| CLAN Research Group | Upcoming Meeting | Directions | Past Meetings |
Date: Monday 15th June, 2026
Location: The Bayes Centre, University of Edinburgh, 47 Potterrow, EH8 9BT
All talks will take place on the top floor in room 5.46.
Invited Speakers:
Isabel Colorado Romero (University of Lancaster)
Anton Izosimov (University of Glasgow)
Iacopo Nonis (University of Leeds)
Michael Shapiro (Michigan State University)
Registration : The registration form closed on Monday 8th June, 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: (outside) room 5.46 |
| 11:45–12:45 | Poisson-Lie groups and cluster structures |
| Michael Shapiro (Michigan State University) | |
| Location: room 5.46 Abstract: It is well known that cluster structures and Poisson structures in the algebra of regular functions on a quasi-affine variety are closely related. In this talk, I will discuss this connection for Poisson structures defined on a simple simply connected complex Lie group G by a pair of classical R-matrices. The key element of the construction is a rational Poisson map from the group with a bracket defined by a pair of suitably chosen standard R-matrices to the same group with an arbitrary pair of R-matrices. In the case of $G=SL_n$ one can build the corresponding cluster structure explicitly and prove its regularity and completeness. Based on joint work with Misha Gekhtman (Notre Dame) and Alek Vainshtein (University of Haifa) |
| 12:45–14:30 | Lunch |
| 14:30–15:30 | w-simple-minded systems in negative cluster categories of type D |
| Isabel Colorado Romero (University of Lancaster) | |
| Location: room 5.46 Abstract: In 2010, König-Liu defined simple-minded systems as the simple-like generators of stable module categories. In 2015, Coelho Simões defined their generalisations, w-simple-minded systems, w-SMSs for short where w>0 is an integer, whose behaviour in negative cluster categories was highly reminiscent of that of cluster-tilting objects in positive cluster categories. In the same paper, she classified w-SMSs in the negative cluster category of type A_n as maximal collections of non-crossing arcs on a disc with marked points on the boundary. In this talk, we will give a combinatorial model for the (-w)-cluster category of type D_n and a classification of its w-SMSs via certain arcs in punctured discs. We will discuss a geometric interpretation of Calabi-Yau reduction, which is a means of constructing a smaller Calabi-Yau category of the same kind, for (-w)-cluster categories of type D_n. Finally, we will give a geometric description of mutation of a w-SMS, which produces a different w-SMS that preserves exactly one object of the original w-SMS. This talk is based on joint work with Raquel Coelho Simões and David Pauksztello. |
| 15:30–16:00 | Coffee Break |
| Location: (outside) room 5.46 |
| 16:00–17:00 | The τ-cluster morphism category of a 0-Auslander extriangulated category |
| Iacopo Nonis (University of Leeds) | |
| Location: room 5.46 Abstract: Let C be a reduced 0-Auslander extriangulated category. Motivated by Pan–Zhu silting reduction for such categories and the theory of signed τ-exceptional sequences developed by Buan and Marsh, we introduce the notion of (signed) presilting sequences in C and establish an explicit bijection between (signed) presilting sequences in C and (signed) τ-exceptional sequences over Λ = End_C(P), where P is a projective generator of C. Motivated by this correspondence, we introduce a new category M(C), called the τ-cluster morphism category of C, whose objects are certain extension-closed subcategories of C and whose morphisms are described in terms of signed presilting sequences. As an application, we recover the τ-cluster morphism category of Λ—a category whose objects are τ-perpendicular subcategories of mod(Λ) and whose morphisms are described in terms of signed τ-exceptional sequences—from M(C). |
| 17:00–18:00 | Cluster structures on simple Lie groups via networks |
| Anton Izosimov (University of Glasgow) | |
| Location: room 5.46 Abstract: Every simple Lie group carries a standard multiplicative Poisson structure. The symplectic leaves of this structure are closely related to double Bruhat cells. Fock and Goncharov showed that every such cell admits an atlas of log-canonical charts whose transition maps are given by Y-type cluster transformations. In type A, these cluster coordinates can be visualized using Postnikov-type networks. I will discuss how this perspective extends to types B and C. Time permitting, I will also present work in progress on an extension to affine groups. |