UIC Singularity Workshop
Laurentiu Maxim
University of Madison-Wisconsin
Euclidean distance degree and the multiview conjecture
Abstract: The Euclidean distance degree of an algebraic variety is a well-studied
topic in applied algebra and geometry. It has direct applications in
geometric modeling, computer vision, and statistics. I will first
describe a new topological interpretation of the Euclidean distance
degree of an affine variety in terms of weighted Euler characteristics.
As a concrete application, I will present a solution to the open
problem in computer vision of determining the Euclidean distance degree
of the affine multiview variety. Secondly, I will present a solution to
a conjecture of Aluffi-Harris concerning the Euclidean distance degree
of projective varieties. Projective varieties appear naturally in low
rank matrix approximation, formation shape control, and all across
algebraic statistics. (Joint work with J. Rodriguez and B. Wang.)
Saturday June 29, 2019 at 9:00 AM in 636 SEO