About

In 1969, Chase and Sweedler published a book on Hopf Algebras and Galois Theory. In it, they stated what it meant for a commutative ring S to be a H-Galois extension of a commutative ring R, where H is some R-Hopf algebra. In the case of a Galois extension of fields (that is when S=L, R=K and L/K is Galois), we may retrieve all the classical notions we know and love (for example, we may set H=K[G] where G is the Galois group of the extension). Hopf-Galois theory is essentially the study of H-Galois extensions.  The theory leads to an analogue of the fundamental theorem of Galois Theory, which in particular applies to non-Galois extensions.
In 1987, Greither and Pareigis showed that the problem of finding Hopf-Galois structures on separable (but not necessarily normal) field extensions could be phrased as a problem in group theory. This sparked a lot of research into classification and counting results - where there is just one Galois group (if it exists), there maybe many Hopf-Galois structures on one extension. My research mainly focuses on using another fundamental result known as Byott's translation to find, count, and describe Hopf-Galois structures on separable field extensions with certain properties.

I have interests spanning any area which has links with Hopf-Galois theory. These include (algebraic) number theory, group theory, Galois theory, skew braces, and a curiosity to get my head around cohomology, representation theory, and algebraic geometry!
Outside of this, I have slightly more recreational interests in modular forms (having written my master's thesis on half integral weight modular forms and the Shimura correspondence under the supervision of Dr. David Lowry-Duda), and really any bit of interesting maths that is presented to me!

That, my friend, is the question we all must ask ourselves...

Excuse me but the premise that mathematicians are boring is simply preposterous! But even if you think mathematicians are usually quite exciting creatures, and that I'm just one of the boring ones, I implore you to believe otherwise (with the second part of this statement that is). When I'm not playing with groups, you'll usually find me either tooting the French horn, scratching my head while attempting to learn Russian, or scrambling half way up a mountain. I'm also a Christian, being a firm believer in God :). An extra fun fact: I spent 10 years at a youth theatre (just once a week though... I still went to school...).