Ahlfors Bers Colloquium
May
19-22, 2005
University of
Michigan
Ann Arbor, Michigan
Registration
Organizers
Dick
Canary
Juha
Heinonen
For website problems, contact webmaster
Plenary
Talks
Abstract Detail
| Complex analysis, impedance tomography and quasiconformal mappings
In tomography, or inverse problems in general, one aims to determine the structure of an object from indirect observations. Such methods have a variety of immediate applications, ranging e.g. from medical imaging to different industrial processes. A typical example is to determine the (conductivity) structure of a body from (electrical) measurements on the boundary. From the mathematical point of view this question has a clear and precise formulation, asking if the Dirichlet-to-Neumann boundary data determines the coefficients of a differential operator in the interior of a domain. In this talk we discuss recent joint work with L. Päivärinta (Helsinki) solving the problem in two dimensions. Complex analysis, quasiconformal methods and, in particular, the function theoretic view to elliptic PDE's, developed by Bers, is unavoidable for the solution in its full generality. If time permits we also discuss other related topics, such as applications of Teichmuller theory for improving algorithms in impedance tomography. | ||
|
|