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Presented By: Learning Seminar in Algebraic Combinatorics - Department of Mathematics

Learning seminar in algebraic combinatorics: The various polyhedral realizations of g-vector fans

Yucong Lei

Last week we introduced cluster algebra with principal coefficients, and F-polynomials. We will pick up from the definition of g-vectors, and talk about several different works on how to construct g-vector fans. In Jahn-Löwe-Stump, the authors constructed the g-vector fan by common refinement of normal fans of Newton polytopes of F-polynomials. In Holhweg-Lange-Thomas, they constructed the generalized associahedron (whose normal fan is the g-vector fan) by deleting inequalities of certain facets. In Bazier-Matte et al., the authors constructed the generalized associahedron by extending the construction of the kinematic associahedra in ABHY to all simply laced Dynkin quivers. In this talk, we will try to give a brief survey of each construction, illustrating them with a type A example.

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