### Richard Montgomery UC Santa Cruz

The Hyperbolic Geometry and three and four -body problems Yeshiva University, 215 Lexington Ave, Room 506. Observe the unusual day and time.We begin by deriving the hyperbolic plane with its geodesic flow as the ‘scale plus symmetry reduction’ of a three-body problem in the Euclidean plane. The potential is homogeneous of degree -2, with denominator being the area squared of the triangle whose vertices are the three masses. The reduction method involves the Jacobi-Maupertuis metric in a central way and was used in my paper `Putting Hyperbolic pants on a three body problem'. We will also review some aspects of that paper and some surprises from work of Connor Jackman on an analogous problem arising in the 1/r*r 4-body problem.