Computational Methods for Investigating Higher Teichmüller Spaces

dc.contributor.advisorStecker, Florian
dc.creatorMalik, Arjun
dc.date.accessioned2020-11-30T15:56:44Z
dc.date.available2020-11-30T15:56:44Z
dc.date.issued2020-11
dc.description.abstractThis paper deals with the discrete subgroup problem, solvable through the study of higher Teichmüller theory. The discrete subgroup problem is as follows: given a Lie group (a group with continuity) such as R, how do you find discrete subgroups, such as Z, particularly those of a type similar to (isomorphic to) a certain group? This paper details how, using theorems pertaining to Higher Teichmüller theory graphing the eigenvalue gaps of a matrix group can be used to figure out if it is a discrete subgroup of a Lie Group. In it, I find two subsets of results: one is working towards an attempt to validate recently found results about a Lie group, and the other is a result about the method itself (specifically, projective convex bending) and how it can be used empirically.en_US
dc.description.departmentMathematicsen_US
dc.identifier.urihttps://hdl.handle.net/2152/83805
dc.identifier.urihttp://dx.doi.org/10.26153/tsw/10800
dc.language.isoengen_US
dc.relation.ispartofHonors Thesesen_US
dc.rights.restrictionOpenen_US
dc.subjectTeichmüller spaceen_US
dc.subjectprojective convex bendingen_US
dc.subjectgroup theoryen_US
dc.subjectrepresentation theoryen_US
dc.subjectgeometric group theoryen_US
dc.titleComputational Methods for Investigating Higher Teichmüller Spacesen_US
dc.typeThesisen_US

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