Undergraduate Research
Detecting Properties from Descriptions of Groups Poster
Detecting Properties from Descriptions of Groups Paper
Current Research
My current research lies at the intersection of algebraic number theory and algebraic geometry, also known as arithmetic geometry. I study the arithmetic of conic bundles and the extent to which they fail the Hasse Principle upon base extension. This work originated from trying to answer a similar question for Chatelet surfaces, which are a special type of conic bundle surface. This research is intimately tied into Brauer groups and the Brauer-Manin obstruction and the extent to which they explain the failure of the Hasse principle for classes of varieties.
Potential Hasse principle violations of Chatelet surfaces (My general exam paper)
PHP violations for Chatelet surfaces slides (Slides for my general exam talk)
Pre-prints
On the Hasse principle for conic bundles over even degree extensions (To be submitted for publication soon)
Weak Approximation for Chatelet Surfaces (with Masahiro Nakahara) Coming Soon!