Fernando Sanz (Universidad de Valladolid):

The talk  is scheduled 4th february 2021 at 17:15 (Madrid time) in the Master School "Geometry, Analysis and Applications" (https://www.ciem.unican.es/gaia-2021/ )

On the problem of the gradient of an analytic function.

In the 70’s, Lojasiewicz and Thom promoted the investigation of geometrical properties of trajectories of a gradient vector field of a real analytic function. By means of a celebrated inequality of Lojasiewicz, bounded trajectories have finite length and accumulate to a single point. Thom conjectured then that they possess a well-defined tangent at the limit point. The problem was revived around 20 years later with the proof of Thom’s conjecture by Kurdyka, Mostowski and Parusinski and also with Moussu’s stronger Non-oscillation Conjecture: a trajectory of a gradient cannot oscillate. The answer to this last conjecture is only known in dimension two, but still open in general. In this talk, we give a panorama of the achievements concerning this problem, a subject that reveals a particular interplay between analysis of ODEs, real analytic and subanalytic geometry and qualitative theory of dynamical systems.


The talk  is scheduled 4th february 2021 at 17:15 (Madrid time) in the Master School "Geometry, Analysis and Applications" (https://www.ciem.unican.es/gaia-2021/ ). It can be followed online at the Teams link


https://teams.microsoft.com/l/meetup-join/19%3ameeting_OTRlOGNhOWYtODljZS00OTU1LTg0MzUtYzY1YWQ1YzExMDky%40thread.v2/0?context=%7b%22Tid%22%3a%222d38419f-fc3d-4d91-b6d3-eb37480c8fe4%22%2c%22Oid%22%3a%220fb99a40-a80d-4621-a05f-29055e75ca3d%22%7d