Events for 09/18/2023 from all calendars

Geometry Seminar

Time: 3:00PM - 3:50PM

Location: BLOC 302

Speaker: Stephen Karp, Notre Dame

Title: Positivity in real Schubert calculus

Abstract: Cchubert calculus involves studying intersection problems among linear subspaces of C^n. A classical example of a Schubert problem is to find all 2-dimensional subspaces of C^4 which intersect 4 given 2-dimensional subspaces nontrivially (it turns out there are 2 of them). In the 1990s, B. and M. Shapiro conjectured that a certain family of Schubert problems has the remarkable property that all of its complex solutions are real. This conjecture inspired a lot of work in the area, including its proof by Mukhin-Tarasov-Varchenko in the 2000s, based on a correspondence between solutions of such a Schubert problem and eigenspaces of a family of commuting operators. I will present a strengthening of this correspondence which explicitly solves the Schubert problem inside the group algebra of the symmetric group. This implies a positive version of the Shapiro-Shapiro conjecture, which thereby resolves some conjectures of Sottile, Eremenko, Mukhin-Tarasov, and myself. This is joint work with Kevin Purbhoo.

Student/Postdoc Working Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Derek Wu, TAMU

Title: Geometry of algebraic curves II: Clifford's theorem