Professor Conley invites you to attend the Master's Project Defense of Jonathan Erickson.

WHEN: Wednesday, February 24th, at 3:00pm

"Simplicial Molecules"

ABSTRACT:

The analysis of molecular vibrations is a classical application of the representation theory of groups to a physical problem. If one models the molecule by a system of point-masses attached by springs, the physical theory of small oscillations gives that the behavior of the system near equilibrium can be described by a second-order matrix differential equation. The representation theory of the symmetry group of the molecule can then be used to obtain the eigenvalues and eigenvectors of the relevant matrix, which correspond to vibrational frequencies and modes of the molecule. Such analysis has typically been conducted for molecules which can be embedded in 3-dimensional space; to our knowledge, the vibrational behaviors of higher-dimensional molecules have not been thoroughly studied. We consider simplicial molecules formed by placing identical point-masses at each vertex of a standard simplex and connecting them by identical springs. While the behavior of the molecule is well-known for two-atom, triangular, and tetrahedral molecules, we characterize the frequencies and modes for simplicial molecules of any dimension.