PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Jason Morton.

Title:Mapping the Connectome with Convex Algebraic Geometry
Seminar:Applied Algebra Seminar
Speaker:Lek-Heng Lim, University of Chicago
Abstract Link:
The latest image of the week (#32) in Scientific American is that of a human brain connectome -- an ambitious project to provide a complete map of neural connectivity and a recent source of excitement in the neuroscience community. Just as the human genome is a triumph of marrying technology (high throughput sequencers) with theory (dynamic programming for sequence alignment), the human connectome is a result of a similar union. The technology in question is that of diffusion magnetic resonance imaging (dMRI) while the requisite theory, we shall argue, comes from a combination of harmonic analysis and algebraic geometry. The two main mathematical problems are (i) reconstructing a homogeneous polynomial representing a real-valued function on a sphere from dMRI data; and (ii) analyzing the homogeneous polynomial via a decomosition into a sum of powers of linear forms. We will survey the algebraic geometry associated with (ii) and discuss a technique that combines (i) and (ii) for mapping neural fibers. This is joint work with T. Schultz of MPI Tubingen.

Room Reservation Information

Room Number:MB106
Date:03 / 14 / 2012
Time:02:30pm - 03:20pm