# 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.

# 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 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.

# 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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