Geometric Structures seminar - Alexey Podobryaev - November 10, 2022 - 2:00 pm (Rome time) - online

[Miruna - Stefana Sorea]

Dear All,

This is to announce the next seminar from the series "Geometric Structures".

Speaker:  Alexey Podobryaev<http://control.botik.ru/?staff=podobryaev&lang=en> (Control Processes Research Center, Program Systems Institute of RAS)

Title: Attainable sets for step 2 free Carnot groups with non-negative controls and inequalities for independent random variables

Time: Thursday, November 10th, 2022, 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:
In recent works H.Abels and E.B.Vinberg considered free nilpotent Lie semigroups and suggested a probability interpretaion of such semigroups of step 2. With a help of an algebraic method they obtained an explicit description of the step 2 rank 3 free nilpotant Lie semigroup. This result implies some non trivial inequalities for a system of three independent random variables x, y, z. For example, if P(x < y) = 3/5 and P(y < z) = 3/5, then P(x < z) >= 1/3 (an obvious bound is 1/5).
We regard these free nilpotent Lie semigroups as attainable sets for some control systems. We describe the boundary of the attainable set with a help of first and second order optimality conditions. It turns out that the curved faces of the attainable set consist of the ends of optimal trajectories with the number of control switching corresponding to the face dimension. We give an explicit answer in the case of rank 3 and upper bounds for the number for control switchings in the case of rank 4.

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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/