Quantum Bruhat graphs and tilted Richardson varieties
- Event Type
- Seminar/Symposium
- Sponsor
- Algebra, Geometry, Combinatorics Seminar
- Location
- 312 David Kinley Hall
- Date
- Nov 9, 2023 3:00 - 3:50 pm
- Speaker
- Jiyang (Johnny) Gao (Harvard)
- Contact
- Alexander Yong
- ayong@illinois.edu
- Views
- 45
- Originating Calendar
- Algebra, Geometry, and Combinatorics Seminar
- A two-point curve neighborhood is the union of degree d rational curves that pass through two given Schubert in a flag variety. These varieties were introduced by Buch-Chaput-Mihalcea-Perrin in 2013. They encode information about the 3-point Gromov-Witten invariants of the flag variety.
In 2005, Postnikov proved there is a unique minimal degree where the curve neighborhood is non-empty. In this case we prove:
- a concrete description in terms of the combinatorics of tilted Bruhat order;
- a stratification with new objects we introduce, called open tilted Richardson varieties;
- a decomposition of open tilted Richardson varieties, extending Deodhar's decomposition of open Richardson varieties.
This is joint work with Shiliang Gao and Yibo Gao.