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