MATHEMATICAL STRUCTURES FOR FOUNDATIONS AND MODELLING

NITheCS Research Programme → Focus Area

Uncovering Universal Theoretical Principles and Building Integrated Mathematical Capacity to Foster South Africa’s Future Scientific, Technological, and Economic Progress

Lead Researchers: Prof. Eric Andriantiana (RU), Dr. Amartya Goswami (UJ), Prof. Zurab Janelidze (SU), Dr. Wen-Chi Kuo (WITS), Dr. Cerene Rathilal (UKZN).

Membership of the Focus Area is open to any South African mathematician or theoretical computer scientist who is a NITheCS Associate and whose research interest touch on mathematical structures. There are currently around 35 members from around 15 South African universities, including 7 HDI’s. To join the Focus Area, please write to the Deputy Coordinator: Dr. Cerene Rathilal (rathilalc@ukzn.ac.za).

The Focus Area aims to:

Advance the study of fundamental mathematical structures by conducting deep, theoretical research into key conceptual frameworks in mathematics.
Foster innovation by encouraging researchers to explore new mathematical structures, invariants, and relationships that have not yet been fully understood.
Promote interdisciplinary engagement, allowing ideas from diverse areas of mathematics and related fields to inform each other and lead to discoveries.
Develop a strong network of mathematical expertise across South Africa, building capacity and enabling collaboration among institutions, while strengthening South Africa’s position in the global research community.
Mentor and train postgraduate students and early-career researchers, with a focus on human capital development in mathematics and a strong emphasis on participation from historically disadvantaged institutions (HDIs).
Contribute to the global mathematical community by ensuring that the results of the Focus Area are disseminated through high-level academic publications, conferences, and international collaborations.
Cultivate structural thinking by developing educational resources, including teaching materials, online lectures, and interactive tools, aimed at introducing structural thinking to school learners and teachers, students and researchers.

Membership of the research programme is open to any NITheCS associate whose work is aligned with the aims of the research programme.
Every member of the research programme must include the following as their second address (after their main university address) in all of their publications: National Institute for Theoretical and Computational Sciences (NITheCS), <name of the city of their university>, South Africa.
Members of the research programme are generally expected to engage in the academic ecosystem of NITheCS, beyond the activities of the specific research programme (e.g., attend and contribute to NITheCS colloquia).

Almanac

September - December 2023

September 2023

🔹 Research visitor of Bruce Bartlett at Stellenbosch University.

🔹 Training: online mathematics lesson for school learners by Cerene Rathilal (1 Sep).

🔹 Training: Cerene Rathilal runs a mathematical exploration olympiad with second-year students at UKZN (4 Sep – 31 Oct).

🔹 Research visit of Andrew Craig (UJ) at the University of Kwa-Zulu Natal (4-8 September). Host: Cerene Rathilal.

🔹 Engagement: invited presentation by Zurab Janelidze with the Georgian pop-musician and singer-songwriter, Nugzar Ergemlidze, at his Author’s Music Evening in Batumi, Georgia, on 10 November. The two discussed similarities in the process of creativity in mathematics and in pop music. A movie of the event can be found here.

🔹 Research: invited talk (Theories of Exactness Properties) by Zurab Janelidze at the Logical & Algebra Seminar (15 Sep), a satellie event to the 108th Peripatetic Seminar on Sheaves and Logic, in Terrasini (Palermo), Sicily (Italy).

🔹 Research: 13^th International Workshop on Non-Classical Models of Automata and Applications (18-19 September, Cyprus): Brink van der Merwe gives two talks, “Formalizing BPE Tokenization” (joint work with Martin Berglund) and “Ordered Context-Free Grammars Revisited”.

🔹 Training: Heidelberg Laureate Forum (23-29 September): Cerene Rathilal and Vivien Visaya presented a workshop in topological data analysis. Cerene Rathilal hosted a Women in Mathematics session at the same Forum and was a panelist at a panel discussion.

October 2023

🔹 Research visit of Andrew Craig (UJ) at Chapman University (USA, 28 September – 18 October). Host: Peter Jipsen

🔹 Research visit of Cerene Rathilal at University of Pavia (1-6 October). Host: Frank Neumann.

