Spring 2026

• [Monday] 02/16/2026 @12:45 (SAS 4201) - Hyun Kyu Kim (김현규) (Korea Institute for Advanced Study)
  Title: Canonical bases for cluster varieties and moduli spaces of local systems on a surface
  Abstract: Cluster varieties are schemes defined by gluing algebraic tori together by special birational maps called cluster mutations. From a quiver, one can construct the cluster A-variety and the cluster X-variety.  Fock and Goncharov’s duality conjectures predict the existence of a canonical basis of the algebra of regular functions on one of these cluster varieties, enumerated by the tropical integer points of the other. I will give an introductory overview of this topic, starting with elementary examples, and later focusing on the class of examples coming from moduli spaces of local systems on a surface. I will briefly mention recent developments involving quantum topology and mirror symmetry of log Calabi-Yau varieties, and present some open problems if time allows.
  
  

• 03/11/2026 - Daping Weng (UNC Chapel Hill)
  Title: Weighted Cycles on Weaves

Abstract: Weaves were first introduced by Casals and Zaslow as a graphical tool to describe a family of Legendrian surfaces living inside the 1-jet space of a base surface. Casals, Gorsky, Gorsky, Le, Shen, and Simental later generalized weaves to all Dynkin types such that the original weaves for Legendrian surfaces belong to Dynkin type A, and they use weaves of general Dynkin types to describe the cluster structure on braid varieties. In my previous joint work with Casals, we gave a topological interpretation of the cluster structures associated with weaves of Dynkin type A by associating the quiver with intersections of certain 1-cycles on surfaces and associating cluster variables with merodromies (parallel transports) along dual relative 1-cycles. In this talk, I will generalize this topological interpretation to all general Dynkin types by introducing a new diagrammatic object called “weighted cycles” and constructing an intersection pairing between them. I will define the merodromy along a weighted cycle and explain how to describe cluster variables using merodromies. If time allows, I will also mention a connection to quantum groups and skein algebras.

• 03/25/2026 - Jim Haglund (University of Pennsylvania)
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• 04/01/2026 - Thiago Holleben (Dalhousie University)
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• 04/08/2026 - Eric Ramos (Stevens Institute of Technology.)
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• 04/15/2026 - Steven Dale Cutkosky (University of Missouri)
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• 04/22/2026 -