Make Schubert calculus calculable
Organizers
Speaker
Haibao Duan
Time
Thursday, May 9, 2024 3:00 PM - 4:00 PM
Venue
A6-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
Hilbert's 15th problem is an inspiring and far-reaching one. It promoted the enumerative geometry of the 19th century growing into the algebraic geometry founded by Van der Waerden and Andre Weil, and integrated Schubert calculus into many branches of contemporary mathematics. However, despite great many achievements in the 20th century the part of the problem on finding an effective rule performing the calculus has been stagnant for a long time, notably, the Schubert's problem of characteristics, or the Weil's problem on the intersection theory of flag manifolds.
This talk surveys the background, content, and solution of the 15th problem. Our main results are a unified formula for the characteristics, and a systematic description of the intersection theory of flag manifolds. We illustrate the effectiveness of the formula and the algorithm by explicit examples.