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Abstract: This talk is on joint work with Srishti Singh (Mizzou). I'll discuss our recent preprint about affine semigroup rings, which are fun and important examples of commutative rings formed from the combinatorial data of an affine semigroup, which is a subset of N^n (or sometimes Z^n) which contains the zero vector and are closed under the usual +. We studied the problem of Frobenius closure in affine semigroup rings, which, due to some theorems of Bruns-Li-Römer, are controlled by the (weak) normalization map. We construct an adjustment to an affine semigroup A which we called the p-weak normalization of A, which depends on a fixed prime number p, and from that we are able to bound Frobenius closure in the corresponding affine semigroup ring over a field of that characteristic. We also provide a script which computes this new weak normalization and then can use Macaulay2 to compute Frobenius closure in affine semigroup rings defined over Z/pZ.

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