Talks

2020

Infinite geodesics in Carnot groups

Infinite geodesics in Carnot groups naturally arise as tangents to sub-Riemannian geodesics. This permits a study of the geodesic …

2019

A metric viewpoint to sub-Riemannian optimal control

The regularity of solutions to Sub-Riemannian optimal control problems is a long standing open problem, of which relatively little is …

Isometric embeddings in Carnot groups of step 2

Classically an isometric embedding between normed spaces must be affine if the norm on the target is strictly convex. The topic of this …

Necessary conditions for length-minimality in sub-Riemannian geometry

The regularity of length-minimizing curves on sub-Riemannian manifolds is a mystery. In this talk, I will discuss the metric blowup …

2018

Regularity from quantified flatness

A differentiable function is infinitesimally linear. This is a qualitative notion as it is only concerned with the existence of limits …

A metric tangent approach to regularity of geodesics in sub-Riemannian manifolds

The regularity of length-minimizing curves on sub-Riemannian manifolds is an open problem, of which quite little is known compared to …

Non-minimality of corners in subriemannian geometry

The regularity of length-minimizing curves on subriemannian manifolds is an open problem, of which quite little is known outside of …

Tangent and asymptotic cones of geodesics in Carnot groups

The tangent cone of a curve contains all the possible tangents of the curve at some fixed point. The differentiability problem of …

2017

Quasiregular ellipticity

Fiber bundles

A fiber bundle is a generalization of a product space, where one of the projections is sacrificed in order to accommodate a more …

2016

Milnor's exotic structures

Non-minimality of corners in subriemannian geometry

The regularity of length-minimizing curves on subriemannian manifolds is an open problem, of which little is known outside of some …

Non-minimality of corners in subriemannian geometry

The regularity of length-minimizing curves on subriemannian manifolds is an open problem, of which little is known outside of some …

The search for non-smooth geodesics in subriemannian geometry

In Euclidean geometry length-minimizing curves are straight lines. In Riemannian geometry, length-minimizers need no longer be lines in …