My research is in commutative and homological algebra, and I have a particular interest in resolutions of modules over commutative rings. An overarching goal in my research is to understand and apply the structure of resolutions, focussing on minimality and differential graded algebra structures. Currently, some of the topics I'm interested in include minimal complexes of (flat) modules, cosupport of finitely generated modules, the Koszul property, and higher analogues of Serre's intersection multiplicity conjectures.
A list of all of my available papers and preprints can be found on the arXiv: http://arxiv.org/a/thompson_p_1, the published versions are linked to below.
- Stable Local Cohomology. Communications in Algebra, Issue 1, Vol 45, 2017.
- Cyclic Adams operations. Joint with M. Brown, C. Miller, and M. Walker. Journal of Pure and Applied Algebra, Volume 221, Issue 7, July 2017, Pages 1589–1613.
- Adams operations on matrix factorizations. Joint with M. Brown, C. Miller, and M. Walker. To appear in Algebra and Number Theory.
- Detecting Koszulness and related homological properties from the algebra structure of Koszul homology. Joint with A. Croll, R. Dellaca, A. Gupta, D. Rangel Tracy, J. Hoffmeier, L. Sega, G. Sosa. Submitted.
- Minimal complexes of cotorsion-flat modules. Submitted.
- Cosupport in a commutative noetherian ring via minimal complexes of cotorsion-flat modules. Submitted.
- Reducibility of parameter ideals in low powers of the maximal ideal. Joint with K. Shultis. In progress.
- Minimal complexes of flat modules. Joint with L. W. Christensen. In progress.
- Immersions of Surfaces. Joint with M. Brown, E. Canton, B. Egg, M. Franke, C. Giusti, J. Hardin, M. Hopkins, H. Lindo, N. Owad, J. Ruiz, K. Shultis, M. Walker, and M. Webb. In progress.