Summary

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.

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 sofia.py. 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.

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.

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.

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.

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.