Preprints:

*G-groups of Cohen-Macaulay rings with n-Cluster Tilting Objects;*https://arxiv.org/pdf/1509.02978v2.pdf (submitted to*Journal of Algebra and Representation Theory)**On the Weak Lefschetz Property for Vector Bundles on \(\mathbb{P}^2\);*https://arxiv.org/abs/1803.10337*(*Joint with Chris Peterson and Gioia Failla; submitted to the*Journal of Algebra)*

Broadly, I am interested in applying geometric and topological techniques to study finitely generated modules over noetherian rings, most often in the graded and local cases. To be more precise, in the local case I am interested in studying certain Quillen K-groups for the category of finitely generated modules. In the graded case, I am interested in studying Lefschetz properties for finitely generated modules over a polynomial ring. The following papers provided significant inspiration and direction and encapsulate the main themes of my work:

I am also interested in local cohomology (especially the computation of), generic splitting types of vector bundles (in particular, vector bundles arising from syzygies) and the structure of endomorphism rings of certain finitely generated modules over local rings.

*The Weak and Strong Lefschetz Properties for Artinian K-algebras*(T. Harima et al), arxiv.org/pdf/math/0208201v1.pdf*K-groups for Rings of Finite Cohen-Macaulay type*(H. Holm), arxiv.org/pdf/1211.3445v2.pdf- K'-theory of a Local Ring of Finite Cohen-Macaulay type (V. Navkal), arxiv.org/pdf/1108.2000v2.pdf

I am also interested in local cohomology (especially the computation of), generic splitting types of vector bundles (in particular, vector bundles arising from syzygies) and the structure of endomorphism rings of certain finitely generated modules over local rings.

Pictured: The Crestone group from the summit of of Humboldt Peak (14, 064') in September 2016. Photo credit: Sam Pine

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