🔹 Engagement: invited public presentation in the Music Department of Stellenbosch University on the mathematical structure of music (5 October), by Zurab Janelidze, Hans Roosenschoon and their student collaborators.

🔹 Training: online lessons for school learners: Abstract Algebra (6 and 9 October).

🔹 Research visit of Nancy Neudauer at Stellenbosch University (6 Oct – 23 Dec). Co-hosts: Bruce Bartlett and Karin-Therese Howell.

🔹 Training: online lessons for school learners, Mathematics Club at the University of Kwa-Zulu Natal (14 and 21 October).

November 2023

🔹 Training: talk on “The Evolution of the Number Concept from Natural to Real Numbers” by Charles Nsukukazifani Msipha at the Table Mountain Delta 2023, the 14th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics (26 Nov – 1 Dec)

🔹 Engagement: presentation by Zurab Janelidze and Cerene Rathilal on this research programme (Mathematical Structures and Modelling) at a NITheCS annual programme review on 24 November.

🔹 Engagement: invited talk by Zurab Janelidze on Mathematical Structure of Music during a CIMPA School “Blockchain in Theory and Real Applications” at AIMS on 25 November. Zurab Janelidze and Cerene Rathilal championed a Mathematical Exploration Olympiad centered around blockchain on the same day.

December 2023

🔹 Engagement: Fundamano 2 production at Drostdy Theatre (1 Dec), featuring musical improvisations based on mathematical structure of music (a project in the research programme).

🔹 Research: talk by Zurab Janelidze on Nullital Categories at the SAMS Congress (4-7 Dec). Zurab Janelidze and Cerene Rathilal hosted an undergraduate research session at the same congress, featuring research talks by undergraduate participants as well as a plenary talk by Nancy Neudauer on undergraduate research activities in the USA. Such session is organised first time in the history of SAMS Congresses.

🔹 Training: Workshop for postgraduate students: Topology for Tomorrow (9-11 December) co-organised by Cerene Rathilal, who held there a Mathematical Exploration Olympiad.

May - August 2023

May 2023

🔹 Research visit of Cerene Rathilal at Stellenbosch University (10-17 May). Started collaboration with Jean du Plessis, Zurab Janelidze and Bernardus Wessels on chainmails. Cerene Rathilal gives a NITheCS colloquium talk (15 May).

🔹 Research: impromptu mathematical exploration session discovering a concept of entropy of a metric space (20 May). Participants: Zurab Janelidze, Gideo Joubert, Roy Ferguson.

🔹 Research talk by Cerene Rathilal at the University of the Witwatersrand (25 May) in the departmental seminar.

June 2023

🔹 Engagement: strategic meeting on the future of mathematical sciences held in Stellenbosch, “Towards a National Strategy for the Mathematical Sciences“. Main organiser: Zurab Janelidze

🔹 Engagement: invited plenary talk by Charles Nsukukazifani Msipha at the 28th Annual National Congress of the Association for Mathematics Education of South Africa (26-30 June).

🔹 Research visit of Cerene Rathilal at the University of Johannesburg (25 June – 2 July). Host: Vivien Visaya

July 2023

🔹 Research Workshop on Deductive Reasoning in School-Level Mathematics (3 – 7 July). Participants: Charles Nsukukazifani Msipha, Noluntu and Imi Baart, Two Mathematics Teachers from the Merensky High School (Limpopo). The workshop was organised by Zurab Janelidze and concluded with a Wisaarkhu evening on 7 July that showcased two research projects from this research programme (Mathematical Structures and Modelling).

🔹 Engagement: NITheCS session by Bruce Watson and Cerene Rathilal at Functional Analysis and Operator Theory South Africa (3 – 7 July), WITS Rural Facility, Limpopo.

🔹 Training: online lessons for school learners in Abstract Algebra (10 and 11 July).

🔹 Training: presentation for postgraduate students by Cerene Rathilal about the “Future Mathematicians Programme and Community Engagement” at the Annual Research Meeting of the CoE-MaSS. Zurab Janelidze gives an invited presentation about mathematical structures and modelling at the same meeting (26 July). The audience are the CoE-MaSS funded postgraduate students.

