Institute for Pure and Applied Mathematics (IPAM)
Graduate Summer School on Mathematics in Brain Mapping
University of California, Los Angeles, CA
July 12-23, 2004


Plenary Speaker

Conformal Mapping of Brain Surfaces: Circle Packing and the Riemann Mapping Theorem

Ken Stephenson, Department of Mathematics, University of Tennessee, Knoxville

The talk concerns mathematical efforts to "flat map" the human cortex, the highly convoluted but essentially 2D surface of neuronal tissue covering the brain. Flat maps identify the cortex or cortical fragments with regions in the standard geometries: the (round) sphere, the plane, and the hyperbolic plane. The richest mathematical structures on these surfaces are the "conformal" structures and the famous Riemann Mapping Theorem (1851) guarantees that these can be preserved during flat mapping --- there exist "conformal flat maps". However, it is only recently that these maps have become computable in practice. The talk will briefly describe preliminary surface extraction and meshing, then will illustrate various flat map options and associated manipulations available using circle packing methods. The main goal is not visualization but rather development of tools which can bring conformal geometry into the analysis/comparison of cortical structure and function. (Joint work with Monica Hurdal.)



Copyright 2004 by Ken Stephenson. All rights reserved.