Event
Christiane Rousseau, Université de Montréal
Tuesday, September 26, 2017 15:30to16:30
The Geometry behind the Stokes Phenomenon
One way of understanding the structure of the solution set of a linear differential system in the neighbourhood of a singular point is to bring the system to a normal form through a change of coordinates: this highlights some special solutions that are eigensolutions of the monodromy around the singular point. It is also a way of deciding if two systems are locally analytically equivalent. However, the normalizing change of coordinates generically diverges in the neighbourhood of an irregular singular point. Why? Since an irregular singular point is a multiple singular point, this mysterious phenomenon becomes natural when one embeds the differential system in an unfolding that separates the singular points. The obstruction to the convergence is explained by the fact that it is not the same solutions that are eigensolutions of the monodromy around different singular points. The phenomenon is studied through constructing the modulus space for the germs of unfoldings of linear systems under analytic equivalence. In the case of nonresonant irregular singularities, this construction has been achieved in joint works with Caroline Lambert and Jacques Hurtubise. (Slides will be in English; the language of presentation will be decided at the lecture.)
CRM, UdeM, Pavillon André-Aisenstadt, 2920, ch. de la Tour, salle 4336