Johan Sebastian Heesemann Rosenkilde
Building: 303B, 146
2800 Kgs. Lyngby
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 Error-Correcting 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 well-known 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 ever-increasing amounts of data and new communication paradigms keep challenging the error-correction 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 communication-methods 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, public-key cryptography, computation of discrete logarithms, as well as proof-theory and compact representation of proofs.
More information and publications can be found on my homepage:
Publication: Research - peer-review › Journal article – Annual report year: 2016
Publication: Research - peer-review › Article in proceedings – Annual report year: 2016
Publication: Research - peer-review › Paper – Annual report year: 2015
Additional searchable ISSN (Electronic): 1573-7586
Springer New York LLC, United States
ISI indexed (2013): ISI indexed yes, BFI (2015): BFI-level 1, Scopus rating (2015): 0.649 1.166
Additional searchable ISSN (Electronic): 1557-9654
I E E E, United States
ISI indexed (2013): ISI indexed yes, BFI (2015): BFI-level 2, Scopus rating (2015): 1.433 2.001
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