Within the broader context of commutative algebra, I study infinite free resolutions of modules over graded rings. Polynomial rings over a field (and quotients thereof) are especially nice because they can be viewed as direct sums of finite dimensional vector spaces, and the same is true for their modules. Not only do such graded rings and modules arise in many settings, including the study of projective varieties, algebraic statistics, and combinatorics, but they also have beautiful properties that make their study interesting in its own right.
Opportunities for Students
If you are interested in research with me, here's how to get started:
- Complete Modern Algebra (MATH 325W)
- Complete the following tutorials on the Home tab of web.macaulay2.com:
- Welcome Tutorial
- Basic Introduction to Macaulay2
- Mathematicians' Introduction to Macaulay2
- Read parts of Questions in Boij-Soederberg Theory by Daniel Erman and Steven V. Sam:
- Section 1 for background on the types of problems I work on
- Skim section 3 and subsection 9.3 for the particular type of results I'm currently interested in generating
- There are two foundational papers that drive my current research in this area. You need not read them in their entirety, but you may wish to get a flavor for the results by skimming through these papers:
- I have worked on these types of problems with other students, and you can see that work by viewing the following papers:
- Download this list and complete the homework problems on the second page. Where helpful, specific references to (parts of) the above papers are included to help you focus your reading.