Keywords
Computer Algebra

Abstract algebra

Error correction

Number theory
Algebra
I'm interested in a broad variety of applications of algebra and
the computational methods which support them.
Algebra has many facets all over mathematics:
 from number theory, that is, primes, solution of polynomial
equations, etc.;
 over group theory, which has applications in any discipline
within mathematics;
 to symbolic manipulation of mathematical objects, which is
strongly related to formal language methods in informatics.
"Modern" algebra has been developed through the last three to
four centuries and is deep and very diverse. Much younger is the
discipline of computability within algebra, that is, the
study of which objects and equations can be computed and solved
(efficiently) on a computer, as well as what the algorithms for
doing this should look like. Here we are still seeing major
advances on fundamental questions, and many others are left still
unanswered.
For me, the most exciting is when beautiful mathematical
structures connect with computability and applicability.
Algebraic Coding Theory
I am specialised within the application Algebraic Coding
Theory.
Coding Theory, or ErrorCorrecting Codes, concerns how data
should be represented such that it can again be recovered when it
is later read or received, even when errors or failures occur. A
wellknown example is a DVD which can be played even though it has
many scratches that actually prevent the laser from reading the
bits underneath. However, error correcting codes are completely
pervasive in our modern electronic world, and it is vital in all
electronic communication devices that we use.
The everincreasing amounts of data and new communication
paradigms keep challenging the errorcorrection soulutions that we
have, while improved computational power opens new possibilities.
I'm especially interested in applications where beautiful algebraic
constructions turn out to be the best (or only) solutions: this is
for instance in systems where guarantees on reliability
levels are vital, and in very recent storage and
communicationmethods which guarantee privacy in a distributed
setting.
Algebraic coding theory also touches upon many other questions
within mathematics, both fundamental as well as applied. For this
reason, I'm also dabbling in questions like factoring, publickey
cryptography, computation of discrete logarithms, as well as
prooftheory and compact representation of proofs.
More information and publications can be found on my
homepage:
http://jsrn.dk