2022 Academic Activities

Summary

• Initiated seven new collaborative research projects within the Mathematical Structures research programme, that includes researchers and postgraduate students from various universities in South Africa: operator semigroups, measure structures, metric frames, canonical extensions, ranked monoids, sum structures, lower topology.
• Supervised and co-supervised nine postgraduate students (two honors, two masters, and five phd).
• Represented South Africa at the General Assembly of the International Mathematical Union along with a colleague in Mathematics Education.
• In collaboration with colleagues and students, developed and delivered a successful math-music theatrical production for the celebration of the International Year of Basic Sciences for Sustainable Development. The production was supported by NITheCS, ASSAf and DSI.
• Developed and delivered four national postgraduate courses online: SOFiA on python, mathematical structures (in collaboration), introductory set theory (in collaboration), category theory.
• Executed presidential duties for SAMS: chairing of SAMS council meetings, of the AGM, opening and closure of the SAMS congress, etc. Prepared and delivered presidential address at the AGM (in consultation with the SAMS Council) to give a direction to SAMS activities in the coming years.
• Elected as NITheCS associate co-representative, and in this role, served on the NITheCS management committee monthly meetings.
• Ran the national research programme in mathematical structures under NITheCS along with three other principal investigators in the research programme.
• Two co-authored papers published, one in Journal of Symbolic Logic. Co-authored paper in Order accepted for publication.
• Served on the programme committee of the international conference "Topology, algebra and categories in logic" held in Coimbra, Portugal.
• Gave two interviews (radio and youtube).
• Taught and co-taught and/or convened six modules at Stellenbosch University, including two engineering mathematics modules, one honors module and two third-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 2022

• Research discussion (9 December) with Dr. Christian Budde: started research project on the category theory of operator semigroups.
• Chaired the Annual General Meeting of the South African Mathematical Society (8 December).
• Gave a SAMS Congress talk on the noetherian form of sets.
• Gave opening and closing speeches at the 65th Congress of the South African Mathematical Society (6-8 December), held at Stellenbosch University. 
• Gave an opening speech at the special meeting of the Mathematics section of National Graduate Academy (5 December).
• Chaired the fourth Council Meeting of the South African Mathematical Society (2 December).
• Conducted weekly 6-hour tutorial sessions in November for students in Foundations of Abstract Mathematics I for additional assessment opportunity.
• The paper on ordinal number systems fully published in the Journal of Symbolic Logic.
• Submitted author comments on the journal proofs of the paper on stack combinatorics (joint work with Helmut Prodinger and Francois van Niekerk). The paper is being published by Springer Order.
• Hosted research visit (18-20 November) of Dr. Cerene Rathilal. Started joint work on measure structures.
• Submitted a report on the Mathematical Structures Research Programme at NITheCS and delivered a talk at the NITheCS Associates Workshop on the progress of the research programme.
• Made progress with Kishan Dayaram on diagram lemmas in the context of noetherian forms.
• Fundamano production (4 November) was a success -- full house attendance and well received. See: videos, press release.

September-October 2022

• Gave a talk on at the "Topology, Algebra, and Category Theory" international conference (19-22 September) dedicated to the 65th birthday of Themba Dube. The subject of the talk was metric frames.
• Supervised original honors projects of Gregor Feierabend and Gideo Joubert. 
• Gave a semester honors course on Logic.
• Taught the English group of Engineering Mathematics 242 in the second semester of 2022.
• Chaired the third Council Meeting of the South African Mathematical Society (7 October).
• Hosted research visit (20 September - 8 October) of my PhD student, Noluntu Baart, to work on deductive reasoning in intermediate-phase mathematics education.
• Hosted research visit (9 October - 9 December) of my PhD student, Kishan Dayaram, to make progress on three joint papers.
• Hosted research visit (9-26 October) of Dr. Partha Pratim Ghosh. Joint work on canonical extensions started.
• Rehearsed and prepared for the Fundamano production in a team of students. This is a theatrical production bringing mathematics on stage, celebrating the international year for basic sciences.
• Drafted a paper based on the research on the category of near-vector spaces (co-authored with my MSc student, Daniella Moore, and the co-supervisor, Dr. Sophie Marques).
• Gave a National Graduate Academy course on category theory. Click here for videos and lecture notes.
• Gave a South African Theory School course on mathematical structures (jointly with Dr. Cerene Rathilal and Dr. Partha Pratim Ghosh). Click here for videos and lecture notes.
• Spoke on "Is Maths Trauma a real thing?" at the radio show Weekend Breakfast with Refiloe Mpakanyane. Click here for the podcast.

