CLAN (Clusters and their Applications in the North)

Date: Monday 9th February, 2026

Location: Lancaster University.

Invited Speakers:
David Cueto Noval (University of Edinburgh)
Oleg Karpenkov (University of Liverpool)
Veronica Kelsey (University of Manchetser)

Registration formally closed on Monday 2nd February, 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: PSC Building

11:45–12:45	SL(2,Z)-tilings in higher dimensions
	Oleg Karpenkov (University of Liverpool)
	Location: PSC Lecture Theatre (A54) Abstract: In this talk we are discussing natural generalisations of SL(2,Z)-tilings to the multidimensional case. We employ geometrical methods to describe the analogue of tameness (decomposability) for different constructions of hypertilings and study necessary and sufficient conditions for hypertilings to be tame. In particular we show how tameness of hypertilings depends on Cayley’s hyperdeterminant.

12:45–14:30	Lunch

14:30–15:30	Cluster Algebras, Stratified Character Varieties with Parabolic Defects and Quantized Multiplicative Quiver Varieties
	David Cueto Noval (University of Edinburgh)
	Location: PSC Lab 2 Abstract: To a gauge quiver and a dimension vector, one can associate an algebra of quantum differential operators D_q. The algebra D_q is constructed as the braided tensor product of algebras associated to each edge, given by RLL-like relations similar to Fock-Rosly approach to character varieties, but with different dimensions at each vertex. We relate such algebras to stratified character varieties with parabolic line defects. We present a way to realize the algebra for each edge inside an upper cluster algebra via transport matrices on a plabic graph. Moreover, we explain how to obtain a cluster description of the whole algebra D_q by gluing the cluster quivers of the different edges, whenever the gauge quiver is a tree. Quantized multiplicative quiver varieties are obtained via quantum Hamiltonian reduction from D_q.

15:30–16:00	Coffee Break
	Location: PSC Building

16:00–17:00	Matroids arising from block designs and their symmetry groups
	Veronica Kelsey (University of Manchetser)
	Location: PSC Lab 2 Abstract: We’ll begin by introducing Steiner systems, IBIS groups and matroids through the running example of the Fano plane. The fact that the Fano plane can be used to construct examples of these three objects is no coincidence, as will become clear when we look at a 1959 result of Hartmanis and a 1995 result of Cameron and Fon-Der-Flaass. Finally we’ll discuss the results of some ongoing explorations into these connections being carried out by Carl-Fredrik Nyberg Brodda and me.

17:00–17:40	Flash Talks
	Location: PSC Lab 2 Benjamin Dequene (University of Leeds) : Resolving subcategories for gentle trees. Hin Chung Henry Tsang (University of Lancashire) : Y-frieze patterns from frieze patterns.