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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 9-th of October 2025, 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 12.Mar.2026, 17:00 Central European Time
Thursday 12.Mar.2026, 17:00 Central European Time
The ubiquity of the quantum dilogarithm:
from Macdonald Functions to cluster algebra
The ubiquity of the quantum dilogarithm:
from Macdonald Functions to cluster algebra
Philippe Di Francesco
(Université Paris Saclay,
University of Illinois at Urbana-Champaign,
Académie des Sciences, Institut de France).
Philippe Di Francesco
(Université Paris Saclay,
University of Illinois at Urbana-Champaign,
Académie des Sciences, Institut de France).
Abstract. The theory of q-Whittaker functions for classical types is known to have a (quantum) cluster algebra realization. In this framework, a natural connection with the quantum dilogarithm is known. We show how this extends to the more general case of Macdonald theory in type A. We propose new Givental-like and Mellin-Barnes-like expressions for the Macdonald functions, and explore their properties. These involve heavy use of quantum dilogarithms.
(loosely based on ongoing collaborations with M. Bershtein, J.-E. Bourgine, R. Kedem, V. Pasquier and J. Shiraishi).
Upcoming Talks
Upcoming Talks
Thursday 12 March 2026:
Philippe Di FrancescoThursday 9 April 2026: tba
Thursday 14 May 2026: tba
Thursday 11 June 2026: tba
Previous Talks
Previous Talks
Thursday 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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