Abstract: This talk will give an overview of some problems in the theory of (quasi)conformal maps that arise in computer science.

 

1. The field of computer vision motivated the problem of computing Teichmuller maps, also called extremal quasiconformal maps. I will describe an algorithm that computes Teichmuller maps, and mention some (theoretical and applied) open problems.

2. We will see how the concept of harmonic measure can be used to analyze security aspects of routing algorithms in networks.

3. We will see how the theory of flat surfaces and billiards can be used to construct efficient algorithms for data aggregation in networks. 

4. Finally, we will see how hyperbolic geometry is related to a major unsolved problem in the field of data structures in computer science, called the dynamic optimality conjecture. I will end with an open problem in geometry that is equivalent to this conjecture.