Talks

2024

Extendability of sub-Riemannian geodesics

Sub-Riemannian length-minimizing curves that satisfy a geodesic equation can be extended while preserving local optimality. …
Jan 5, 2024 15:00 Helsinki
Slides

2022

Sub-Riemannian manifolds and their abnormal curves

One of the features distinguishing sub-Riemannian geometry from Riemannian geometry is the existence of so called abnormal curves, …
Dec 1, 2022 12:15 Helsinki
Slides

2021

Sub-Riemannian abnormal extremals

The abnormal extremals are the obstruction to regularity of sub-Riemannian geodesics. Even in the case of 3-dimensional analytic …
Dec 1, 2021 16:45 Online
Slides

2020

Carnot groups and abnormal dynamics

The existence of so called abnormal curves is one of the features distinguishing sub-Riemannian geometry from Riemannian geometry. The …
Nov 3, 2020 16:00 Online
Slides

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 …
Feb 25, 2020 14:00 Paris, France

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 …
Oct 15, 2019 16:00 Trieste, Italy

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 …
May 13, 2019 14:15 Jyväskylä, Finland
Slides

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 …
Feb 6, 2019 14:15 Jyväskylä, Finland

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 …
Nov 9, 2018 14:15 Jyväskylä, Finland

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 …
Oct 18, 2018 14:00 Grenoble, France

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 …
Apr 24, 2018 12:30 Padova, Italy

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 …
Feb 22, 2018 15:00 Jyväskylä, Finland
Slides

2017

Quasiregular ellipticity

Oct 23, 2017 10:15 Jyväskylä, Finland
Scanned notes

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 …
Feb 17, 2017 13:00 Jyväskylä, Finland

2016

Milnor's exotic structures

Nov 18, 2016 10:15 Jyväskylä, Finland
Slides

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 …
May 12, 2016 00:00 Voss, Norway
Slides

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 …
May 3, 2016 14:15 Jyväskylä, Finland

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 …
Feb 26, 2016 13:00 Jyväskylä, Finland