UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.

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Author: search.filters.author.Greenberg, Zachary

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    Cluster Algebras and Polylogarithm Relations
    (2021) Greenberg, Zachary; Zickert, Christian; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    We seek to illuminate the connection between multiple polylogarithm relations and cluster algebras in two ways. First, we give a uniform description of the cluster modular group of affine and doubly extended cluster algebras. This will be critical for the future work of extracting polylogarithm relations from infinite type cluster algebras. Second, we introduce a differential one form, ωn, associated to each multiple polylogarithm, which can be used to compute multiple polylogarithm relations. This form satisfies a clean recurrence relation, mirroring the inductive definition of multiple polylogarithms. We are able to use this recurrence to find several families of “small” polylogarithm relations that hold in any weight. Finally for small values of n, we extract polylogarithm relations from type An and Dn cluster algebras.