Pierre-Guy Plamondon (Université de Versailles Saint-Quentin)
Thursday, July 9, 2026, 14:00-16:00, Room IC 03/447

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David Whiting (Michigan State University)
Thursday, June 18, 2026, 14:00-16:00, online

Title: tba

Abstract: tba

Esther Banaian (Universität Paderborn)
Thursday, June 11, 2026, 14:00-16:00, Room IC 03/447

Title: Twists, Higher Dimers, and Webs in Grassmannian Cluster Algebras

Abstract: The homogenous coordinate ring of the Grassmannian of k-planes in n-space has an intriguing cluster structure. Some of the seeds of this cluster algebra are indexed by “plabic" graphs. Marsh-Scott and Muller-Speyer showed that dimer covers of plabic graphs encode cluster expansions of (twists of) degree one cluster variables. We give a higher dimer generalization of this result. The coefficients which appear come from an “immanant map” by Fraser-Lam-Le, which relates the coordinate ring of the Grassmannian with the ring of SL_r tensor invariants. It is common to study SL_r tensor invariants through certain planar diagrams called “webs.” We demonstrate that Kuperberg’s SL_3 web basis is (nearly) dual under the immanant map to the recently demonstrated SL_4 web basis of Gaetz-Pechenik-Pfannerer-Striker-Swanson. Combining our two results yields a direct cluster expansion formulas for certain Grassmannian cluster algebras. This is based on joint work with Catania, Gaetz, Moore, Musiker, and Wright which can be found at arXiv:2507.15211.

Alexis Langlois-Rémillard (Universität Bonn)
Thursday, May 21, 2026, 14:00-16:00, Room IC 03/447

Title: On a supercentraliser in the tensor product of a rational Cherednik and a Clifford algebras

Abstract: The Dunkl representation of a rational Cherednik algebra can be seen as a deformation of Weyl algebra by a reflection group and Dunkl operators. We study the supercentraliser of an orthosymplectic Lie superalgebra inside the tensor product of a rational Cherednik algebra and a Clifford algebra. It is called the Dunkl total angular momentum algebra, TAMA for short. A generating set was exhibited in work of Oste, but a full set of relations is not yet proven. In the (non-deformed) Weyl--Clifford algebra, Calvert--De Martino--Oste have conjectured the full ideal of relations, which they proved to be complete for small ranks using a diagrammatic calculus. We report on progress on the representation theory of the TAMA and on joint work with Kafando and Papageorgiou-Kafka on the Weyl--Clifford case.

Khrystyna Serhiyenko (University of Kentucky)
Thursday, May 7, 2026, 14:00-16:00, online [Zoom link]

Title: Flow polytopes and gentle algebras

Abstract: Flow polytopes model the space of unit flows on directed acyclic graphs. They appear in many areas of mathematics including optimization, toric geometry, diagonal harmonics, and representation theory.  Furthermore, many important families of polytopes are examples of flow polytopes including associahedra, generalized permutohedra, Gelfand-Tsetlin polytopes, and certain order polytopes.  In this talk, we will discuss an interesting new connection between combinatorics of flow polytopes and representation theory of gentle algebras.  In particular, DKK triangulations of flow polytopes correspond to tau-tilting posets of the associated gentle algebras.

Kyungmin Rho (Universität Bonn)
Thursday, April 30, 2026, 14:00-16:00, Room IC 03/447

Title: Homological mirror symmetry via tensor-triangular geometry

Abstract: Homological mirror symmetry (HMS) conjectures an equivalence between the Fukaya category of a symplectic manifold and the derived category of coherent sheaves on its mirror scheme. We discuss a tensor-triangular geometric approach to HMS. In particular, we present a necessary and sufficient condition for a Fukaya category to be equivalent to the perfect derived category of a Noetherian scheme. This perspective also provides a method for constructing a mirror scheme from purely Fukaya-categorical data and leads to a natural construction of an A∞-functor.