UNSW Sydney
I am a PhD student in pure mathematics and a tutor at the School of Mathematics and Statistics, UNSW Sydney. My PhD project is under the primary supervision of Professor Daniel Chan and secondary supervision of Dr. Behrouz Taji.
My research interests are primarily in algebra and (non-commutative) algebraic geometry. In particular, I am currently looking at the birational geometry of orders on surfaces. In much the same way that rings of integers are models for number fields or varieties are models of function fields, orders are (sheaves of) noncommutative algebras which we think of as models for central simple algebras. Moreover, rings of integers and varieties are in some sense 'integral' with respect to the object they model—the same is true for orders. Surprisingly, much of the study of orders on surfaces can be reduced to the underlying (commutative) geometry of the surface alongside some extra "ramification data" obtained from the order itself. To learn more about this, see Daniel Chan's lectures on orders and the preprint Stable Orders over Surfaces by Michael Artin and Aise Johan de Jong. I am also broadly interested in birational classification, the minimal model program, the Sarkisov program, and their non-commutative counterparts in the setting of orders.
Joseph Baine and I run the UNSW Maths PhD/Masters seminar. Contact me or fill out this form if interested in attending or speaking and I will add you to the mailing list!
I am organising a weekly reading group working through Serre's Local Fields. Let me know if you would be interested in participating.
I am also the current UNSW Mathematics and Statistics HDR representative.