I am a PhD student at the University of Copenhagen (since October 2011), working in the Algebra and Number Theory group, under the supervision of Ian Kiming.
My main research
interest is in algebraic number theory; in particular, the beautiful
connections that exist between three types of objects coming from: Algebra
(Galois representations), Geometry (abelian varieties), and Analysis (modular
forms). To objects of each of these types, we can associate L-functions.
Interesting number theoretic information is revealed when we are able to attach
objects from each of these different realms together in natural ways so that
their corresponding L-functions agree.
Examples of subjects in this line
of research are Class Field Theory (the study of the character theory of the
absolute Galois group, i.e. the abelian extensions of Q), Artin's higher
reciprocity laws, the Langlands program (which attempts to generalize class
field theory), and various natural questions coming from arithmetic geometry.
This type of machinery that developed in the late 20th century from
the work of Andrew Wiles et. al. finally
gave us the answer to a long-standing open problem: the confirmation of Fermat's Last Theorem.
Visit my blog to get an idea of what's usually on my mind (caveat: it's not updated very frequently, though I hope that will change eventually). Check the recommended reading section.