| CLAN Research Group | Upcoming Meeting | Directions | Past Meetings |
Date: Monday 31st March, 2025
Location: Durham University, Department of Mathematical Sciences and Computer Science building.
Invited Speakers:
Zachary Greenberg (Max Planck Institute for Mathematics in the Sciences, Leipzig)
Alexander Shapiro (University of Edinburgh)
Anja Sneperger (University of Leeds)
Registration : The registration form closed on Monday 24th March, but please email the CLAN Chief directly if you still wish to register.
If you have any questions about the conference then please contact the Clan Chief:
| 11:00–11.45 | Registration and Coffee & Tea. |
| Location: NE2 (second floor, next to room 2033) |
| 11:45–12:45 | Bounded Ratios on Finite Cluster Algebras |
| Zachary Greenberg (Max Planck Institute for Mathematics in the Sciences, Leipzig) | |
| Location: MCS 2068 (2nd floor) Abstract: A classic problem is to find inequalities which are satisfied by polynomials of minors of any totally positive matrix. In 2000, Fallat and Johnson restricted the question to study multiplicative inequalities, an inequality that holds between two products of minors. This is equivalent to identifying the set of ratios of minors which are bounded as functions over the set of totally positive matrices. As these minors are cluster coordinates of cluster algebra, it is natural to generalize this question to an arbitrary cluster algebra. With M. Gekhtman and D. Soskin, we classified these bounded ratios over any finite cluster algebra. Surprisingly the extreme rays of the bounded cone are related to the "U-variables" used to define cluster configuration spaces. |
| 12:45–14:30 | Lunch |
| 14:30–15:30 | Some determinants and relations in cyclic Heronian friezes |
| Anja Sneperger (University of Leeds) | |
| Location: MCS 2068 (2nd floor) Abstract: Motivated by computational geometry of point configurations on the Euclidean plane, and by the theory of cluster algebras of type A, Sergey Fomin and Linus Setiabrata have recently introduced Heronian friezes - the Euclidean analogues of Coxeter’s frieze patterns. I will explain the way these friezes arise from a polygon in the complex plane, and that a sufficiently generic Heronian frieze is uniquely determined by a small proportion of its entries. Then, I shall proceed to some of my results, that hold in the cyclic case, i.e. when the vertices of the polygon are placed on the circle. Namely, I will speak about vanishing of certain determinants in the cyclic case, as well as explain some interesting algebraic relations that hold between the entries of the cyclic Heronian frieze. |
| 15:30–16:00 | Coffee Break |
| Location: NE2 (second floor, next to room 2033) |
| 16:00–17:00 | Whittaker transform and morphisms of cluster varieties |
| Alexander Shapiro (University of Edinburgh) | |
| Location: MCS 2068 (2nd floor) Abstract: Oftentimes in a mathematical context the word "geometry" stands for a category, whose objects are varieties with certain additional structure respected by morphisms. To the best of my knowledge, all morphisms in cluster geometry are coming from freezing cluster variables and/or deleting the frozen ones. In this talk I will present a new family of morphisms, whose construction relies on the Whittaker transform and is inspired by cutting surfaces in higher Teichmüller theory. This is a joint work with Gus Schrader. |
| 17:00–17:40 | Flash Talks |
| Location: MCS 2068 (2nd floor) Anna Barbieri (University of Verona) : Categories from tilings of marked surfaces. Sofia Franchini (University of Lancaster) : A negative Calabi-Yau version of discrete cluster categories. Bethany Rose Marsh (University of Leeds) : Presentations of the braid group of the complex reflection group G(d,d,n). David Pauksztello (University of Lancaster) : Geometric models permit "basis-free" computation via an example. |