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Algebra Seminar - Skein Relations for Punctured Surfaces

Wednesday, February 5, 2025 11:15 AM – 12:05 PM
  • Location
    Monteith Building
  • Description
    Since the introduction of cluster algebras by Fomin and Zelevinsky in 2002, these algebras have garnered significant attention, particularly for their surface-type variants. These algebras enable the construction of various combinatorial structures, such as snake graphs, \(T\)-paths, and posets, which serve as tools for proving key properties like positivity and the existence of bases. In this talk, we will present a cluster expansion formula that employs poset representatives for arcs on triangulated surfaces. Leveraging these posets and the expansion formula, we will establish skein relations that resolve intersections or incompatibilities between arcs. As a result, we will demonstrate that bangles and bracelets form spanning sets and exhibit linear independence, thereby proving the existence of the bangle and bracelet bases in punctured surfaces with boundaries and closed surfaces of genus 0. This is a joint work with Esther Banaian and Elizabeth Kelley.
  • Website
    https://events.uconn.edu/mathematics-department/event/737820-algebra-seminar-skein-relations-for-punctured
  • Categories
    Conferences & Speakers

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