Quasiconformal methods in impedance tomography:  
       Solution to the Calderon Problem

            Kari Astala (Helsinki)

I will discuss recent joint work with Lassi Paivarinta.  Impedance 
tomography is a method whereby one tries to obtain the internal 
structure of an object (such as brains or other organs) purely from 
electrical measurements of the boundary or surface of that object. 
The theoretical question is to decide whether one can fully recover 
the internal structure from these boundary measurement and this is 
known as the Calderon problem.  This problem has been solved in a 
number of cases,  but usually with the apriori assumption that the 
internal structures are smooth,  which is usually (and in cases of 
particular importance where one might be trying to identify 
discontinuities in structure (such as tumors)) not a very realistic 
assumption.

Here we will talk about a new approach,  solving the Calderon problem 
generally in two dimensions using quasiconformal methods.  The 
methods lead to potential practical implementations.