SPACE-LIKE MATHEMATICAL STRUCTURES AND RELATED TOPICS IN ALGEBRA, LOGIC AND COMPUTATION 

Research Programme Team:

PI – Principal investigator (programme manager) | SI – Senior investigator | I – Investigator

Papers Published or In Press

  1. C. A. Finnocchiaro, A. Goswami, and D. Spirito, Distinguished classes of ideal spaces and their topological properties, Communications in Algebra (in press)
  2. A. Goswami and T. Dube, Ideal spaces: An extension of structure spaces of rings, Journal of Algebra and its Applications, (published online, in press)
  3. J.R.A. Gray, A note on images of cover relations, Theory and Applications of Categories 38, 2022, 311-318.
  4. M. Hoefnagel, P.-A. Jacqmin, and Z. Janelidze, The matrix taxonomy of finitely complete categories, Theory and Applications of Categories 38, 2022, 737-790.
  5. M. Hoefnagel, P.-A. Jacqmin, Matrix taxonomy and Bourn localization, Applied Categorical Structures, 2022 (published online, in press).
  6. K.-T. Howell and S. Marques, Toward an intuitive understanding of the structure of near-vector spaces, Communications in Algebra 50, 2022, 36643677.
  7. Z. Janelidze, H. Prodinger, and F. K. van Niekerk, Combinatorics arising from lax colimits of posets, Order (in press). Preprint.
  8. 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, Cambridge University Press, 24pp (published online, in press).
  9. H. Prodinger, Partial skew Dyck paths: A kernel method approach, Graphs and Combinatorics 38, 2022, 11pp.
  10. H. Prodinger, Partial sums of Horadam sequences: sum-free representations via generating functions, Integers 22, 2022, #A20, 2pp.
  11. 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.
  12. H. Prodinger, Skew Dyck paths with catastrophes, Discrete Mathematics Letters 10, 2022, 9-13.
  13. H. Prodinger, Deepest nodes in marked ordered trees, Annales Mathematicae Silesianae 36 (2022), 215-227.
  14. B. van der Merwe and M. Berglund, 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.

Papers Submitted

  1. L. Boonzaaier and S. Marques, Near-field structures induced by multiplicative automorphisms, their limits and generalized means for complex numbers, submitted for publication.
  2. A. Fošner, Y. Hardy and B. Zinsou, Block determinants, partial determinants and the exponential map, submitted for publication.
  3. B. Daavz, A. Goswami, and K.-T. Howell, Structure spaces of hyperrings, submitted for publication
  4. T. Dube and A. Goswami, Spectral topologies on skew braces, submitted for publication
  5. P. P. Ghosh, Internal neighbourhood structures II: Closure and closed morphisms, submitted for publication
  6. A. Goswami, Proper spaces are spectral, submitted for publication
  7. A. Goswami, Multidimensional population modelling with transition structures, submitted for publication
  8. A. Goswami, Normal structure spaces of groups, submitted for publication
  9. A. Goswami, Primitive ideals and Jacobson’s structure spaces of noncommutative semigroups, submitted for publication
  10. A. Goswami, Iséki spaces of semirings, submitted for publication
  11. A. Goswami, Jacobson program for Lie algebras, submitted for publication
  12. M. Hoefnagel, Huq centrality and commutativity of finite products with coequalizers, submitted for publication
  13. M. Hoefnagel and P.-A. Jacqmin, When a matrix property implies the Mal’tsev property, submitted for publication
  14. M. Hoefnagel, P.-A. Jacqmin, Z. Janelidze, and E. van der Walt, On binary matrix properties, submitted for publication
  15. S. Marques and D. Moore, Near-linear algebra, submitted for publication
  16. S. Marques and E. Mrema, Quadratic cyclotomic moduli spaces, submitted for publication

