Conferences / Workshops

 

Apollonian Circle Packings

23 June - 27 June 2014


Aim and description
An ancient theorem of Apollonius of Perga, circa 200BC, proves that for any three mutually tangent circles or lines there are precisely two other circles or lines which are tangent to all three. Thus given four mutually tangent circles, one of them internally tangent to the other three, there is a unique way to inscribe a circle into each of the curvilinear triangles that appear between the circles; iterating this procedure indefinitely gives a construction called an Apollonian circle packing.

One can study an Apollonian circle packing (ACP) from many different angles. Such packings are certainly of interest in classical geometry. But ACP's encode fascinating information of an entirely different flavor: an infinite family of so-called integer ACP's encodes beautiful and mysterious number theoretic properties. Many of these properties can be observed or conjectured experimentally, and the statements of conjectures or theorems in this area can be pleasingly simple. But these properties turn out to be fantastically difficult to prove. ACP's are intimately related to questions on orbits of thin groups, and the summer school will adopt this modern point of view, which has led to recent breakthroughs by employing methods involving geometric group theory, equidistribution, expanders, and the affine sieve.

The aim of the European Women in Mathematics summer school is to provide a stimulating intellectual environment for PhD students from different countries and different mathematical disciplines to learn new mathematics (outside the scope of their own research) and to meet new colleagues. We hope that these contacts will help the forming and development of a network for PhD students and between PhD students and established mathematicians.

Lecturers
Elena Fuchs (UC Berkeley)
Hee Oh (Yale University)

Homepage
EWM/EMS summer school 2014

Practical information
The Institut Mittag-Leffler will provide accommodation, breakfasts, lunches and a conference dinner.

How to apply
The deadline has now passed.

Contact information
If you have any questions regarding the scientific part of the summer school, please contact the organizers on acp.stockholm@gmail.com.
Organizers
Alina Bucur
University of California, San Diego
Pirita Paajanen
University of Helsinki
Lillian Pierce
Duke University