Characterising differential operators with non-trivial centralizers

par Prof. JACQUES-ARTHUR WEIL (XLIM, UMR CNRS n°7252)

jeudi 26 nov. 2026, 10:00 → 11:00 Europe/Paris

XR203 (XLIM)

This is joint work with Carlos Arreche (Dallas, TX) and Sonia Rueda (Madrid). 
Differential operators are elements of rings of differential operators such as C(x)[d/dx] (where multiplication by d/dx is the composition operators). In general, given a differential operator L in C(x)[d/dx], the only differential operators A which commute with L, i. e A.L=L.A are the elements of C[L]. 
Characterizing operators which have a non-trivial centralizer is a long standing open problem. It has important ramifications and applications - the conditions on the coefficients of L to have a non-trivial centralizer are linked to (hierarchies of) partial  differential equations such as KDV, KP equations, etc. 
In this work, we provide a complete algorithmic answer to the question of characterizing operators which have a non-trivial centralizer. The results will be presented with a limited quantity of tools so that everyone can follow most of the talk without being overwhelmed.