Created on Oct 17, 2018 12:10 PM PDT
Updated on Oct 18, 2018 11:19 AM PDT
A Hopf monoid is an algebraic structure that many families of combinatorial objects share. The collection of multiplicative functions defined on a Hopf monoid forms a group, called the character group. Aguiar and Ardila (2017) proved that the character groups for the Hopf monoids of permutahedra and associahedra are exponential power series under multiplication and composition, respectively. In this talk I will introduce the Hopf monoid of orbit polytopes, and then I will discuss some of my recent work on determining the structure of the character group of this Hopf monoid.Updated on Oct 18, 2018 02:17 PM PDT
Created on Oct 17, 2018 12:14 PM PDT
The N-body problem in d-dimension space has symmetry group SE(d).
Centre of mass reduction leads to a system with SO(d) symmetry acting
diagonally on positions and momenta. For N=3, d=4 reduction of the SO(4)
symmetry is complicated because the tensor of inertia is non-invertible.
The fully reduced system has 4 degrees of freedom and a Hamiltonian that
is not polynomial in the momenta. The most surprising property of the
reduced Hamiltonian is that it has equilibria that are minima.Updated on Oct 03, 2018 09:54 AM PDT
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