we are happy to announce that the "Sub-Riemannian Seminars" will resume in hybrid mode.

https://sites.google.com/view/srseminars

The next session will be held on Tuesday April 5th at 14.30 Paris time (CET), both on Zoom and at Math Department of University of Padova in room 1BC45.

Direct Zoom link:
https://unipd.zoom.us/j/88365065397
Meeting ID: 883 6506 5397

The speaker will be André Belotto (IMJ-PRG, Paris), who will give a talk with title:
"Strong Sard Conjecture in three dimensional analytic manifolds".

Abstract: .
Given a totally nonholonomic distribution of rank two $\Delta$ on a three-dimensional manifold $M$, it is natural to investigate the size of the set of points $\mathcal{X}^x$ that can be reached by singular horizontal paths starting from a same point $x \in M$. In this setting, the Sard conjecture states that $\mathcal{X}^x$ should be a subset of the so-called Martinet surface of 2-dimensional Hausdorff measure zero.

I will present a reformulation of the conjecture in terms of the behavior of a (real) singular foliation. Next, I will present a recent work in collaboration with A. Figalli, L. Rifford and A. Parusinski, where we show that the (strong version of the) conjecture holds in the analytic category and in dimension 3. Our methods rely on resolution of singularities of surfaces, foliations and metrics; regularity analysis of Poincaré transition maps; and on a symplectic argument, concerning a transversal metric of an isotropic singular foliation.
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