Info: The AGDM seminar is a joint seminar of the University of Vienna and TU Wien. In winter semesters, we meet on Tuesdays from 15:00 to 16:30 at the University of Vienna. In summer semesters, we meet on Tuesdays from 15:15 to 16:45 at TU Wien.
Since 2025, we use a mailing-list to advertise the seminar. You can register here.
Place: University of Vienna, Oskar-Morgenstern-Platz 1, BZ 09 (first room on the right on the 9th floor)
Time:Tuesday, 15:00-16:30
| Date: | Tuesday 16.12.2025 |
| Title: | A Probabilistic Bijection from the Twenty-Vertex Model to Arrowed Gelfand-Tsetlin Patterns |
| Speaker: | Atsuro Yoshida (University of Vienna) |
| Abstract: | Di Francesco proved that the number of configurations of a certain twenty-vertex model with fixed west boundary is equal to the number of domino tilings of the so-called Aztec triangle and conjectured that those numbers are counted by a product formula reminiscent of the famous Robbins numbers. Later, this conjecture was proved by Koutschan. Shortly thereafter, Fischer and Schreier-Aigner showed that a certain signed weighted enumeration of so-called arrowed Gelfand-Tsetlin patterns is also equal to the same product formula. This leads to the question of whether there exists a direct combinatorial connection between these three classes of objects. In this talk, we provide a probabilistic bijection between twenty-vertex configurations with free west boundary, generalizations of those with fixed west boundary, and the set of arrowed Gelfand-Tsetlin patterns with bounded entries, with no three equal entries in a row, and with no special little triangles. Since such arrowed Gelfand-Tsetlin patterns are the fixed-point set of arrowed Gelfand-Tsetlin patterns under a certain involution on arrowed Gelfand-Tsetlin patterns at the specialization giving the product formula, our map provides a combinatorial explanation of the equality of the numbers of the two aforementioned objects when the west boundary is fixed to a specific pattern. |
Maintaining a respectful environment is essential to fostering meaningful dialogue and intellectual growth. Participants are expected to refrain from any form of disrespectful or inappropriate behaviour, including offensive comments, harassment, or disruptive conduct. Questions and contributions should be constructive, relevant to the topic, and posed in a professional manner that encourages healthy academic exchange. Harassment of any kind—including verbal, moral or physical—will not be tolerated, and all attendees are urged to uphold these principles to ensure a safe and welcoming atmosphere for everyone.
| 13.01.2026 | Abdulhafeez Abdulsalam | |
| 20.01.2026 | Markus Reibnegger | |
| 27.01.2026 | Mona Gatzweiler |
| 09.12.2025 | Alin Bostan (INRIA, Sorbonne Université) | On Deciding Transcendence of Power Series |
| 09.12.2025 | Anastasia Matveeva (École polytechnique) | On the Integrality of Some P-recursive Sequences |
| 02.12.2025 | Marcus Schönfelder (University of Vienna) | The $1/4$-phenomenon of placement probabilities of tilings in the Aztec diamond |
| 25.11.2025 | Joshua Jeishing Wen (University of Vienna) | Tesler identities for wreath Macdonald polynomials |
| 18.11.2025 | Fabián Levicán (University of Vienna) | Embeddings of weighted projective spaces |
| 11.11.2025 | Nicolas Allen Smoot (University of Vienna) | Some New Examples of Modular Congruence Multiplicities |
| 04.11.2025 | Eva-Maria Hainzl (TU Wien) | Functional equations with catalytic variable 101 |
| 28.10.2025 | Shane Chern (University of Vienna) | The Koutschan-Krattenthaler-Schlosser determinants and their combinatorics |
| 21.10.2025 | Sergio Alejandro Fernandez de Soto Guerrero (TU Graz) | MathMagic: A positroidal action over a deck of cards |
| 14.10.2025 | Christian Krattenthaler (University of Vienna) | Two Topics, Four Lessons |
| 07.10.2025 | Matija Bucic (University of Vienna) | Equiangular lines via improved eigenvalue multiplicity |