Formalized results on the localization of a finite direct product of commutative semirings.
View PR #19042 →Characterized a commutative semiring with a maximal nilradical as a local ring.
View PR #17549 →Showed that the localization map is surjective for finite direct products where each semiring has maximal nilradical.
View PR #26372 →Verified that the canonical map from the product of completions of a number field to that of a finite extension is a base field algebra homomorphism.
View PR #270 →Proved an isomorphism between the tensor product of the extension field with the product of base field completions and the product of completions of the extension field.
View PR #385 →Confirmed that tensoring with a finitely presented module commutes with arbitrary direct products.
View PR #527 →Established continuity of the scalar action of a non-Archimedean local field on its algebraic non-Archimedean local field extension, where the base field valuation is induced by the extension.
View PR #2 →Providence, RI (June 2020 - July 2020)
Conducted computational mathematics research on the use of randomness to efficiently compute kernel matrices and low-rank approximations. Co-authored a research paper and created a website displaying coding investigations.
Salisbury, MD (January 2020 - May 2020)
Worked with Dr. Joseph Anderson and two other undergraduate students to conduct computer science research in randomized Monte Carlo methods.