- two talks given in the Rose Math Seminar, Fall 2006
- talk at the Indiana MAA spring meeting 2007.

**Title:** Geometry from Chemistry I - Understanding Molecular Dynamics of Bucky Balls

**Abstract:** Buckminsterfullerene is a complex molecule consisting of sixty carbon atoms is an arrangement like a soccer ball, and so the molecules are often called bucky balls. Trying to understands the molecular dynamics of bucky balls leads to some interesting problems in geometry, algebra and differential equations. In the talk, the theory will be described in some detail for very simple objects such as triangular molecules such as water. We then will examine the geometrical issues that come about in modeling the much more complex bucky balls. We are only go to talk about classical dynamics as quantum mechanics add a level of complexity well beyond an hour's talk This work is a collaboration with Dan Jelski of the chemistry department and Guo-Ping Zhang of the ISU physics department. We do not have complete results at this stage, in fact I'd like to describe some problems that could be tackled by undergraduates. I don't plan to use much more beyond multi variable calculus, though understanding of differential equations helps.

**Materials**

- PDF of beamer slides - GeomChem-I.pdf
- Maple Scripts showing molecular vibrations - body3-bond2angle1.mws threebody-threebonds.mws

**Abstract:** Carbon nanotubes are an interesting but as of yet incompletely understood part of
nanotechnology, an area of science that has really grown up in just that last 15 years. From the mathematical
perspective nanotubes have an interesting molecular structure based on the hexagonal honeycomb structure
of graphite. In this talk I will describe the geometry and symmetries of nanotubes. There is an infinite
family of such nanotubes, so describing the structure takes some care. Multivariable calculus should
provide plenty of background to make this talk accessible. There will be a brief recap from lecture
I of this series to motivate the atom labeling problem - a graph theory problem - for nanotubes.

**Materials**

- PDF of beamer slides - GeomChem-II.pdf
- Matlab scripts showing nanotube constructions in the plane - nanoregion.m nanolabeling.m

**Title: **Geometry from Chemistry - Bucky Balls and Nanotubes

This talk summarizes some the main points in Talk I and Talk II into a short talk given at the INMAA spring meeting.

**Abstract:** Nanotechnology has recently become a very hot topic in science and engineering. There
are also some interesting
mathematical questions in geometry and group theory that arise when modeling "nano-dots" and "nano-wires".
This talk
will focus primarily about the geometry behind "single walled carbon nano-tubes" one the most
intensely studied areas in
nano-technology. The talk should be accessible to students who have studied a year of so of calculus.

- PDF of beamer slides - GeomChemINMAA.pdf

Email: allen.broughton@rose-hulman.edu Webpage: http://www.rose-hulman.edu/~brought/ This page last updated on 26 Mar 07.