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2021 Academic Activities


  • Elected as the President of the South African Mathematical Society.
  • Papers on exactness properties published in Journal of Algebra and Advances in Mathematics.
  • Invited to give a plenary talk at the BRICS Mathematics Conference.
  • Secured funding for a national research programme in mathematics.
  • First computer implementation of the SOFiA proof system developed.
  • Supervised four postgraduate students (two PhD and two MSc).
  • Two papers on matrix properties submitted.
  • Served as the mathematical sciences programme coordinator and on a university research committee.
  • Taught and/or convened two semester modules and two year modules.
  • Progress made on existing and new research projects and delivered talks on those.
  • Carried out duties in the role as mathematical sciences programme coordinator and member of a university research committee.
  • Carried out refereeing and editorial duties (not listed below).

November-December 2021

  • Finalized marks for Foundations of Abstract Mathematics I, II and an honors module in Logic.
  • Resumed research on a noetherian form of sets.
  • The binary matrix properties paper submitted for publication (corresponding author: M. Hoefnagel) - see the submitted version of the paper here.
  • The revised version of the paper on matrix taxonomy re-submitted for publication (corresponding author: M. Hoefnagel) - see the new version here.
  • Talk given at SAMS Congress on the matrix project - see the write-up of the talk here.
  • At the SAMS AGM held during the congress, I was appointed to serve on the SAMS Council as the President of the South African Mathematical Society for 2022-2023.
  • Plenary talk given at the 4th BRICS Mathematics Conference on noetherian forms (slides, recording). This talk was given jointly with Amartya Goswami.
  • Funding awarded for the NITheCS research programme in Mathematics, entitled "Space-like mathematical structures and related topics in algebra, logic and computation", which was expanded to include 20 mathematicians in South Africa.
  • Mathematical Sciences Programme tasks continued.

September-October 2021

  • Paper published: linear exactness properties in Journal of Algebra. See the paper on the journal's website here.
  • Some progress made on the SOFiA project, including implementation of an intuitive command-line proof building interface for Used this tool in the delivery of the Foundations of Abstract Mathematics I seminar in the fourth term.
  • The binary matrix properties paper finalized from my side.
  • Worked on the revision of the matrix taxonomy paper. Revision in progress can be found here
  • Together with Amartya Goswami, gave a NITheCS mini-school (October 2021) on Elementary Introduction to Category Theory. See this blog for the write-up and links to video-recordings of lectures. 
  • Talk given at SIC on forms vs monoidal categories. See the write-up and the recording of the talk here. See the recordings of all talks here.
  • Examiners nominated for the MSc Thesis of Paul Hugo, to be finalized by the end of the year.
  • Developed a NITheCS national programme in Mathematics for 2022, under collaboration with Amartya Goswami, Partha Pratim Ghosh and Yorick Hardy.

July-August 2021

  • Further progress made on the binary matrix properties paper.
  • Started writing a book in abstract algebra jointly with Amartya Goswami. You can follow the progress here.
  • Started work on some tasks related to the Mathematical Sciences Programme.
  • Teaching Foundations of Abstract Mathematics II in the third term and honor module in Logic in the second semester.
  • Started sketching ideas for a NITheCS national programme in Mathematics for 2022.

May-June 2021

  • The paper on linear exactness properties, joint work with Pierre-Alain Jacqmin, was accepted for publication in Journal of Algebra (it is scheduled for publication in October 2021 - follow the link).
  • Started (co-)supervision of PhD studies of Brandon Laing on SOFiA.
  • Started supervision of PhD studies of Ineke van der Berg on categorical algebra of algebraic logic.
  • Started a new research project on applications of forms to physics.
  • Continued with the teaching of Engineering Mathematics 214 and Set Theory and Topology. 
  • Busy with marking of Foundations of Abstract Mathematics I first term seminar final assignments.

March-April 2021

  • Started work on matches of digraphs: pioneering joint work with Francois van Niekerk and Jade Viljoen (research grew out from her honors project).
  • Started work on binary matrix properties: joint work with Michael Hoefnagel, Pierre-Alain Jacqmin and Emil van der Walt (undergraduate student) on the structure of the poset of matrix properties. The project grew out from Emil solving problems that Michael and I suggested to him in the fall of 2021, which naturally evolved from a joint work with Michael and Pierre-Alain.
  • Made some progress with SOFiA: joint work with Louise Beyers, Gregor Feierabend and Brandon Laing. First python implementation of the SOFiA proof system produced. As a result, its deduction rules were refined.
  • Started supervision of MSc studies of Daniella Moore on categorical aspects of near-vector spaces (cosupervised by Karin Howell).
  • Teaching Engineering Mathematics 214 (together with Liam Baker, Ronalda Benjamin, and Michael Hoefnagel) in the first semester and giving a Foundations of Abstract Mathematics I seminar in Mathematical Reasoning in the first term. Also teaching an honors module, Set Theory and Topology, in the first semester.

January-February 2021

  • The paper on stability of exactness properties under pro-completion, a 7 year old joint work with Pierre-Alain Jacqmin, was published in Advances in Mathematics.
  • The paper on matrix taxonomy has been submitted for publication.
  • Revisited research on a noetherian form of sets: together with Francois van Niekerk, we are elaborating the proof of our recent theorem that the category of sets provides a model for the self-dual axiomatic setup for homomorphism theorems proposed in my publication no. 35. Significant progress was made with the corresponding paper, but it still needs to more work.
  • Serving on the Subcommittee B of the Research Committee of Stellenbosch University for 2021, as well as on the Programme Committee of the Faculty of Science.
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