want to know how to say what we mean, yet mean what we say to a machine built for...

With recent advances in computing power, numerical studies of nonlinear dynamical systems have become increasingly more popular. However, errors inherent to such studies may obscure the dynamics, or in the very least raise doubts about the existence...

We will see how Hodge theory can be a systemic way of finding geometric structures hidden in (higher dimensional) data.

We construct our understanding of the world solely from neuronal activity generated in our brains. How do we do this? Many studies have investigated how the electrical activity of neurons (action potentials) is related to outside stimuli, and maps...