Abstract: The totally positive flag variety is the subset of the complete flag variety Fl(n) where all Plücker coordinates are positive. By viewing a complete flag as a sequence of subspaces of polynomials of degree at most n-1, we can associate a sequence of Wronskian polynomials to it. I will present a new characterization of the totally positive flag variety in terms of Wronskians, and explain how it sheds light on conjectures in the real Schubert calculus of Grassmannians. In particular, a conjecture of Eremenko (2015) is equivalent to the following conjecture: if V is a finite-dimensional subspace of polynomials such that all complex zeros of the Wronskian of V are real and negative, then all Plücker coordinates of V are positive. This conjecture is a totally positive strengthening of a result of Mukhin, Tarasov, and Varchenko (2009), and can be reformulated as saying that all complex solutions to a certain family of Schubert problems in the Grassmannian are real and totally positive.
- Cet évènement est passé.
08
octobre
Vendredi
Steven Karp (UQAM): Wronskians, total positivity, and real Schubert calculus
08 octobre 2021, 11:00
- 08 octobre 2021, 12:00
Détails
Date :
octobre 8, 2021
Heure :
11:00 am - 12:00 pm
Lieu
Venue Name:
PK-4323