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A monthly online seminar to try and keep up with cluster developments
Welcome to the website of the Cluster Colloquium!
On the 12-th of March 2026, at 17:00 CET we have resumed activities. The second Thursday of every month, we have guest speakers delivering one-hour online talks on current research topics related to cluster algebras and cluster varieties.
Thursday 11 June 2026, 17:00 Central European Time
Thursday 11 June 2026, 17:00 Central European Time
Skein relations in the derived category of gentle algebras
Skein relations in the derived category of gentle algebras
Khrystyna Serhiyenko
(University of Kentucky)
Khrystyna Serhiyenko
(University of Kentucky)
Abstract. Derived categories of gentle algebras can be described via the geometry of surface dissections, where complexes of projective modules correspond to arcs in the surface. Furthermore, morphism are encoded by crossings between the arcs and their cones are given by resolving the crossings. We associate a Laurent polynomial to every (finite) complex and show that the skein relations hold whenever the corresponding arcs cross in the interior. Furthermore, we discuss various specializations of these Laurent polynomials with relations to Grothendieck rings, homology of complexes, and the cluster character map.
This is joint work in progress with Esther Banaian, Azzurra Ciliberti, Ilaria Di Dedda, Yadira Valdivieso-Diaz and Kayla Wright.
Upcoming Talks
Upcoming Talks
Thursday 11 June 2026: Khrystyna Serhiyenko
Previous Talks
Previous Talks
Thursday 14 May 2026: Martin Kalck. Cluster-tilting objects as obstructions to tilting on singular projective varieties
Thursday 9 April 2026: Alexander Shapiro. BFN Coulomb branches and cluster varieties
Thursday 12 March 2026:
Philippe Di Francesco. The ubiquity of the quantum dilogarithm:
from Macdonald Functions to cluster algebraThursday 08.Jan.2026: Lidia Angeleri Hügel. The lattice of torsion pairs and the Ziegler spectrum.
Thursday 11.Dic.2025: Melissa Sherman-Bennett. Plabic tangles, promotion maps, and quasi-cluster homomorphisms.
Thursday 13.Nov.2025: Sergey Fomin. Cyclically ordered quivers.
Thursday 09.Oct.2025: Fan Qin. Quantum cluster structures on simple algebraic groups and the Berenstein–-Zelevinsky conjecture.
Thursday 10.Jul.2025: Thomas Lam. Topology of cluster varieties.
Thursday 12.Jun.2025: Dani Kaufman. Positivity and noncommutative cluster algebras.
Wednesday 14.May.2025: Léa Bittmann. Infinite friezes of affine type D.
Thursday 10.Apr.2025: James Drummond. Tropicalised braid automorphisms for Grassmannian cluster algebras.
Thursday 13.Mar.2025: Ralf Schiffler. Knot theory and cluster algebras.
Thursday 13.Feb.2025: Lauren Williams. Cluster duality and mirror symmetry for Schubert varieties in the Grassmannian.
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