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.