Spring 2026

• [Monday] 02/16/2026 @12:45 (Room TBA) - Dr. Kyun Kyu Kim (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.
  
  

• 03/25/2026 - 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 -