KEN STEPHENSON
MATHEMATICIAN

Ken Stephenson - Circle Packing
Ken Stephenson
Mathematician

Ken Stephenson
BACKGROUND & RESEARCH
KEN STEPHENSON
BACKGROUND & RESEARCH

I spent my academic career as a mathematics professor at the Univ. of Tennessee, and I'm still actively involved with research. My research interest revolves around circle packing: connections to analytic function theory, Riemann surfaces, computational conformal structures, and applications.

A circle packing is a configuration of circles with a specified pattern of tangencies. The circles typically must assume a variety of different sizes in order to fit together in a prescribed tangency pattern. It is easy to confuse this with the well known topic of 'sphere packing', how many ping pong balls fit in a box car, but there is almost no contact between these two topics!

Circle packings were introduced by William Thurston in his Notes. Maps between circle packings, which preserve tangency and orientation, act many ways as discrete analogues of analytic functions. Moreover, work flowing from a 1985 conjecture of Thurston, proven by Burt Rodin and Dennis Sullivan, shows that classical analytic functions and more general classical conformal objects can be approximated using circle packings. Circle packings are computable, so they are introducing an experimental, and highly visual, component to research in conformal geometry and related areas. Circle packings are also useful in graph embedding, and have interesting connections to random walks.

Additional research topics I'm interested in are analysis, computational and applied mathematics, and probability and stochastic processes. Please contact me if you have questions about my research, or would like to discuss any other topics.

BACKGROUND & RESEARCH

I spent my academic career as a mathematics professor at the Univ. of Tennessee, and I'm still actively involved with research. My research interest revolves around circle packing: connections to analytic function theory, Riemann surfaces, computational conformal structures, and applications.  

A circle packing is a configuration of circles with a specified pattern of tangencies. The circles typically must assume a variety of different sizes in order to fit together in a prescribed tangency pattern. It is easy to confuse this with the well known topic of 'sphere packing', how many ping pong balls fit in a box car, but there is almost no contact between these two topics!

Circle packings were introduced by William Thurston in his Notes. Maps between circle packings, which preserve tangency and orientation, act many ways as discrete analogues of analytic functions. Moreover, work flowing from a 1985 conjecture of Thurston, proven by Burt Rodin and Dennis Sullivan, shows that classical analytic functions and more general classical conformal objects can be approximated using circle packings. Circle packings are computable, so they are introducing an experimental, and highly visual, component to research in conformal geometry and related areas. Circle packings are also useful in graph embedding, and have interesting connections to random walks.

Additional research topics I'm interested in are analysis, computational and applied mathematics, and probability and stochastic processes. Please contact me if you have questions about my research, or would like to discuss any other topics.
Circle Packing
Dodecahedral tiling
Cannon, Floyd & Parry
Circle Packing
Circle packing image
Ken Stephenson, Mathematician
Graphics property of Ken Stephenson
Ken Stephenson, Mathematician
Graphics property of Ken Stephenson