Thematic day on sub-Lorentzian geometry



DATE: NOVEMBER 12, 2014,

in the framework of the Institute Henri Poincare scientific trimester

"Geometry Analysis and Dynamics on sub-Riemannian manifolds"


ORGANISERS:

Marek Grochowski, Associate Professor, Department of Mathematics, Cardinal Wyszynski University, Warsaw, Poland, (m.grochowski at uksw.edu.pl)
and
Irina Markina, Professor, Department of Mathematics, University of Bergen, Bergen, Norway, (irina.markina at uib.no)


PARTICIPANTS

1. Marek Grochowski, Associate Professor, Department of Mathematics, Cardinal Wyszynski University, Warsaw, Poland, (m.grochowski at uksw.edu.pl)

Title of the talk: Invariants for sub-Lorentzian structures in dimension 3.

Abstract: I will construct invariants for contact sub-Lorentzian structures on 3D manifolds. Then I will show how to apply them to the Martinet type sub-Lorentzian structures.

2. Irina Markina, Professor, Department of Mathematics, University of Bergen, Bergen, Norway, (irina.markina at uib.no)

Title of the talk: Recent progress in sub-Lorentzian geometry.

Abstract: I will present short introductory talk briefly explaining the main ideas of the sub-Lorentzian geometry.

3. Fátima Silva Leite, Professor, Department of Mathematics and Institute of Systems and Robotics, University of Coimbra, Coimbra, Portugal, (fleite at mat.uc.pt)

Title of the talk: Rolling Lorentzian spheres and quadratic Lie groups.

Abstract: Rolling a manifold over another manifold, under the non-holonomic constraints of no twisting and no slipping, fits into the framework of sub-Riemannian geometry. In this talk we will discuss rolling motions of pseudo-Riemannian submanifolds, with particular emphasis to Lorentzian spheres and quadratic Lie groups.

4. Ben Warhurst, Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, Poland, (benwarhurst68 at gmail.com)

Title of the talk: Symmetries of certain Sub-Lorentzian contact Lie groups.

Abstract: This talk will discuss some applications of Tanaka Theory and Cartan equivalence to the problem of determining the symmetries of some three dimensional Sub-Lorentzian contact Lie groups. Some connections with the geometry of second order ordinary differential equations will also be discussed.

5. Stephan Wojtowytsch, PhD student, Department of Mathematics, University of Durham, Durham, UK, (Wojtowytsch at stud.uni-heidelberg.de, Stephan.Wojtowytsch at gmail.com)

Title of the talk: The Alexandrov Topology in sub-Lorentzian Geometry.

Abstract: Unlike sub-Riemannian metrics, sub-SemiRiemannian ones do not induce a metric distance function. In sub-Lorentzian Geometry, instead we can obtain a partial ordering on the manifold which in the interpretation of general relativity carries meaning relating to causality. The interval topology with respect to this partial order in particular is linked to the property of strong causality. This talk investigates similarities and differences between these phenomena in the classic Lorentzian and the sub-Lorentzian setting.

6. Mauricio Godoy Molina, Postdoc, Department of Mathematics, University of Bergen, Bergen, Norway, (mauricio.godoy at gmail.com)

Title of the talk: The recent history of sub-semi-Riemannian geometry.

Abstract: This talk is an extension of prof. Markina's overview, with a view towards a natural generalization of sub-Lorentzian geometry, namely sub-semi-Riemannian geometry. We discuss Grochowski's introduction of the sub-Lorentzian Heisenberg group, via control systems; applications to some problems in electromagnetism; and then focus our attention on the analogue of $H$-type groups in this context, and their classification.

7. Alexander Vasiliev, Professor, Department of Mathematics, University of Bergen, Bergen, Norway, (alexander.vasiliev at math.uib.no)

8. Erlend Grong, Postdoc, Department of Mathematics, University of Luxembourg, Luxembourg, (grongpost at gmail.com)

9. Christian Autenried, PhD student, Department of Mathematics, University of Bergen, Bergen, Norway, (christian.autenried at math.uib.no)

10. Dmitri Alekseevsky, Professor, Department of Mathematics, Mazaryk University, Brno, Czech Republic, (daleksee at staffmail.ed.ac.uk)

11. Yacine Chitour, Professor, University of Paris XI, Paris, France, (yacine.chitour at lss.supelec.fr)

12. Yuri Sachkov, Chief of Control theory laboratory at Program Systems Institute, Professor, University of Pereslavl, Pereslavl, Russia, (achkov at sys.botik.ru)

Title of the talk: Sub-Lorentzian geodesics in the Engel group joint work with Qihui Cai, Tiren Huang, Xiaoping Yang.

Abstract: We consider the rank 2 left-invariant sub-Lorentzian structure on the Engel group. First we study geometric prperties of horisontal curves of the underlying distrubution. Second, we obtain an explicit parameterization of sub-Lorentzian geodesics by Jacobi's elliptic functions. Third, we study symmetries and Maxwell points of the exponential mapping and derive the corresponding lower bounds on the cut time.

13. Alexei Mokhovikov, PhD student, Sobolev Institute of Mathematics, Novosibirsk, Russia, (moxobukob@gmail.com)

Title of the talk: Reachable set in sub-Lorentzian geometry on the Engel group.

Abstract: The talk is focused on the description of the set that can be attained by non-spacelike future directed curves. The Engel group is considered as a sub-Lorentzian manifold with a special choice of an orthonormal basis with respect to the Lorentzian metric on 2-dimensional distribution. The behavior of the curves that approach the boundary of the reachable set is described.


Tentative program for the thematic day on sub-Lorentzian geometry can be found HERE


Recent progress in the sub-Lorentzian geometry and references you can find HERE


If you want to add something, please, do not hesitate to write by e-mail to Irina Markina (irina.markina at uib.no)