Today: Geometric Structures seminar - Yuri Sachkov - February 16, 2023 - 2:00 pm (Rome time) - online only

[Miruna - Stefana Sorea]

Dear All,

This is to announce today's seminar from the series "Geometric Structures".

Speaker: Yuri Sachkov (Program Systems Institute, Russian Academy of Science)<http://control.botik.ru/?staff=sachkov&lang=en>

Title: Sub-Lorentzian problem on the Heisenberg group (Yu. Sachkov, E. Sachkova)
Time: Thursday, February 16th, 2023, 2:00 pm (Rome time)
Venue: online only
on zoom at this link:
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
Passcode: geometry

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Abstract:  The sub-Riemannian problem on the Heisenberg group is well known, it is a cornerstone of sub-Riemannian geometry.
It can be stated as a time-optimal problem with a planar set of control parameters, a circle.
The talk will be devoted to its natural variation, the time-optimal problem with a hyperbola as a set of control parameters.
This variation is the sub-Lorentzian problem on the Heisenberg group.

For this problem we will describe the following results:
1) The reachable set from the identity of the group,
2) Pontryagin maximum principle, parameterization of extremal trajectories, exponential mapping,
3) Diffeomorphic property of the exponential mapping, its inverse,
4) Optimality of extremal trajectories, optimal synthesis,
5) Sub-Lorentzian distance,
6) Sub-Lorentzian spheres of positive and zero radii.
Results 1), 2) were obtained by M.Grochowski (2006), the rest results are new.

The talk will be based on the work
https://arxiv.org/abs/2208.04073

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More information can be found here: https://sites.google.com/view/geometric-structures/
Everyone is welcome!

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Miruna-Stefana Sorea
Postdoctoral Researcher
Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy
https://sites.google.com/view/mirunastefanasorea/