July-August 2022

• Organised a Research Workshop (5 July) on the occasion of visit (5 July) of Dr. Francois Schulz. Collaboration started on ranked monoids.
• Organised a Research Workshop (14 July) on the occasion of the research visit of Prof. Dharmanand Baboolal and Dr. Cerene Rathilal. Collaboration started on metric frames.
• Represented South Africa at the General Assembly of the International Mathematical Union (July 3-4, the report of the meeting is available here). 
• Gave the August NITheCS mini-school on Elementary Introduction to Set Theory together with Dr. Amartya Goswami.
• Gave a Foundations of Abstract Mathematics I seminar on arithmetic and proof composition.
• Started research on the category of near-vector spaces (joint work with Dr. Sophie Marques and Daniella Moore).
• Leading programme renewal discussions in Mathematics in the second semester of 2022.

May-June 2022

• The paper on matrix taxonomy was published in Theory and Applications of Categories.
• Hosted research visit (1-4 June) of Dr. Charles Msipha to advance progress on sum structures.
• Continued research on a noetherian form of sets -- see the updated paper.
• Chaired the second Council Meeting of the South African Mathematical Society (26 May).
• Prepared an International Year for Basic Sciences for Sustainable Development project, which would later be called Fundamano. The project is listed on the official website of this international initiative. Dr. Charles Msipha and Dr. Sophie Marques are co-founders of the project.
• Elected as a NITheCS Associate Representative. Duties include serving on the NITheCS Management Committee (meetings are held monthly).
• Served on the programme committee of the international conference "Topology, algebra and categories in logic" held in Coimbra, Portugal.

March-April 2022

• Revisited research on a noetherian form of sets (joint work with Dr. Francois van Niekerk).
• Organised a Research Workshop on Monoidal Sum Structures at Stellenbosch University (20-25 March) and hosted the visit of Dr. Charles Msipha (Tshwane University of Technology). See the Mathematical Structures Research Programme website for further information. Two research projects dealing with sum structures were initiated at this workshop.
• Organised a Research Workshop on Lower Topology at Stellenbosch University (3-10 April) and hosted the visit of Dr. Amartya Goswami and Ms. Micheala Hoenselaar (University of Johannesburg). A research project on lower topology was initiated at this workshop.
• Gave an interview at the Meet a Mathematician series (see https://youtu.be/lOLIc8Jnja4).
• Supervised a 3rd year research project by Jean du Plessis (under Foundations of Abstract Mathematics II).

January-February 2022

• Serving on the Subcommittee B of the Research Committee of Stellenbosch University for 2022.
• Serving on the Programme Committee of the Faculty of Science of Stellenbosch University for 2022.
• Setting up Mathematical Structures Research Programme at the National Institute for Theoretical and Computational Sciences, along with Prof. Yorick Hardy, Dr. Partha Pratim Ghosh, and Dr. Cerene Rathilal.
• Delivered online lecture series Python-Based Introduction to Mathematical Proofs for the The 12th CHPC Introductory Programming School and The 4th NITheCS Summer School on the Foundations of Theoretical and Computational Science.
• Teaching Engineering Mathematics 214 (together with Dr. Liam Baker, Dr. Ronalda Benjamin, and Dr. Michael Hoefnagel) in the first semester and giving a Foundations of Abstract Mathematics I seminar in Mathematical Reasoning in the first term. Also teaching a third-year module, Topology, in the first semester. 
• Convening Foundations of Abstract Mathematics I & II (year modules) and Topology (semester module) in 2022.
• Started/resumed (co-)supervision of the following postgraduate students: Noluntu Baart (PhD), Roy Ferguson (MSc), Kishan Dayaram (PhD), Paul Hugo (PhD), Brandon Laing (PhD), Daniella Moore (MSc), Ineke van der Berg (PhD).
• The paper on ordinal number systems appeared online in the Journal of Symbolic Logic (joint work with Ineke van der Berg).
• Assumed the role of the President of the South African Mathematical Society for the term 2022-2023. Chaired the first Council meeting (11 Feb).
• Under the research assistantship of Gregor Feierabend, the first prototype of a Haskell implementation of the SOFiA proof assistant was produced. See source code on GitHub or the live software.

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2021 Academic Activities

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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