Keri Ann Sather-Wagstaff (Clemson University)
Title: Codeword Ideals
Abstract: Combinatorial Commutative Algebra is rich with connections to other areas of Mathematics, Science, and Engineering. This talk will focus on connections with Cryptography, Coding Theory, and Information Theory. (No background on these topics will be assumed for the talk.) Specifically, we investigate the codeword ideal K(C) of a linear code C over a field F. This is the ideal in a polynomial ring over F generated by the squarefree monomials given by the nonzero codewords of C. Algebraic information about K(C) can be seen in the code C, and vice versa. For instance, it is known that the prime decomposition of K(C) is determined by information-theoretic aspects of C, and the generalized Hamming weight of C is determined by the minimal free resolution of K(C). The talk will focus primarily on these known connections and results, with appropriate background, and will end with partial progress on open questions about the free resolutions and symbolic powers of these ideals. This is joint work with Felice Manganiello and Joseph Skelton.