🔹 Research visit of Miroslav Haviar (Matej Bel University, Slovakia) at University of Johannesburg (27 July – 6 August). Host: Andrew Craig (UJ)

🔹 Engagement: invited public presentation in the Music Department of Stellenbosch University on the mathematical structure of music (27 July) by Zurab Janelidze and Hans Roosenschoon.

🔹 Engagement: NITheCS colloquium on “A New Horizon for Teaching and Learning of Mathematics” (31 July) by Zurab Janelidze. See the video of the talk here.

🔹 Research visit of Michael Hoefnagel to Belgium and Germany. Michael Hoefnagel gave a talk (“On the commutativity of products with coequalisers”) at the International Category Theory Conference 2023.

August 2023

🔹 Engagement: NITheCS session by Zurab Janelidze and Bernardus Wessels at the 7th Biennial International Group Theory Conference held at NWU, in Potschefstroom, 7-11 August.

🔹 Training: online mathematics lessons for school learners by Cerene Rathilal (18 Aug and 25 Aug)

🔹 Engagement visit of Zurab Janelidze to the University of Kwa-Zulu Natal, the gravity research group (14-18 August). Host: Sudan Hansraj. Zurab Janelidze and Cerene Rathilal run a mathematical expedition session at a local school under the Future Mathematicians Programme. Zurab Janelidze gives a public talk on What Makes Mathematics Tick? The video of the public talk is available here.

🔹 Engagement: Zurab Janelidze jointly with Jonathan Shock convene Mathematical Exploration Olympiad for undergraduate students at Stellenbosch University (27 August). Two teams from UCT and two teams from SU participate.

🔹 Research and training: visit of Diana Rodelo (Portugal) at Stellenbosch University to work with Michael Hoefnagel. Diana also gave an intensive lecture course on categorical algebra for the undergraduate and postgraduate students.

🔹 Research: invited talk at the XIII Annual International Conference of the Georgian Mathematical Union (29 Aug – 3 Sep) by Zurab Janelidze on Mystery of Binary Matrix Properties of Categories.

January - April 2023

January 2023

🔹 Training: Logic at the intersection of Algebra, Categories and Topology, a CIMPA summer school aimed at early career academics and senior postgraduate students (2-13 Jan). Main organizer (from the Mathematical Structures Research Programme): Willem Conradie

🔹 Research visit of Peter Jipsen at Stellenbosch University (20-21 January). Host: Zurab Janelidze

🔹 Research Workshop on Graph Theory 2023 (22-29 January). Main organizer (from the Mathematical Structures Research Programme): Sonwabile Mafunda

🔹 Research visit of Brink van der Merwe: to Umeå, Sweden.

🔹 Engagement: Undergraduate Mathematics Research Workshop at Stellenbosch University (30 January). Main speaker: Nancy Neudauer (USA). Organizers: Zurab Janelidze and Karin Howell. Link: talk post of Zurab Janelidze

February 2023

🔹 Research visit of Prof Anke Kalauch (TU Dresden) at the University of the Witwatersrand. Hosts: W. Kuo, J. Homann and B.A. Watson.

March 2023

🔹 Training: Cerene Rathilal gives an online Grade 12 Term 1 revision class (3 and 10 March).

🔹 Engagement: Cerene Rathilal co-organises International Day of Mathematics zoom event (11 March), featuring presentations by Claudette Robinson, Keegan Anderson, and Simo Mthethwa. NITheCS Public lecture in celebration of the International Day of Mathematics (13 March) given by Zurab Janelidze. Links: slides, recording.

🔹 Research: Stellenbosch Category Theory Seminar (17 March) organised by James Gray. Speakers: Hans Porst, Michael Hoefnagel, Bruce Bartlett. Link: blog post by Zurab Janelidze.

🔹 Research visit of Marino Gran at Stellenbosch University. Colloquium talk by Marino Gran (20 March). Workshop in Categorical Algebra (26 March) attended by students and staff of UCT, SU and University of Louvain-la-Neuve. Speakers: Michael Hoefnagel, Gideo Joubert, Emma Theart, and a PhD student of Marino Gran.

🔹 Research: Women in Mathematics and its Applications Research Day (23 March), held at the African Institute for Mathematical Sciences. Organised by Karin-Therese Howell and Nancy Ann Neudauer. Among the attendees where female undergraduate students from Stellenbosch University. Cerene Rathilal gave a talk on “S-metrizable frames”.

