Speaker : Professor Myriam Ounaies (University of Strasbourg)
Title : On Casas-Alvero conjecture
Time : 2013-03-08 (Fri) 16:00 - 17:00
Place : Seminar Room 609, Institute of Mathematics (NTU Campus)
Abstract: If a complex polynomial P of degree d has a common zero with each of his d ? 1 first derivatives, then it is of the form . This was conjectured by E. Casas-Alvero in 2001 and is still an open problem. We prove a certain number of restrictions that should be satisfied by a hypothetical counter-example. Some of theses constraints do not depend upon the degree (for instance, there should be at least five distinct roots). Some others are for degrees of the form d = p +1 (p prime) and lead us to a computational verification of the conjecture in degree d = 12 (so far the smallest degree for which the problem was open).