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| Teaching | |
| Vita |
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| Math Arxiv |
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| commalg.org |
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| mathscinet |
My main interests lie in commutative algebra, the study of commutative rings and modules over them. One of my projects involves approximating Artinian local rings by Gorenstein Artin local rings using the notion of Gorenstein colength. Part of my work deals with studying bounds on this number and the other involves constructing Gorenstein Artin local rings. Techniques used include studying inverse systems, maps from the injective hull of the residue field to the ring, the Hoskin-Deligne formula, the strong Lefschetz property and fiber products and connected sums of Gorenstein Artin local rings. My current work deals with studying multiplicities and minimal reductions of the maximal ideal in a local ring. Part of the work is to understand when the maximal ideal is 3-standard, using tools from the world of positive characteristic and applying the technique of reducing to prime characteristic. Another project I am working on is to generalize an inequality of Lech involving the multiplicity and colength of an ideal primary to the maximal ideal. |
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Journal of Algebra 302 (2008)
3438-3446. |
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| 2. Computing Gorenstein Colength. | Journal of Commutative Algebra, vol. 1, no. 3, (2009) 343-359. |
| 3. Three-Standardness of the Maximal Ideal |
Work in Progress |