🔹 Research: Mathematics meets rock music collaborative session at Stellenbosch University (24 March). Zurab Janelidze meets with students in mathematics and music for experimenting composition of rock music based on mathematical “gestalt diagrams” (joint work with Hans Roosenschoon, Bethany Robinson and Gerhard Woithe).

🔹 Research meeting on abstract connectedness at Stellenbosch University (31 march). Start of a collaborative project with Jean du Plessis and Bernardus Wessels.

🔹 Research visit of Nancy Ann Neudauer at Stellenbosch University. Co-hosts: Bruce Bartlett and Karin-Therese Howell.

April 2023

🔹 Training: Abstract Algebra Online Holiday Programme for School Learners, Grades 8+ (5 & 6 April) launched by Cerene Rathilal. First session (5 April) was presented by Cerene Rathilal and Sophie Marques. Second session (6 April) was presented by Zurab Janelidze and Sophie Marques.

🔹 Research visit of Noluntu Baart at Stellenbosch University (17-21 April) for joint work with Zurab Janelidze and Erna Lampen on mathematical structures in primary education.

🔹 Research and Engagement: Zurab Janelidze visits Amartya Goswami at Univesity of Johannesburg for a research discussion and has a preliminary discussion with the CEO of SACNASP about imlementing mathematical enrichment classes in South African schools for better preparation in science (April 25).

🔹 Research and Engagement: Emerging Perspectives in Mathematics II conference in Zingwazi (near Durban): Cerene Rathilal contributes a talk, “Locally non-separating sublocales”. Zurab Janelidze contributes a talk on a joint work with Helmut Prodinger and Francois van Niekerk (April 28). Dharmanand Baboolal contributes a talk: “A topologist’s apology”. Zurab Janelidze and Cerene Rathilal introduce the Mathematical Structures and Modelling research programme of NITheCS to the participants of this conference in a special session.

September - December 2022

September 2022

🔹 Research visit of Noluntu Baart at Stellenbosch University (20 September – 8 October). Host: Zurab Janelidze

🔹 Research: Mathematical Structures Workshop (12 September – 14 September) presented at Witwatersrand University by Professor Biswajit Mitra (University of Burdwan, India) and Sourav Koner (University of Burdwan, India)

October 2022

🔹 Research: Kishan Dayaram visiting Categorical Algebra research group at Stellenbosch University (9 October – 9 December). Collaborator: Zurab Janelidze

🔹 Research: Partha Pratim Ghosh visiting Categorical Algebra research group at Stellenbosch University (9-26 October). Collaborator: Zurab Janelidze

November 2022

🔹 Engagement: Fundamano production (4 November), science engagement/entertainment event for the celebration of the International Year of Basic Sciences for Sustainable Development, see https://conceptualroots.blogspot.com/ for more information. YouTube channel: https://www.youtube.com/@fundamano

🔹 Research: Workshop at Stellenbosch University on measure structures organized by Zurab Janelidze (18-20 November). Participants: Kishan Dayaram, Zurab Janelidze, Gideo Joubert (Honours Student), Cerene Rathilal

December 2022

🔹 Training: Topology for Tomorrow a workshop at AIMS aimed at early career academics and senior postgraduate students (3-5 Dec). Main organizer (from the Mathematical Structures Research Programme): Cerene Rathilal

May - August 2022

May 2022

🔹 Training: Online Math School (5 and 19 May) presented by Cerene Rathilal

June 2022

🔹 Research stay of Charles Msipha at Stellenbosch University (1-4 June). Hosts and collaborators: Roy Ferguson, Michael Hoefnagel, Zurab Janelidze, Sophie Marques, Emma Theart.

🔹 Training: Online Math School (2 June) presented by Cerene Rathilal

🔹 Research Workshop (6-10 June) at the University of Johannesburg presented by Andrew Craig, Themba Dube, Yorick Hardy, Amartya Goswami, and Apostolos Tzimoulis. Organized by Amartya Goswami and assisted by Cerene Rathilal

🔹 Research Workshop in Algebraic Geometry (20-30 June) presented by Sophie Marques. Workshop participants: Chad Brache, Damas Mgani and Elizabeth Mrema.

