It is indeed the state capital of Louisiana, on the Mississippi, Baton Rouge, so whether he likes it or not, Software now has a new shiny crimson baton to replace the one that somebody apparently ran off with at the end of the last round. Garth Brooks' recording of Callin' Baton Rouge apparently reached number two on the US country charts, and there is also a Lou Reed song with the title Baton Rouge. And then, of course, there's Me and Bobby McGee, which Janis Joplin took to number one.

As for the geographical connection, I did try to give a highly qualified answer. The red stick that Baton Rouge is named after was a boundary marker, and boundaries—even those that don't follow features of physical geography—do fall into the category of "abstract geographical features". But maybe I pushed the definition a little too far, and if so I apologise. :)

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Oh right, I see... also I looked it up and the mayor has a sonorous title, as you said right at the beginning.

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OK, here goes: VEGETABLE and MINERAL with possible ABSTRACT connotations.

Bravo to the setter and the guesser, lovely.