Today the algebra group is happy to welcome a new PhD student: Marie Frank vom Braucke! She will be supervised by Maria (main supervisor) and Peter (co-supervisor). During her PhD time, Marie will be looking at various invariants of algebraic curves and study their connection with applications in algebraic coding theory.
Marie’s PhD project is a part of and funded by Maria’s Villum YIG project CREATE.
Jonathan, who currently is a PhD student in the algebra group with Maria and Peter, just got his single-author paper “Non-isomorphic maximal function fields of genus q-1” accepted for publication in the internationally recognized journal Finite Fields and Their Applications. You can find a preprint version of the paper here. Congratulations Jonathan!
In the period March 3-7 we had a very productive visit from the french/italian researcher Elena Berardini from the university of Bordeaux. Elena recently co-authored a fantastic article on a new application of algebraic curves in the area of sum-rank metric codes. During her stay we worked on pushing her results further. We have no doubt that a nice article will come out of this in the near future. Thanks for visiting us!
Elena’s visit was made possible by Maria’s Villum YIP project CREATE.
As a final spin off of our former Ph.D. student Lara Vicino’s work in the algebra group, a new preprint on a maximal curve with third largest genus is now available on arXiv here. This preprint completes a series of now three articles in which the three families of maximal curves with third largest genus are investigated. Apart from Lara, the authors are algebra group members Peter Beelen and Maria Montanucci.
Anina, who currently is a postdoc in the algebra group, participated in the joint mathematics meeting (JMM), which took place 8-12 January in Seattle. She gave a talk “Codes for random access efficiency in DNA storage“. Her talk was very well received and gave rise to interesting scientific discussions.
The article “A family of non-isomorphic maximal function fields” by the algebra group members Peter Beelen, Maria Montanucci and Jonathan Tilling Niemann together with Luciane Quoos from the Federal University of Rio de Janeiro in Brazil has been accepted for publication in Mathematische Zeitschrift.
The paper deals with the problem of understanding whether two given function fields are isomorphic (well-known to be difficult), particularly when the aim is to prove that an isomorphism does not exist. In the article we investigate a family of maximal function fields that arise as Galois subfields of the Hermitian function field. We compute the automorphism group, the Weierstrass semigroup at some special rational places and the isomorphism classes of such function fields. In this way, we show that often these function fields provide in fact examples of maximal function fields with the same genus, the same automorphism group, but that are not isomorphic.
The paper was initiated when Luciane visited the algebra group in connection with the Ph.D. defence of Lara Vicino last January. For more info, take a look here.
A new preprint on the Geometry of Codes for Random Access in DNA Storage is now available on arXiv here.
It was written by algebra group members Anina Gruica and Maria Montanucci together with Ferdinando Zullo from the University of Campania, Italy. The work was initiated when Ferdinando visited the algebra group in connection with Maria’s Villum YIP project CREATE.
Effective and reliable data retrieval is critical for the feasibility of DNA storage, and the development of random access efficiency plays a key role in its practicality and reliability. In this paper, we study the Random Access Problem, which asks to compute the expected number of samples one needs in order to recover an information strand. Unlike previous work, we took a geometric approach to the problem, aiming to understand which geometric structures lead to codes that perform well in terms of reducing the random access expectation (Balanced Quasi-Arcs). As a consequence, two main results are obtained. The first is a construction for k=3 that outperforms previous constructions aiming to reduce the random access expectation. The second is the proof of a conjecture for rate 1/2 codes in any dimension.
The algebra group is happy to host Researcher Ferdinando Zullo from the University of Campania “Luigi Vanvitelli” as a guest in the period October 9 – October 19. Ferdinando has already collaborated with both Maria and Anina in the past, obtaining interesting results between the interplay of finite geometry/combinatorics and coding theory.
During his stay Ferdinando, as a key partner of Villum YIP project CREATE, will work with Anina and Maria on the use of geometric tools to construct good codes for random access in the context of DNA data storage. Thanks for joining us Ferdinando!!
The article “On the automorphism group of a family of maximal curves not covered by the Hermitian curve” by the algebra group member Maria Montanucci, together with co-authors Giovanni Zini (from Italy) and Guilherme Tizziotti (from Brazil) has been accepted for publication in the journal Finite Fields and Their Applications. In this article, we investigate the In this paper we compute the automorphism group of the curves introduced in Tafazolian et al. in 2016 as new examples of maximal curves which cannot be covered by the Hermitian curve. They arise as subcovers of the first generalized GK curve (GGS curve). As a result, a new characterization of the GK curve, as a member of this family, is obtained. A preprint of this article can be found here.
A new preprint on the intersection of irreducible curves and the famous Hermitian curve is now available on arXiv here.
It was written by algebra group members Peter Beelen, Maria Montanucci and Jonathan Tilling Niemann together with Mrinmoy Datta from the Indian Institute of Technology Hyderabad. The work was initiated when Mrinmoy visited the algebra group in connection with Maria’s Villum YIP project CREATE.
Update (March 2025): the preprint has been accepted for publication in the Journal of Algebra, which is a high level general audience mathematics journal.