Department of Mathematics - Master Calendar

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

E-Mail

ayong@illinois.edu

Views

44

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.