July 2022

🔹 Research visit of Francois Schulz at Stellenbosch University (4-8 July). Host and collaborator: Ronalda Benjamin. July 5: workshop organized by Zurab Janelidze and delivered by Francois Schulz on “Generalized rank, trace, and determinant”. Workshop participants: Ronalda Benjamin, Zurab Janelidze, David Olabiyi (MSc student), Dimby Rabearivony (PhD student), Francois Schulz, Tolotranirina Andrianarisoa (PhD students).

🔹 Research visit of Dharmanand Baboolal and Cerene Rathilal at the University of the Western Cape (10-16 July). Host and collaborator: Paran Pillay. July 14: research workshop organized by Zurab Janelidze and delivered by Dharmanand Baboolal on “Metric frames”. Workshop participants: Dharmanand Baboolal, Roy Ferguson (MSc student), Zurab Janelidze, Paran Pillay, Cerene Rathilal, Ineke van der Berg (PhD student).

🔹 Research visit of C.A. Finocchiaro at the University of Johannessburg. Host and collaborator: A. Goswami

August 2022

🔹 Training: Elementary introduction to set theory, NITheCS mini-school presented by Amartya Goswami and Zurab Janelidze

January - April 2022

January 2022

🔹 Engagement: online meetings for setting up the Research Programme.

February 2022

🔹 Training: Lecture Series on Python-Based Introduction to Mathematical Proofs

🔹 Research: online seminar (24 February) presented by Yorick Hardy and Partha Pratim Ghosh

March 2022

🔹 Research: online seminar (3 March) presented by Amartya Goswami

🔹 Research: online Math School (4 March) presented by Cerene Rathilal

🔹 Research: online Math School (11 March) presented by Cerene Rathilal

🔹 Engagement: Meet a mathematician Part I and Part II (14 March) hosted by Cerene Rathilal

🔹 Research Workshop on Monoidal Sum Structures at Stellenbosch University (20-25 March). Participants: Roy Furgeson, Michael Hoefnagel, Zurab Janelidze, Charles Msipha, Emma Theart. Organized by Zurab Janelidze

April 2022

🔹 Research Workshop on Lower Topology at Stellenbosch University (3-10 April). Participants: Amartya Goswami, Michael Hoefnagel, Micheala Hoenselaar, Zurab Janelidze, Ineke van der Berg. Organized by Zurab Janelidze

🔹 Training: Online Math School (21 April) presented by Cerene Rathilal

Outputs (2022-2023)

Published or In Press (28)

