Author

Jessica Otis

Date of Award

Summer 2019

Document Type

Open Access Thesis

Department

Mathematics

First Advisor

Matthew Ballard

Abstract

Let R be a regular local ring and take ! to be an isolated singularity on R. Taking Z/2-graded R-modules, X and Y , a matrix factorization of ω is a pair of morphisms (ϕ, ψ) such that ϕ⃝◦ψ = ω and ψ⃝◦ϕ = ω are satisfied in the diagram X ϕY ψX. We will discuss the category of matrix factorizations of ! in R and lead into the homotopy category of matrix factorizations as well as its historical development. Finally, we will conclude with the statement of the Kapustin-Li formula for the duality pairing on the morphisms in the matrix factorization category of (R, ω) and discuss its implementation in SageMath.

Included in

Mathematics Commons

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