{"ID":2894938,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.10407","arxiv_id":"2507.10407","title":"Numerically Computing Galois Groups of Minimal Problems","abstract":"I discuss a seemingly unlikely confluence of topics in algebra, numerical computation, and computer vision. The motivating problem is that of solving multiples instances of a parametric family of systems of algebraic (polynomial or rational function) equations. No doubt already of interest to ISSAC attendees, this problem arises in the context of robust model-fitting paradigms currently utilized by the computer vision community (namely \"Random Sampling and Consensus\", aka \"RanSaC\".) This talk will give an overview of work in the last 5+ years that aspires to measure the intrinsic difficulty of solving such parametric systems, and makes strides towards practical solutions.","short_abstract":"I discuss a seemingly unlikely confluence of topics in algebra, numerical computation, and computer vision. The motivating problem is that of solving multiples instances of a parametric family of systems of algebraic (polynomial or rational function) equations. No doubt already of interest to ISSAC attendees, this prob...","url_abs":"https://arxiv.org/abs/2507.10407","url_pdf":"https://arxiv.org/pdf/2507.10407v1","authors":"[\"Timothy Duff\"]","published":"2025-07-14T15:53:58Z","proceeding":"cs.CV","tasks":"[\"cs.CV\",\"cs.SC\",\"math.AG\"]","methods":"[]","has_code":false}