A Counterexample to the Jacobian Conjecture in Dimension Three

Seed Seminar of Mathematics and Physics
AI and the Future of Mathematics and Physics 
The Jacobian conjecture states that for any polynomial map from  to itself, if it is everywhere a local diffeomorphism, then it admits a polynomial global inverse. In this talk, I will present the three-dimensional counterexample to this conjecture posted by L. Alpöge on  and credited to Claude. 
After stating the conjecture and the counterexample, I will explain the geometric interpretation of the counterexample which was posted by A. Jiang and credited to ChatGPT. Finally I will give some observations about the history of the conjecture and its significance.
We answer this problem coming from representation theory using topological tools. On the representation theory side we define extensions of Habiro type rings. On the topological side, we construct a universal Jones link invariant and a universal Alexander link invariant. Putting these together, our universal invariants of geometrical nature take values in the extended Habiro rings that we construct.
More information: https://seedseminar.pages.math.cnrs.fr/program/#november-4-2026
========
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM » (indiquez vos propres prénom et nom) et laissez le corps du message vide.