Dr. Shipman was invited to present at Cornell:

The OLIVER CLUB presents
Barbara Shipman, University of Rochester
Thursday, March 12 1998 4:15 p.m.
328 White Hall, Cornell University

The geometry of momentum mappings on generalized flag manifolds, connections with a dynamical system, quantum mechanics and the dance of honeybee.

The momentum mapping on a generalized flag manifold sends each orbit of the complex diagonal torus to a convex polytope whose real dimension is the complex dimension of the orbit. This mapping is useful in understanding the types of singularities that arise in a completely integrable system known as the Toda lattice and it also has connections with quantum mechanics and biology. 

In the flag manifold of S1(3,C), the images under the momentum mapping of certain orbits of a 1-dimensional affine group correspond to patterns that arise in the dance that honeybees use to communicate the location of a food source. The geometry contains parameters for both the distance and direction to the source and reflects the discontinuous change in form from the “waggle dance” used for distant sources, into the “round dance” for nearby sources. 

While much is known about how distance and direction are encoded in the dance, little is understood about how a bee processes information biologically to produce the dance. It is known that the dance incorporates physical influences including polarized light, gravity, and the earth's magnetic field. The mathematics has a quantum mechanical interpretation that suggests that the bees may also be perceiving certain quantum fields and using them in the choreography of the dance.

Refreshments will be served at 3:45 in the Math Department Lounge

posted by PLB

PS. I am trying to get hold of the ABJ article, from 1996, if anyone is interested. 

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