Work in Progress

  1. T. Apostolos, K. Dayaram, P. P. Ghosh and Z. Janelidze, Understanding canonical extensions, work in progress
  2. D. Baboolal, R. Ferguson, Z. Janelidze, P. Pillay, C. Rathilal, and I. van der Berg, Digital frames, work in progress
  3. D. Baboolal, P. Pillay, and C. Rathilal, Convexity in metric frames, work in progress
  4. R. Benjamin and C. Budde, On the order Lozanovsky spectrum of a positive operator, work in progress
  5. R. Benjamin, Z. Janelidze, G. Joubert and F. Schulz, Ranked monoids, work in progress
  6. R. Benjamin and A. Goswami, Investigating open problems on the spectral synthesis for Banach algebras, work in progress
  7. R. Benjamin and F. Schulz, On peripherally multiplicative maps on Banach algebras, work in progress
  8. R. Benjamin and C. Schwanke, Exploring open questions in Banach lattice algebras, work in progress
  9. L. Boonzaaier and S. Marques, Nier-field structures on a given scalar group, work in progress
  10. B. Blum-Smith and S. Marques, Barycentric subdivisions, parameter subrings, and a negative answer to a question of S. Murai, work in progress
  11. K. Dayaram, A. Goswami, and Z. Janelidze, Formal analysis of Yoneda-Quillen exact categories, work in progress
  12. K. Dayaram, A. Goswami, and Z. Janelidze, Self-dual axiomatic approach to diagram lemmas, work in progress
  13. K. Dayaram, A. Goswami, and Z. Janelidze, A survey of the butterfly lemma, work in progress
  14. K. Dayaram, A. Goswami, J. S. Joao, and Y. Hardy, Local monoid structure of positive semi-definite matrices, work in progress
  15. K. Dayaram, Z. Janelidze, G. Joubert, Cerene Rathilal, Measure detecting maps, work in progress
  16. A. Dwarkesh and A. Goswami, Primitive ideals of Novikov algebras, work in progress
  17. G. Feierabend, Haskell implementation of SOFiA on GitHub and live software
  18. R. Ferguson, M. Hoefnagel, Z. Janelidze, C. Msipha, E. Theart, Extensivity for sum structures, work in progress
  19. R. Ferguson, M. Hoefnagel, Z. Janelidze, C. Msipha, E. Theart, Some remarks on the canonical morphism from the sum to the product, work in progress
  20. A. Goswami, M. Hoenselaar, Z. Janelidze, and I. van der Berg, Relative lower topology, work in progress
  21. J. Gray and T. Janelidze-Gray, A note on Huq commutativity of normal monomorphisms, work in progress
  22. M. Hoefnagel, On commutativity of finite products with coequalizers in general categories, work in progress
  23. M. Hoefnagel and P.-A. Jacqmin, On atomicity of arithmeticity, work in progress
  24. M. Hoefnagel and D. Rodelo, Jonsson categories, work in progress
  25. M. Hoefnagel and D. Rodelo, Mitschke’s theorem in regular categories, work in progress
  26. M. Hoefnagel and E. Theart, On extensivity of morphisms
  27. 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
  28. Z. Janelidze, S. Marques, and D. Moore, On the category of near-vector space, work in progress
  29. S. Marques and E. Mrema, 2-cyclotomic extensions, work in progress
  30. S. Marques and L. Pagano, Jet algebra ramification groups, work in progress
  31. C. Rathilal, Wallman compactification and S metrizable Frames, work in progress
  32. C. Rathilal, Locally non-separating sublocales, work in progress
  33. C. Rathilal and A. Pultr, Local non-separation and fitness, work in progress
  34. F. K. van Niekerk, Monads and noetherian forms, work in progress

Research Workshops, Seminars and other Events

January

  • Online meetings for setting up the Research Programme.

February

March

  • Online seminar (3 March) presented by Amartya Goswami
  • Online Math School (4 March) presented by Cerene Rathilal
  • Online Math School (11 March) presented by Cerene Rathilal
  • 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

  • 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
  • Online Math School (21 April) presented by Cerene Rathilal

 

 

May

June

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

  • 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, and a postgraduate student in Mathematics Division.
  • 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

September

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

  • Kishan Dayaram visiting Categorical Algebra research group at Stellenbosch University (9 October – 9 December). Collaborator: Zurab Janelidze
  • Partha Pratim Ghosh visiting Categorical Algebra research group at Stellenbosch University (9-26 October). Collaborator: Zurab Janelidze

November

  • 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 
  • 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

  • Topology for Tomorrow: workshop at AIMS (3-5 Dec)