Plenary Speakers
| Dr Chimere Anabanti |
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| Short Biography: Chimere Anabanti is a Senior Lecturer in the Department of Mathematics and Applied Mathematics of the University of Pretoria. He earned a PhD in Mathematics from Birkbeck, University of London (2017) and an MSc in Mathematics from the University of Warwick (2013). In 2017, he was awarded the Gilchrist Educational Trust PhD Student's Prize as the college's postgraduate researcher who made the most outstanding contribution to their field in 2016/2017. He taught Mathematics at the University of Nigeria, Nsukka (2013-2014; 2017-2019). From 2019 to 2021, he served as a Postdoctoral researcher (University Assistant) at the Graz University of Technology (TU Graz), Austria, where he also designed and taught postgraduate courses in Group theory for masters and doctoral students in 2020. He joined the University of Pretoria as a Senior Lecturer in 2021. His research is mainly on solving combinatorial problems with group theory motivation. He has taught the use of a computer algebra package called GAP at several workshops, including Sage Days 102 at the University of Ibadan, Nigeria in July 2019, the 7th Biennial International Group Theory Conference (7BIGTC) at North West University in August 2023 and a workshop at the Department of Mathematics, University of Salerno, Italy in February 2024. He holds an NRF Y1 rating (from 2022). He is a recipient of the 2024 Exceptional Young Researcher's Award of the University of Pretoria. |
| Title: Product-free sets in finite groups |
| Abstract: A well-known result of Schur asserts that for any partition of the positive integers into a finite number of parts, one of the parts fails to be sum-free; that is, it contains three integers x, y and z, with x+y=z. Schur's theorem is regarded as one of the foundation stones of the important topic of Ramsey theory. The sum-free condition concerns the additive structure of the integers. It has been extended to arbitrary groups, where it is more usual to use multiplicative notions: so we call a set product-free if it does not contain three elements x, y and z with xy=z. Many questions now arise, such as: (i) how large can a product-free set be? (ii) Which finite groups contain maximal by inclusion product-free sets of a given size? We shall discuss the results of many research studies (including some of our results) on these questions. Furthermore, we shall discuss applications of product-free sets in Algebraic Combinatorics and Finite Geometry. (This is joint work with Sarah Hart) |
| Dr Zwelithini Dhlamini |
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| Short Biography: Dr Zwelithini Bongani Dhlamini is a Senior Lecturer in Mathematics Education at the University of Limpopo. He holds a PhD in Mathematics Education from the University of Limpopo, Master of Education from the University of Johannesburg and Honours in Mathematics Education from the University of the Witwatersrand. He is a researcher with an interest in Mathematics learner cognition, knowledge and alignment of educational components. He has published in local and international peer-reviewed journals and presented in local and international conferences in Mathematics Education such as AMESA and ICME. Has supervised four Master dissertations and 24 Honours students to completion. Currently, there are three Masters and two PhD students currently being supervised and five Honours. Has Examined Masters and PhD from the University of Johannesburg and University of South Africa. He represents the Association for Mathematics Educators South Africa (AMESA) to serve in the South African National Committee of International Mathematics Union (SANCIMU) from 2024-2027. |
| Title: The myth and possibilities of equitable mathematics education: Striving for quality and relevance in the era of digital technologies |
| Abstract: Mathematics remains the gateway subject to access all careers in STEM Education and others in South Africa and globally. Past inequalities are still prevalent in teaching, learning, and assessment of mathematics in schools and higher education. In the schooling system, only two languages are well established to teach, learn and assess mathematics. While most parts of the country lack access to resources such as network coverage, computers, smartphones and qualified mathematics teachers. Consequently, majority learners especially the poor are marginalised from accessing crucial tools such as calculators, GeoGebra and other software that are developed to demystify the indoctrinations that mathematics is difficult. While policies and initiatives to redress these inequalities are slow, affluent Provinces, schools and learners enjoy access to a variety of resources such as digital classrooms that give them advantage over poor schools and learners. The most accessible resource to the poor communities is the identification and use of artifacts in their immediate environments. An example is the Ndebele paintings, to make accessible complex mathematics concepts such as Algebra, Geometry and Trigonometry. Similarly, access can be advanced through collaborations of rich and poor schools and Provinces to emancipate the entire population of Mathematics learners through sharing all crucial resources. |
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| Short Biography: Abdul H Kara completed all his studies at Wits University and in all, but one year, has been at Wits from Junior Lecturer through to Professor; the one year being served as a school teacher. His PhD thesis involved a range of topics around the Symmetries of Differential Equations, Euler-Lagrange equations and their relationship with Conservation Laws. Abdul has published with collaborators from China, the US, Russia, Pakistan and with his students from SA and abroad. He continues to apply his work in mathematical physics, engineering and relativity and extend his ideas to Discrete Equations and Fractional Differential Equations. | |
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Title: Symmetries & Conservation Laws of differential equations - 1918 to now and beyond |
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| Abstract: The theory and reasoning behind the construction of symmetries for differential equations (DEs) is now well established and documented. Moreover, the application of these in the analysis of DEs, in particular, for finding exact solutions, is widely used in a variety of areas from relativity to fluid mechanics. Secondly, the relationship between symmetries and conservation laws has been a subject of interest during the 1800s and culminated in Noether's celebrated work for variational DEs. The extension of this relationship to DEs which may not be variational has been done more recently. The first consequence of this interplay has lead to the double reduction of DEs. The talk will broadly cover these ideas; past, present and future. |
| Prof Dorette Pronk |
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| Short Biography: Dorette Pronk completed her PhD in mathematics in September 1995, under the supervision of Dr. Ieke Moerdijk at Utrecht University in the Netherlands. After this, she held a postdoctoral fellowship at Dalhousie University in Halifax, Canada until August 1998, under the supervision of Dr. Robert Paré and Dr. Keith Johnson. From 1998 till 2000 she held a 2-year assistant professorship at Calvin College, in Grand Rapids, USA. From there she returned to Dalhousie to take a tenure track position that has led to her current position as professor of mathematics. Her research is in category theory, in particular in topos theory and double categories, with applications to orbifolds and programming semantics. She is maintaining an active research group with several graduate students and postdoctoral fellows. Dorette cares greatly about math outreach, to challenge and assist each student to expand their mathematical talents and see how they connect to their other interests. She has served as a faculty mentor for the Nova Scotia Math Circles program bringing engaging mathematical presentations and activities into the schools from grade 1 to grade 12. She is also serving as the chair of the Mathematical Competitions Committee for the Canadian Mathematical Society (CMS). She has served in various leadership roles for the Canadian teams for the International Math Olympiad and the European Girls Math Olympiad. The CMS awarded her the Graham Wright Award for Excellence in Service in 2023. |
| Title: Groupoid Representations for Orbifolds and with Applications to Orbifold Homotopy Theory |
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Abstract: Orbifolds were introduced by Satake in [6], under the name of V - manifolds, as smooth spaces with singularities induced by taking quotients under finite group actions. They were further popularized by Thurston in the nineties under the name orbifold, and found new applications in string theory and mathematical physics.
