$9,000; AMS-Simons Research Enhancement Grants for Primarily Undergraduate Institution (PUI) Faculty

Advances in Iwasawa Theory and Applications to Diophantine Geometry

Principal Investigator: Jeffrey Hatley, associate professor of mathematics

The American Mathematical Society (AMS) Simons Research Enhancement Grants for Primarily Undergraduate Institution (PUI) Faculty foster and support research collaboration by full-time mathematicians at primarily undergraduate institutions in the United States who have earned a PhD at least five years prior the start of the grant.

This three-year award will support PI Hatley’s research focused on the various arithmetic properties of modular Galois representations, particularly how these properties vary in families of such representations. These representations will be observed using the lens of Iwasawa theory, thereby contributing to our understanding of Iwasawa theory and number theory more broadly.

Critical to the success of this research are PI Hatley’s collaborations with scholars at the University of Ottawa (Ottawa, ON, CA), The University of Texas Rio Grande Valley (Edinburg, TX), and at Union. By supporting reciprocal visits between campuses, this grant will enhance and strengthen these collaborations. In-person collaboration is key to advancing research goals, as it provides uninterrupted, sustained time to brainstorm creative approaches to problems, identify and overcome technical obstacles, and begin writing proofs of results. Additionally, this award supports PI Hatley’s participation at international and domestic conferences. Participating in conferences is critical to not only disseminating research results and remaining apprised of advancements in the field, but it also provides opportunities to connect with existing collaborators from outside of North America and create to form new collaborations.