In the current project the PI intends to explore some open problems about self-similar fractals and related geometric structures. The fractals considered often arise from the dynamics of groups or the dynamics of maps under iteration, and often a better understanding of their quasiconformal geometry is of crucial relevance. Specific topics for investigation include the geometry of Sierpinski carpets, dynamics of expanding Thurston maps, and instances of entropy rigidity in coarse and metric geometry.

Fractal and self-similar features can be seen in many natural phenomena such as coast- and fault lines, snowflakes and crystal growth, electric discharge or plant growth patterns. This projects intends to contribute to the development of basic methods and tools that are necessary for a deeper understanding of such structures. An important part of this activity is the involvement of young researchers. The goal is to provide them with the mathematical expertise necessary for independent investigations of fractal phenomena.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
1162471
Program Officer
Edward Taylor
Project Start
Project End
Budget Start
2012-07-01
Budget End
2016-06-30
Support Year
Fiscal Year
2011
Total Cost
$405,000
Indirect Cost
Name
University of California Los Angeles
Department
Type
DUNS #
City
Los Angeles
State
CA
Country
United States
Zip Code
90095