My primary research interests revolve 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 fitin 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.

Contact me if you have questions about my research, or would like to discuss any other topics.

Contact me if you have questions about my research, or would like to discuss any other topics.

The Theory of Discrete Analytic Functions"

Image 2 - Snow Better

Image 2 - Mixed Example

Image 2 - Carpet

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!

Contact me if you have questions about my research, or would like to discuss any other topics.

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The Theory of Discrete Analytic Functions"

Image 2 - Snow Better

Image 2 - Mixed Example

Image 2 - Carpet

Contact me if you have questions about my research, or would like to discuss any other topics.

Dodecahedral Tiling

Cannon, Floyd, Parry Pattern

Pinwheel

Circle Packing

Collage from my book

Circle Packing images

Image 1 - Lace Agg

Image 2 - Snow Better

Image 1 - Snow Cube

Image 2 - Mixed Example

Image 1 - Dimer Detail

Image 2 - Carpet

A circle packing is a configuration of circles with aspecified 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 fitin 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 in many ways as discrete analogues of analytic functions. Moreover, work flowing from a1985 conjecture of Thurston, proven by Burt Rodin and Dennis Sullivan, shows that classical analytic functions and more general classical conformal objects can be approximated usingcircle packings. Circle packings are computable, so they are introducing an experimental, and highly visual, component toresearch in conformal geometry and related areas. Circle packings are also useful in graph embedding, and have interesting connections to random walks.

Contactme if you have questions about my research, or would like to discuss any other topics.

Dodecahedral Tiling

Cannon, Floyd, Parry Pattern

Pinwheel

Circle Packing

Collage from by book

Circle Packing

Image 1 - Lace Agg

Image 2 - Snow Better

Image 1 - Snow Cube

Image 2 - Mixed Example

Image 1 - Dimer Detail

Image 2 - Carpet

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 ina 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, actin many ways as discrete analogues ofanalytic functions. Moreover, work flowing from a1985 conjecture of Thurston, proven byBurt Rodin and Dennis Sullivan, shows that classical analytic functions and more general classical conformal objects can be approximated using circlepackings. Circle packings are computable, so they are introducing anexperimental, 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.

Contactme if you have questions about my research, or would like to discuss any other topics.