My name is Daniel Kráľ. In 2018, I moved to the Faculty of Informatics of Masaryk University in Brno, Czech Republic, where I have been the inaugural holder of the newly established Donald Ervin Knuth Professorship, which the university has created with the permission of Donald Knuth. I am co-heading the Laboratory of Discrete Methods and Algorithms (DIMEA) of the Faculty. I am also honorary professor at the University of Warwick, where, before moving to Brno, I was a professor of mathematics and computer science and a member of its research centre DIMAP.
My research addresses several topics in mathematics, computer science and their interface. Most of my research is focused on topics related to my (now past) ERC Consolidator grant LADIST, which built on the ERC Starting grant CCOSA. These include problems concerning structural and extremal graph theory, graph algorithms and graph limits. In particular, the theory of graph limits, which was also the main subject of Lovász's Abel Prize Lecture, is a new area of mathematics which provides analytic tools to study large graphs, e.g., graphs representing social networks. These analytic methods have led to new ways to deal with notoriously difficult extremal combinatorics questions and established new links between analysis, combinatorics, ergodic theory, group theory and probability theory. Further details on my research work, including a short introduction accessible to non-specialists, can be found here.
Advances in Combinatorics is an overlay combinatorial journal, which follows a model established by the journal Discrete Analysis for diamond open access. The journal aims to be a diamond open access journal at the level of the very top combinatorial journals. It has no printed copies; instead the journal provides links to the published versions of the articles on arXiv. Additional information on the aims of the journal and ethical publishing in general can be found in this blog post and this blog post by Tim Gowers.
The journal Advances in Combinatorics was launched in June 2018 and the first papers were published in October 2019; also see the submission and acceptance statistics. Advances in Combinatorics is a member of the Free Journal Network, indexed by MathSciNet and Scopus, and also listed in the Directory of Open Access Journals. The editorial board currently consists of Béla Bollobás, Julia Böttcher, Maria Chudnovsky, Louis Esperet, Timothy Gowers, James Oxley, Wojciech Samotij, Gábor Sárközy, Alex Scott and Asaf Shapira, with Louis, Tim and myself also acting as the managing editors of the journal. The financial and administrative support for the journal is provided by Queen's University Library.
While I support open access publishing, in particular, in its diamond form as represented by journals Advances in Combinatorics, Discrete Analysis, Electronic Journal of Combinatorics, and more recently founded Innovations in Graph Theory and TheoretiCS, I do not support implementation of the Plan S for several reasons including those expressed in this statement by the ERC Scientific Council.
In my view, this Informatics Europe report on open access is a very good read in regard to the current status of open access publishing.