Quantum Schubert calculus for smooth Schubert divisors in Fl_n

Speaker: Prof. Changzheng Li，Sun Yat-sen University

Inviter: Prof. Yalong Cao，MCM, CAS

Title: Quantum Schubert calculus for smooth Schubert divisors in Fl_n

Language: Chinese 

Time & Venue: 2026.09.03   10:30-11:30   MCM410

Abstract: The cup product of Schubert classes in the classical cohomology of Schubert varieties can be directly read off from that in the classical cohomology of flag varieties. Unlike ordinary cohomology, quantum Schubert calculus for Schubert varieties does not follow from that of flag varieties due to lack of functorial properties in quantum cohomology. In this talk, we will discuss the quantum Schubert calculus for smooth Schubert divisors X in the complete flag varieties Fl_n, including a Borel-type ring presentation of the quantum cohomology, the quantum Schubert polynomials and an Monk-Chevalley formula. We will also explain how this was motived by an on-going project on Peterson program initiated by Rietsch, Yang and myself. This talk is based on my joint work with Jiayu Song, Rui Xiong and Mingzhi Yang.