Cluster Algebras and Polylogarithm Relations

Simple item page
dc.contributor.advisorZickert, Christianen_US
dc.contributor.authorGreenberg, Zacharyen_US
dc.contributor.departmentMathematicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2022-02-04T06:37:41Z
dc.date.available2022-02-04T06:37:41Z
dc.date.issued2021en_US
dc.description.abstractWe 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.en_US
dc.identifierhttps://doi.org/10.13016/ea70-lsmf
dc.identifier.urihttp://hdl.handle.net/1903/28451
dc.language.isoenen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pqcontrolledTheoretical mathematicsen_US
dc.subject.pquncontrolledAssociahedronen_US
dc.subject.pquncontrolledCluster Algebrasen_US
dc.subject.pquncontrolledCluster Modular Groupen_US
dc.subject.pquncontrolledPolylogarithmsen_US
dc.titleCluster Algebras and Polylogarithm Relationsen_US
dc.typeDissertationen_US

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Greenberg_umd_0117E_22100.pdf
Size:
4.02 MB
Format:
Adobe Portable Document Format
Download

Collections

UMD Theses and Dissertations
Mathematics Theses and Dissertations