Abstract: This talk is a continuation of the presentation ``Shellability of Kohnert posets" given last week. In this talk, we proceed in our quest for a full characterization of graded and (EL-)shellable Kohnert posets. In addition to expanding upon results established during the previous talk, we focus on families of Kohnert diagrams that are of historical and representation-theoretic importance; namely, key diagrams and Rothe diagrams. Key diagrams and Rothe diagrams correspond to Demazure characters and Schubert polynomials, respectively, and both families of diagrams are examples of so-called ``southwest" diagrams. Our presentation will conclude with a conjectured characterization of graded and (EL-)shellable southwest diagrams. Examples and some brief background will be included; however, we assume most of the preliminaries established during the previous talk. The work here represents a portion of an undergraduate research project that began in Spring 2023.
| 4/24 | Celia Kerr'26 & Nick Russoniello | Southwest diagrams and their Kohnert posets |
| 4/17 | Celia Kerr'26 & Nick Russoniello | Shellability of Kohnert posets (Slides) |
| 4/10 | Run Zheng (Hong Kog Poly. U.) | Linear maps preserving certain unitarily invariant norms of tensor products |
| 4/03 | Sarah Day | TDA — a role for algebraic topology in analyzing models and data (Slides) |
| 3/27 | Fan Ge | Logarithmic Derivative of Riemann $\zeta$ and its Random Matrices Analogues, II |
| 3/20 | Vladimir Bolotnikov | Carathéodory interpolation problem over quaternions (Slides) |
| 3/06 | Ethan Shelburne (UBC) | The Schur-positivity of generalized nets (Slides) |
| 2/28 | Joshua Erlich (W&M Physics) | Stochastic processes, quantum fields, and gravity |
| 2/07 | Reem Mahmoud (VCU) | Equitable coloring in 1-planar graphs (Slides) |