Discrete mathematical modelling seminar

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Organizer(s) Tetsuji Tokihiro, Ralph Willox

2023/08/30

16:30-17:30   Room #370 (Graduate School of Math. Sci. Bldg.)
Joshua Capel (University of New South Wales)
Classical structure theory for second-order semi-degenerate super-integrable systems (English)
[ Abstract ]
Second-order superintegrable systems have long been a subject of interest in the study of integral systems, primarily due to their close connection with separation of variables. Among these, the 'non-degenerate' second-order systems on constant curvature spaces have been particularly well studies, and are mostly understood.

A non-degenerate system in n-dimensions comprises an (n+1)-dimensional vector space of potentials, along with 2n-1 second-order constants that commute with the Hamiltonian of the system.

In contrast, a semi-degenerate system is characterised by having fewer than n+1 parameters. In this talk, we will discuss the structure theory of truly n-dimensional potentials (meaning potentials that are not just restrictions of (n+1)-dimensional counterparts). We will see that the classical structure theory appears just as rich as the non-degenerate case.

This talk is joint work with Jeremy Nugent and Jonathan Kress.