Mathematics Wiskunde

Tuesday 12 December 2023

Algorithmic Classification of Singularities with a non-degenerate Newton Boundary

Speaker: Dr Magdaleen Marais, University of Pretoria
Time: 13:00
Venue: Mathematics Division, Room 1006

Arnold classified complex isolated hypersurface singularities with modality up to 2 or Milnor number up to 16 by right-equivalence, and devised an algorithm to identify their normal forms. In this talk, we extend Arnold’s work to a large class of singularities which is unbounded with regard to modality and Milnor number. We prove a normal form theorem which describes for any corank 2 germ with a non-degenerate Newton boundary a normal form of its stratum with constant Milnor number. We develop an algorithmic classifier, which computes for a given such germ a normal form, as well as its equivalence class, which amounts to determining the moduli parameters.