D. Barrish, S. Kroon, B. van der Merwe, Making Superhuman AI more Human in Chess, Advances in Computer Games 2023 (accepted)
M. Berglund and B. van der Merwe, Ordered Context-Free Grammars, In: Caron, P., Mignot, L. (eds) Implementation and Application of Automata, Lecture Notes in Computer Science 13266, 2022, International Conference on Implementation and Application of Automata, 53-66
B. Davvaz, A. Goswami, and K.-T. Howell, Primitive hyperideals and hyperstructure spaces of hyperrings, Categories and General Algebraic Structures with Applications (accepted), 2023
B. Davvaz, K-T Howell, and J.R. Rabie “Hyper near-vector spaces”, Palestine Journal of Mathematics (accepted for publication), 2023
T. Dube and A. Goswami, Ideal spaces: An extension of structure spaces of rings, Journal of Algebra and its Applications (published online, in press), 2022
C. A. Finnocchiaro, A. Goswami, and D. Spirito, Distinguished classes of ideal spaces and their topological properties, Communications in Algebra 51, 2023, 1752-1760
P. P. Ghosh, Another closure operator on pre neighbourhood spaces, Categories and General Algebraic Structures with Applications (accepted), 2023
P. P. Ghosh, Internal neighbourhood structures II: Closure and closed morphisms, Categories and General Algebraic Structures with Applications 18, 2023, 155-223
A. Goswami, Iséki spaces of semirings, Bollettino dell’Unione Matematica Italiana (online ready), 2022
A. Goswami, Proper spaces are spectral, Applied General Topology, Applied General Topology 24(1), 2023, 95-99
A. Goswami, Normal structure spaces of groups, Rendiconti del Circolo Matematico di Palermo Series 2 (published online, in press), 2022
A. Goswami, Multidimensional population modelling with transition structures, Applicationes Mathematicae 49(2), 2022, 165-174
A. Goswami, Terminal spaces of monoids, Communications of Korean Mathematical Society (accepted), 2023
J.R.A. Gray, A note on images of cover relations, Theory and Applications of Categories 38, 2022, 311-318
M. Hoefnagel, P.-A. Jacqmin, and Z. Janelidze, The matrix taxonomy of finitely complete categories, Theory and Applications of Categories 38, 2022, 737-790
M. Hoefnagel, P.-A. Jacqmin, Matrix taxonomy and Bourn localization, Applied Categorical Structures, 2022 (published online)
M. Hoefnagel, P.-A. Jacqmin, Z. Janelidze, and E. van der Walt, On binary matrix properties, Quaestiones Mathematicae (published online), 2023
K.-T. Howell and N. Neudauer, On independence in near-vector spaces and their matroids, Linear Algebra and its applications (published online), 2023
K.-T. Howell and S. Marques, Toward an intuitive understanding of the structure of near-vector spaces, Communications in Algebra 50, 2022, 3664–3677
Z. Janelidze, H. Prodinger, and F. K. van Niekerk, Combinatorics arising from lax colimits of posets, Order (published online), 2023
Z. Janelidze and I. van der Berg, A Dedekind-style axiomatization and the corresponding universal property of an ordinal number system, The Journal of Symbolic Logic 87 (2022), 1396-1418
A. Kalauch, W. Kuo, B.A. Watson, A Hahn-Jordan decomposition and Riesz-Frechet representation theorem in Riesz spaces, Quaestiones Mathematicae (accepted), 2023.
H. Prodinger, Partial skew Dyck paths: A kernel method approach, Graphs and Combinatorics 38, 2022, 11pp
H. Prodinger, Partial sums of Horadam sequences: sum-free representations via generating functions, Integers 22, 2022, #A20, 2 pp
H. Prodinger, Skew Dyck paths having no peaks at level 1 (Sequence A128723), Journal of Integer Sequences 25, 2022, Article 22.1.6, 10 pp
H. Prodinger, Skew Dyck paths with catastrophes, Discrete Mathematics Letters 10, 2022, 9-13
H. Prodinger, Deepest nodes in marked ordered trees, Annales Mathematicae Silesianae 36, 2022, 215-227
C. Rathilal, S-Metrizability and the Wallman basis of a frame, Categories and General Algebraic Structures with Applications, published online in 2023

Submitted for Publication (35)

