I am Lukas Kölsch and currently a tenure track Assistant Professor at the University of South Florida. I finished my PhD at the University of Rostock in Germany in 2020.

I do math with applications to cryptography and coding theory. Recently, I have been working on semifields, rank-metric codes and non-linear Boolean functions like APN functions. Generally, I like to combine ideas from algebra, combinatorics and number theory to solve specific problems that are related to applications in coding theory or cryptography.

Contact

You can contact me via email: lukas (dot) koelsch (dot) math (at) gmail (dot) com, or koelsch (at) usf (dot) edu.

CV

Download here. Last updated: October 2023.

News

(10-10-2023) My paper Value distributions of perfect nonlinear functions was published in Combinatorica!

(02-06-2023) Check out my new preprint on Value distributions of perfect nonlinear functions (joint work with Alexandr Polujan)

(08-09-22) Check out my new preprint on c-differential uniformity of Boolean functions and their relation to differential attacks on block ciphers (joint work with Daniele Bartoli and Giacomo Micheli)

(07-27-22) Check out my new preprint on counting the Taniguchi semifields. Here, we give a new best lower bound on the total number of semifields of odd order. (joint work with Faruk Göloglu)

(July 2022) My paper on a new family of commutative semifields was accepted for publication in Transactions of the American Mathematical Society! In this paper, we present a new family of commutative semifields and prove that the total number of commutative semfields of order p^n is exponential in n, solving what has been called the “biggest problem in the theory of commutative semifields”! The previous best known bound was quadratic in n. (joint work with Faruk Göloglu)

(07/18/2022-07/22/2022) I co-organized the CodebreakHERS cybersecurity camp for grade 8-12 girls at the University of South Florida. Check out our Instagram page for pictures!

Upcoming Talks and Events

I will be at Canadam 2023 in Winnipeg in June 2023. I will give an invited talk in the minisymposium on Design Theory and Coding Theory.

I am a Program Committee member of BFA 2023. For more details, see also the Talks section.