The paper “Point-line incidence on Grassmannians and majority logic decoding of Grassmann codes” by Peter and Prasant Singh appeared online in the journal Finite Fields and Their Applications. In this paper Peter and Prasant, a former postdoc of the algebra group, explain how to use the subtle structure of lines on Grassmannians to correct errors using Grassmann codes with an old technique called majority logic decoding. The result is a fast decoding algorithm for Grassmann codes.
Peter and Maria participated from 31st May – 4th June 2021 in the biannual conference AGCT, where researchers from all over the world discuss algebraic geometry/number theory and their applications. This year the conference was held online, due to the covid19 situation. Peter gave a talk “On a conjecture by Sørensen” on Thurday, 3rd June, in which he explained his work with Mrinmoy Datta and Masaaki Homma on the maximal number of intersection points on a non-degenerate Hermitian variety and a surface of degree d. This work has appeared recently in Proc. Amer. Math. Soc. 149 (2021), no. 4, 1431–1441. A preprint is available here.
Peter and Maria participated in the online conference “Curves over Finite Fields”, which took place 24-28 May. The conference was originally planned to take place in Benasque, but was held online, due to the covid19 situation.
Peter was an invited plenary speaker and gave two talks: “Asymptotic results: an overview” and “Asymptotic results: what is next?”. In the first talk, he gave an overview of results on asymptotically families of curves over a finite field with many rational points. In the second talk, several open problems and very recent developments were explained.
Maria was an invited semi-plenary speaker and gave the talk “On the automorphism group of algebraic curves in positive characteristic”. In the talk, she gave an overview on the latest developments on relation between various invariants of algebraic curves, such as p-rank, genus, and their automorphism groups.
We are happy to say that the given talks were well received!
Peter has been one of the lectures in an international workshop organized by leading technical universities in India: IIT Bombay, IIT Jammu and SGGS-IET. The online event took place March 8-12 and had many participants from all over the world. Peter gave two lectures on the decoding of Reed-Solomon codes. Slides of his and other talks are available here.
In the issue of this month of the prestigious journal IEEE Transactions on Information Theory, you can find the article “Fast Encoding of AG Codes over C_ab Curves” by Peter, Johan, and Grigory. In this article it is explained how to convert a message into a codeword (encoding) as well as the reverse process (unencoding) fast for a significant class of algebraic geometry codes. A preprint is available here.
Starting the first of March 2021 Johan left DTU for a job at GitHub as a Research Engineer. The algebra group would like to thank him for his input, energy and enthusiasm throughout the years. Best of luck with your new job!
After a highly successful postdoc in the algebra group, Sven obtained a new position as a postdoc at the Technical University of Munich. We would like to thank Sven for his work in the algebra group and wish him all the best for the future!
As part of the DTU outreach activities towards high schools, Peter gave a guest lecture on solving cubic polynomial equations. The activities are organized within the framework of an InterMat workshop (see https://matematicum.dtu.dk/intermat for information. Danish only). With various high school students listening online, an explanation was given on how to use Tschirnhaus transforms to obtain the famous Cardano solution formulas. The same method can be used to solve the quartic equation.
On the 15th of October, a new PhD student named Lara Vicino started in the algebra group. She will be supervised by Peter Beelen and co-supervised by Maria Montanucci. Her project is about determining upper bounds on the number of points on a curve defined over a finite field in terms of the degree of the curve.
This month, the paper “Hyperplane Sections of Determinantal Varieties over Finite Fields and Linear Codes” appeared in the September issue of the journal Discrete Mathematics. The paper is written by Peter and Prof. Sudhir Ghorpade from IIT Bombay, a regular guest of the algebra group with whom Peter has written several papers before. A preprint can be found here.