Mathematical Timeline (starting from January 2021)

July-August 2021

  • Current plan: finialize the binary matrix properties paper.
  • Started writing a book in abstract algebra jointly with Amartya Goswami. You can follow the progress here.

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 supervision of PhD studies of Brandon Laing on the SOFiA project.
  • Started supervision of PhD studies of Ineke van der Berg.
  • Mostly absent from research due to various circumstances, including administrative/refereeing duties.
  • Started a new (highly ambitious) research project on conceptualizing the form of space-time.

March-April 2021

  • Started research on matches of digraphs: pioneering joint work with Francois van Niekerk and Jade Viljoen (research grew out from her honors project).
  • Started research 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 the joint work with Michael and Pierre-Alain. My co-authors finalized a paper based on Emil's results and I have rejoined them as a co-author.
  • Revisited research 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 Mooore on categorical aspects of near-vector spaces (cosupervised by Karin Howell)

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.
  • Revisited research on the 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. The paper is almost complete.

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Publications

Lecture Notes

Research Topic: Matrix Properties

Research Topic: Noetherian Forms