Office: Boyd 408(F) Boyd 326 (S)
Office Phone: 2-2587
Description
I lead a
research
oriented focus group on circle packing. Circle packing were first
introduced by Koebe (1930), forgotten for along time,
re-discovered by Andreev (1970) and got their publicity by
Thurston (1980's).
Circle packing are very useful in understanding various aspects of
conformal and low dimensional topology.
We will pretty much follow the
group interests. Topics for further research may include:
Discrete analytic Functions
Approximation of conformal maps by circle mapping
maps
Creating new discrete analytic maps using circle
packing
Apollonian packing
Random walks and Circle packing
and much more. This is a field which leads quickly to open
questions and so far the techniques in the field have been a
beautiful mix of combinatorics, conformal maps, differential geometry
and topology. If you can program and enjoy it, you will have many
opportunities to use your skills and experiment
mathematics.
Prerequisites
While the very first
definitions in this field are simple, the theory becomes quite involved
and tricky very quickly.
You definitely need to be beyond your series of Linear Algebra and
Calculus. Exposure to Differential geometry and\or complex analysis
and\or programming is highly desired. Equally important for me (and
probably even more) is how self motivated and self starter you are.
In order for you to see if the subject is of interest to you and for me
to get a gauge of your compatibility with what I require, please
do the following:
1. Have a look at the Gallery ;
if the pictures are something you would like to understand, read a
little bit