BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yibo Gao (Peking University) DTSTART:20231127T070000Z DTEND:20231127T083000Z DTSTAMP:20260422T161047Z UID:HKUST-AG/28 DESCRIPTION:Title: Quantum Bruhat graphs and tilted Richardson varieties\nby Yibo Gao ( Peking University) as part of Algebra and Geometry Seminar @ HKUST\n\nLect ure held in 3598.\n\nAbstract\nThe quantum Bruhat graph is introduced by B renti-Fomin-Postnikov to study structure constants of the quantum cohomolo gy ring of the flag variety\, with very rich combinatorial structures. In this talk\, we provide an explicit formula for the minimal degree appearin g in the quantum product of any two Schubert classes. Building upon that\, we obtain an Ehresmann-like criterion for the tilted Bruhat order studied by Brenti-Fomin-Postnikov. These results motivate the definition of tilte d Richardson varieties\, which provide geometrical interpretations of tilt ed Bruhat orders. Tilted Richardson varieties are indexed by pairs of perm utations and generalize Richardson varieties in the flag variety. Moreover \, they equal the two-pointed curve neighborhoods of opposite Schubert var ieties studied by Buch-Chaput-Mihalcea-Perrin. We establish several geomet rical properties of tilted Richardson varieties including a Deodhar-like d ecomposition. This is a joint work with Jiyang Gao and Shiliang Gao.\n LOCATION:https://researchseminars.org/talk/HKUST-AG/28/ END:VEVENT END:VCALENDAR