Galois/Monodromy Groups in 3D Reconstruction

Algebra Seminar
Tuesday, April 16, 2024 - 11:00am for 1 hour (actually 50 minutes)
Skiles 005
Tim Duff – University of Washington
Changxin Ding

Please Note: The seminar has been rescheduled from Monday to Tuesday.

Galois groups embody the structure of algebraic equations arising in both enumerative geometry and various scientific applications where such equations must be solved. I will describe a line of work that aims to elucidate the role of Galois groups in applications where data taken from multiple images are used to reconstruct a 3D scene. From this perspective, I will revisit two well-known solutions to camera pose estimation problems, which originate from classical photogrammetry and are still heavily used within modern 3D reconstruction systems. I will then discuss some less-classical problems, for which the insight we gleaned from computing Galois groups led to significant practical improvements over previous solutions. A key ingredient was the use of numerical homotopy continuation methods to (heuristically) compute monodromy permutations. Time-permitting, I will explain how such methods may also be used to automatically recover certain symmetries underlying enumerative problems.