Tue, September 5, 2017
3:00 pm - 4:00 pm
Math Tower 154
Title: On the quantum K-rings of flag varieties of type A
Speaker: Hsian-Hua Tseng (Ohio State University)
Abstract: The quantum $K$-ring of a smooth projective variety $X$, introduced by Givental and YP Lee, is a deformation of the Grothendieck ring of coherent sheaves on $X$ defined using holomorphic Euler characteristics on moduli spaces of stable maps to $X$ (these are $K$-theoretic version of Gromov-Witten invariants). In this talk we discuss some properties of the quantum $K$-rings of $X=Fl_{r+1}$, the variety of complete flags in $C^{r+1}$, including:
- a presentation of the quantum $K$-ring;
- finiteness of quantum product;
- canonical polynomial representatives of Schubert classes.
This is based on joint work in progress with David Anderson and Linda Chen.
Seminar URL: https://research.math.osu.edu/agseminar/