Finiteness of central configurations of n bodies in the plane via tropical geometry

Time: 9:30 - 11:30, 13 January 2026

Venue: Room 507, A6, Institute of Mathematics

Online (Zoom meeting): https://zoom.us/j/99636681387?pwd=0WscBnehOJig68SqctGluVuA3RwraE.1

Meeting ID: 996 3668 1387

Passcode: 123456

Abstract: We present a new method to attempt proving that, for a given n, there are finitely many equivalence classes of planar central configurations in the Newtonian n-body problem for generic masses.

Our technique relies on tropical geometry and massive polyhedral computation. We have completed a computer-assisted proof for n > 4 and made progress toward a proof for n=6, which is the next unsettled case for this version of Smale's sixth problem. (Joint with Anders N. Jensen).