Inspired by results from topos theory, [3] represented orbifolds by a particular type of topological or smooth groupoids. Such a groupoid consists of a topological space (or a manifold) G0 of “objects” and a second topological (or smooth) space G1 of “arrows”. We think of each point g in G1 as an arrow from a point s(g) in G0 to a second point t(g) in G1. So a groupoid has as part of its structure the continuous (or smooth) functions s, t: G1G0. We also require that there be identity arrows for each point in G0, given by a continuous/smooth function u: G0 → G1, and furthermore there are functions that encode composition of a composable pair in G1 and the inverse of an arrow in G1. In this talk I will show how to construct a groupoid from an orbifold atlas. In order to ensure that a topological groupoid indeed encodes an orbifold, we need further conditions as I will discuss in this presentation, and show how to return. The To define maps between orbifolds we start by considering the natural notion of maps between these groupoids: pairs of functions that preserve all the structure. We need to adjust this to deal with the Morita equivalences. I will discuss the notion of maps we obtain this way in further detail in the talk. The notion of orbifolds as Morita equivalence classes of smooth groupoids leads to the question whether every orbifold could perhaps be represented by a manifold with a single group action. This was established in the affirmative in [2]. This result leads us to two types of orbifold cohomology: the Borel type (as presented in [4]) and the Bredon type (as presented in [5]. I will give examples of both. To further develop orbifold homotopy theory we need a notion of path space. To avoid issues with smoothness, I will present this part of the talk for orbispaces; i.e, in terms of spaces with continuous group actions. I will discuss a way to give the maps between orbispaces the structure of a (potentially infinite dimensional) orbispace (i.e, as a topological groupoid) and present the properties this groupoid has. This is an extension of the work done by Chen in [1]. I will also spell out several examples related to the wallpaper groups. The first part of this work is joint work with Ieke Moerdijk (Utrecht University). References [1] Chen, W (2006). On a notion of maps between orbifolds I: function spaces, Commun. Contemp.
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| Prof Jan Harm van der Walt |
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| Short Biography: Jan Harm van der Walt is an associate professor in the Department of Mathematics and Applied Mathematics at the University of Pretoria. In 2008, he received a doctorate in Mathematics from the University of Pretoria, and the following year, he was appointed as a lecturer in the Department. He conducts research in Functional Analysis, with an emphasis on the interaction between vector lattices, convergence structures and spaces of continuous functions. His contributions to his field include a purely topological characterisation of hyper-Stonean spaces, which solves a longstanding open problem. He serves on the editorial board of Quaestiones Mathematicae, the journal of the South African Mathematical Society, and holds a C1 rating from the NRF. |
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Title: Order continuous functionals on C(X) |
| Abstract: Order continuous functionals play an important role in the theory of vector- and Banach lattices, as well as in the theory of operator algebras. For instance, the W*-algebras are precisely the monotone complete C*-algebras which admit plenty of order continuous functionals. In this talk, starting with a basic continuity result for the Riemann integral, we discuss the existence of order continuous functionals on spaces of continuous functions on a not necessarily compact topological spaces X and mention some applications. The results are basically negative in nature: we provide sufficient conditions for C(X) not to admit any nontrivial order continuous functions. It is therefore natural to ask for positive results: When does C(X) admit plenty of order continuous functionals? For the case of a compact space K, we give an answer to this question, namely, a purely topological characterisation of the so-called Hyper-Stonean spaces. |
- Conference Duration
- 4 December 2024 - 6 December 2024
- Registration
- 17 July 2024 - 29 November 2024 [CLOSED]
- Call For Abstracts
- 1 July 2024 - 18 November 2024
- Name
- SAMS 2024 LOC
- Contact Email
- [email protected]
- Contact Number
- +27 (0)12 420 2837
- Special Session: Functional Analysis and Operator Theory
- Finite Groups and Combinatorics
- Special Session: Categories, Algebra, Topology and Logic
- Special Session: Lie symmetries and other approaches in solving nonlinear differential equations
- Graph Theory and Number Theory
- Analysis of PDEs, Numerical Analysis and Dynamical Systems
- General Mathematics
- Tertiary Mathematics Education
- Special Session: Mathematics of Gravity
- Special Session: Mathematical Modelling of Ecological and Epidemiological Systems
- Plenary