R. Benjamin and C. Budde, On the order Lozanovsky spectrum of a positive operator, submitted for publication, 2022
R. Benjamin and F. Schulz, On peripherally multiplicative maps on Banach algebras, submitted for publication, 2022
L. Boonzaaier and S. Marques, Near-field structures induced by multiplicative automorphisms, their limits and generalized means for complex numbers, submitted for publication, 2022
C. Chun, K-T Howell and N. Neudauer, A characterization of matroids that come from near-vector spaces, Electronic journal of Combinatorics, submitted for publication, 2023
A. Craig, M. Haviar and K. Marais, Dual digraphs of finite meet-distributive and modular lattices, submitted for publication, 2023
A. Craig and C. Robinson, Representable distributive quasi relation algebras, submitted for publication, 2023
A. Craig and C. Robinson, A representation of odd Sugihara monoids via weakening relations, submitted for publication, 2023
A. Fošner, Y. Hardy and B. Zinsou, Block determinants, partial determinants and the exponential map, submitted for publication, 2022
K. Dayaram, A. Goswami, Z. Janelidze and T. van der Linden, Duality in Non-Abelian Algebra V. Homological Diagram Lemmas, 2023
T. Dube and A. Goswami, Spectral topologies on skew braces, submitted for publication, 2022
T. Dube and A. Goswami, Some aspects of k-ideals of semirings, 2023
A. Dwarkesh and A. Goswami, Novikov algebras and their primitive ideals, 2023
A. Goswami, Primitive ideals and Jacobson’s structure spaces of noncommutative semigroups, submitted for publication, 2022
A. Goswami, Jacobson program for Lie algebras, submitted for publication, 2022
A. Goswami, Some remarks on the ring of arithmetical functions, submitted for publication, 2022
A. Goswami, Jacobson’s structure spaces of Novikov algebras, submitted for publication, 2022
A. Goswami, k-spaces of non-domain-valued geometric points, submitted for publication, 2022
A. Goswami, Spectrality and monoids, submitted for publication, 2023
A. Goswami, On z-ideals and z-closure operations of semirings, I, 2023
A. Goswami, Primitive ideals and Jacobson’s structure spaces of semigroups, 2023
A. Goswami, Topological properties of some classes of submodules, 2023
A. Goswami, Spectral hyperspaces of Krasner hyperrings, 2023
A. Goswami, Spectral spaces of normal subgroups, 2023
A. Goswami, On ideals in quantales, I, 2023
A. Goswami, On ideals in quantales, II, 2023
A. Goswami, Some classes of subsemimodule spaces, 2023
J. Gray, A note on split extension classifiers of perfect objects, submitted for publication, 2022
J. Gray and T. Janelidze-Gray, A note on Huq commutativity of normal monomorphisms, submitted for publication, 2022
M. Hoefnagel, Huq centrality and commutativity of finite products with coequalizers, submitted for publication, 2022
M. Hoefnagel and P.-A. Jacqmin, When a matrix property implies the Mal’tsev property, submitted for publication, 2022
Z. Janelidze and F. K. van Niekerk, An axiomatic analysis of optimal noetherian forms of topois and their link to semi-abelian categories, preprint on overleaf, submitted for publication 2023
A. Kalauch, W. Kuo, and B.A. Watson, Strong completeness of a class of L^2-type Riesz spaces, submitted for publication, 2023
S. Marques and D. Moore, Near-linear algebra, submitted for publication, 2022
S. Marques and E. Mrema, Quadratic cyclotomic moduli spaces, submitted for publication, 2022
C. Rathilal, Locally non-separating sublocales, submitted for publication, 2023

In Progress (42)

