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Symbolic Powers of Graph and Code Ideals

Cover ideals of graphs are squarefree monomial ideals in a polynomial ring associated to a vertex cover of a graph G. We are able to combinatorially manipulate the graph in minimal ways to force certain algebraic properties onto the ideal, like vertex decomposability. Symbolic powers of cover ideals have been associated to a useful graph G_k that is constructed from the original graph G. This construction allows us to perform a similar operation that passes the desired properties onto all symbolic powers. In this talk we’ll also show how these ideas connect to linear codes, specifically MDS codes, in cryptography.

Sponsored by: Mathematics

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Yuming Sun

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