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Dmitri Skjorshammer

Picture of Dmitri Skjorshammer.

Thesis

Tops in Higher Dimensions

Advisor
Ursula Whitcher
Second Reader(s)
Dagan Karp

Abstract

Reflexive polytopes can be used to construct families of Calabi-Yau varieties as hypersurfaces in toric varieties. Reflexive polytopes have been classified for $n \leq 4$ by constructing maximal objects that contain all reflexive polytopes as subsets. Given computational constraints, classification becomes intractable for $n = 5$. An alternate approach is to make use of tops, which are generalizations of the notion of half of a reflexive polytope. In this thesis, we investigate classification algorithms for tops and construct a class of four-dimensional tops which can be completed to reflexive polytopes. We then outline how this all relates to fiber bundles on toric varieties.

Proposal

Classification of Tops in Five Dimensions

Additional Materials

Poster