University of Jyväskylä

Dissertation: 15 Sep 2017 Topics in the geometry of non-Riemannian Lie groups (Golo)

Start date: Sep 15, 2017 01:00 PM

End date: Sep 15, 2017 04:00 PM

Location: Mattilanniemi, MaA 211

Sebastiano GoloM.Sc. Sebastiano Nicolussi Golo defends his doctoral dissertation in mathematics ”Topics in the geometry of non -Riemannian Lie groups”. Opponent Dr. Katrin Fässler (Université de Fribourg, Mathématiques, Switzerland) and custos Academy Researcher Enrico Le Donne (University of Jyväskylä). The doctoral dissertation is held in English.

SubRiemannian geometry, as part of Geometry and Analysis on Metric Spaces, has several historical roots. Mostow’s Rigidity Theorem ignited the interest in quasi-conformal mappings on metric spaces. The characterization of groups with polynomial growth posed a bridge between Abstract Algebra and Metric Geometry on Lie groups. The study of hypoelliptic operators found deep connections with the geometry of subRiemannian metrics. Finally, the point of view of Control Theory plays an important role in the study of the regularity of such distances and their geodesics.

 Unlike on Riemannian manifolds, in subRiemannian geometry topological and Hausdorff dimensions may differ, the square of the distance function may be not smooth near the diagonal and small spheres may be not smooth. We are interested in such phenomena on subFinsler manifolds, the general notion of Carnot-Carathéodory spaces.

In the dissertation we tackle several problems that arise in the study of Carnot-Carathéodory spaces, such as the regularity of metric spheres, the asymptotic behaviour of subRiemannian distances and the regularity of minimal surfaces in subRiemannian structures.

Sebastiano Nicolussi Golo has a Master degree in Mathematics at the University of Trento. Since 2012, Sebastiano Nicolussi Golo has been a postgraduate student in Mathematics at the University of Jyväskylä under the supervision of Enrico Le Donne and since 2015 he has worked in cotutelle with the University of Trento with the support of the MAnET project under the supervision of Francesco Serra Cassano.

The dissertation is published in the series Department of Mathematics and Statistics, University of Jyväskylä / Report, number 163, 14 pp., ISBN: 978-951-39-7148-9. It is available at the University Library’s Publications Unit, tel. +358 (0)40 805 3825. Permanent link to the dissertation: http://urn.fi/URN:ISBN:978-951-39-7149-6


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Sebastiano Nicolussi Golo
sebastiano.nicolussi-golo@jyu.fi
+358408053426