I. Allie, B. Du Preez, Z. Hefty, T. Kunene, and S. Mafunda, Proximity and Remoteness in Trees with given Segment Sequence, work in progress, 2023
A. Alochukwu, P. Dankelmann, S. Mafunda, S. Mukwembi, Average Distance and Connected Domination, started 2023
Y. Azouzi, M. Masmoudi, B.A. Watson, The Kakutani-Rokhlin Lemma for conditionally ergodic processes in Riesz spaces, work in progress 2023
C. Bartels, S. Currie, B.A. Watson, Oscillation theory and eigenvalue asymptotic for Sturm-Liouville equations with transfer conditions, work in progress, 2023
Z. Janelidze, C. Rathilal and I. van der Berg, A note on the definition of a metric frame, started 2022
D. Baboolal, P. Pillay, and C. Rathilal, Convexity in metric frames, started 2022
R. Benjamin and A. Goswami, Investigating open problems on the spectral synthesis for Banach algebras, started 2022
R. Benjamin and C. Schwanke, Exploring open questions in Banach lattice algebras, started 2022
P.A. Binding, P.J. Browne, and B.A. Watson, Non-real eigenvalues and Jordan chains for the p-Laplacian, work in progress, 2023
L. Boonzaaier and S. Marques, Nier-field structures on a given scalar group, started 2022
B. Blum-Smith and S. Marques, Barycentric subdivisions, parameter subrings, and a negative answer to a question of S. Murai, started 2022
A. Craig and C. Rathilal, Compactifications of the interval topology, started 2023
K. Dayaram, A. Goswami, and Z. Janelidze, Formal analysis of Yoneda-Quillen exact categories, started 2022
K. Dayaram, A. Goswami, and Z. Janelidze, Self-dual axiomatic approach to diagram lemmas, started 2022
K. Dayaram, A. Goswami, and Z. Janelidze, A survey of the butterfly lemma, started 2022
K. Dayaram, A. Goswami, J. S. Joao, and Y. Hardy, Local monoid structure of positive semi-definite matrices, started 2022
K. Dayaram, Z. Janelidze, G. Joubert, Cerene Rathilal, Measure detecting maps, started 2022
B. Du Preez and S. Mafunda, Proximity and remoteness in triangulations and quadrangulations of prescribed degree and connectivity, started 2022
J. Du Plessis, Z. Janelidze, C. Rathilal and B. Wessels, Chainmails of connected elements in a locally connected frame, started 2023
A. Dwarkesh and A. Goswami, Primitive ideals of Novikov algebras, started 2022
G. Feierabend and Z. Janelidze, A functorial parsing of partially bracketed expressions, started 2023
R. Ferguson, M. Hoefnagel, Z. Janelidze, E. Theart, Extensivity for sum structures, started 2022
R. Ferguson and Z. Janelidze, Some remarks on the canonical morphism from the sum to the product, started 2022
R. Ferguson and Z. Janelidze, Grothendieck topologies and SU forms, started 2023
P. P. Ghosh, N. M. Tshakatumba, and I. Naidoo, Free local algebras, started 2023
J. Gray, A note on the relationship between action accessible and weakly action representable categories, started 2022
M. Hoefnagel, On commutativity of finite products with coequalizers in general categories, started 2022
M. Hoefnagel and P.-A. Jacqmin, On atomicity of arithmeticity, started 2022
M. Hoefnagel and D. Rodelo, Jonsson categories, started 2022
M. Hoefnagel and D. Rodelo, Mitschke’s theorem in regular categories, started 2022
M. Hoefnagel and E. Theart, On extensivity of morphisms, started 2022
Z. Janelidze and G. Joubert, Reverse Cayley representation theorems for monoids and semigroups, started 2023
Z. Janelidze, S. Marques, and D. Moore, On the category of near-vector space, started 2022
Z. Janelidze, B. Robinson, H. Roosenschoon and G. Woithe, On the gestalt structure of music, started 2023
Z. Janelidze, F. van Niekerk, J. Viljoen, and B. Wessels, On the endomatch index of a digraph, resumed 2023
A. Kalauch, W. Kuo., and B.A. Watson, Indecomposability, irreducible and ergodicity for Riesz space processes, work in progress, 2023
W. Kuo and B.A. Watson, The Stein-Chen method and a law of small numbers in Riesz spaces, work in progress, 2023
S. Marques and E. Mrema, 2-cyclotomic extensions, started 2022
S. Marques and L. Pagano, Jet algebra ramification groups, started 2022
S. Mafunda and E. Mwambene, On automorphism groups of Cayley graphs of conjugacy type on PSL(n,q), started 2022
R. Picard, B.A. Watson, Generalized Sturm-Liouville problems and their related time-evolutionary systems, work in progress, 2023
C. Rathilal and A. Pultr, Local non-separation and fitness, started 2022

Paper Embryos (16)

C. Budde and Z. Janelidze, On the category of C0-semigroups, conceived 2022
S. Currie, M. Nowaczyk, B.A. Watson, Some first order one and two parameter inverse spectral problems, work in progress, 2023
S. Currie, B.A. Watson et al, Inverse Sturm-Liouville problems with eigenparameter dependent transmission conditions, work in progress, 2023
G. Feierabend, Haskell implementation of SOFiA on GitHub and live software, conceived 2022
A. Goswami, Prime spectra of modules over quantales, 2023
A. Goswami, k-hyperideals of hypersemirings, 2023
A. Goswami, Some remarks on ring of arithmetical functions, 2023
A. Goswami, Cohen structure theorem for Jacobson semisimple rings, 2023
A. Goswami, M. Hoenselaar, Z. Janelidze, and I. van der Berg, Relative lower topology, conceived 2022
J. Homann, W.Kuo, and B.A.Watson, Information Theory in Riesz spaces, work in progress, 2023
Z. Janelidze and P. Jipsen, A categorical view on relational clones, conceived 2022
Z. Janelidze, G. Joubert and F. Schulz, Ranked monoids, conceived 2022
Z. Janelidze and B. Laing, Assemblers, conceived 2022
W. Kuo, B.A. Watson, et al, Strong mixing in Riesz spaces, work in progress, 2023
T. Ndlovu, B.A. Watson, B. Zinsou, The Kolmogorov n series theorems in Riesz spaces, work in progress, 2023
A. Tzimoulis, K. Dayaram, G. Greco, P. P. Ghosh and Z. Janelidze, Understanding canonical extensions, started 2022