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|
|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
|Date:||03 / 14 / 2012|
|Time:||02:30pm - 03:20pm|