Dube, Themba
Dube, Themba
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Prof Themba Dube is a Professor of Mathematics at the University of South Africa. He has served at the managerial level as Vice-Rector for Academic Affairs at Zululand University. He does research in Topology and Commutative Rings. In 2013, he received the most prestigious award from the South African Mathematical Society (SAMS) for Research Distinction. In 2016, he was appointed by the said organisation to be the editor-in-chief of its accredited and ISI-listed journal called Quaestiones Mathematicae. Incidentally, he is the first person of colour to edit this journal in its history. He has to date published 101 papers in various journals, and he has supervised to completion 4 PhD students from 4 different countries, namely, Republic of Congo, Nigeria, South Africa, and Zimbabwe.
Localic remainders and realcompactness
Localic remainders and realcompactness
Using the notion of localic reminders [2], I will show that a completely regular frame is realcompact if and only if the remainder is the join of the zero-sublocales of that miss . This extends a result of Mrówka which characterizes realcompact spaces in terms of their remainders in Stone–Čech compactifications. I will also show that is Lindelöf if and only if L is of countable type, where the latter is defined for locales exactly as for spaces, subject to replacing subspaces with sublocales. The talk will be based mainly on the some results in [1].
[1] T. Dube, Characterizing realcompact locales via remainders, Georgian Math. J. 28 (2021), 59–72.
[2] M. J. A. Ferreira, J. Picado and S. M. Pinto, Remainders in pointfree topology, Topology Appl. 245 (2018), 21–45.
Ralaivaosaona, Dimbinaina
Ralaivaosaona, Dimbinaina
Dr. Ralaivaosaona is a senior lecturer at the Department of Mathematical Sciences at Stellenbosch University. His research interests include analytic number theory, analysis of algorithms and probabilistic combinatorics. He has an Erdős number 2. He attended the University of Antananarivo where he obtained his “Maîtrise en Mathématiques” (Honours degree) in 2006. This was followed by a Postgraduate Diploma from the African Institute for Mathematical Sciences (AIMS) South Africa in 2007, a Certificate of Advanced Study in Mathematics (now known as Master of Advanced Study -- MASt) from Cambridge University UK in 2008. He obtained his PhD degree from Stellenbosch University in 2012, he wrote a thesis on the limit theorems for integer partitions and their generalisations. He joined Stellenbosch University as a lecturer in 2013 and he was promoted to senior lecturer in 2018. He has many research publications in different fields such as number theory, combinatorics, and computer science. He has served as a referee for various well-respected international journals including the Journal of Number Theory and the Journal of Combinatorics Theory, Series A. He is currently serving as the Junior Coordinator for the Number Theory Focus Area of the Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) in South Africa. He is also a member of the Associate Faculty of AIMS South Africa.
The Phase Transition in Random Digraphs
The phase transition phenomenon (i.e., property of a system that changes abruptly) in random graphs is one of the most studied and widely used results in mathematics. Since the groundbreaking work on this topic in the 1950s, similar phenomena have been observed in complex systems from many disciplines such as statistical physics (e.g. percolation theory), computer science, chemistry, and social science (e.g., small-world phenomenon).
Although the phase transition of random graphs is now fairly well-understood, similar transitions for other structures remain largely unexplored. In this talk, I will introduce a novel analytic approach to the study of the phase transition for random directed graphs. The approach shows a nice interplay between combinatorics, complex analysis, and probability theory.
This talk is based on a joint work with Elie de Panafieu, Sergey Dovgal, Vonjy Rasendrahasina,´ and Stephan Wagner.
Motlatsi, Molati
Motlatsi, Molati
Dr Molati obtained BSc (Mathematics & Physics) from the National University of Lesotho (NUL) in 1998 and pursued further studies in Applied Mathematics at the University of the Witwatersrand (WITS); he obtained BSc Honours (2001), MSc (2003) and PhD (2010). He joined NUL in 2003 as an Assistant Lecturer and is currently an Associate Professor and serving a fourth two-year term as Head of Department (HoD) of Mathematics & Computer Science. His main area of research is Lie Group Analysis of Differential Equations and he also has interest in Continuum Mechanics, Relativity, Mathematical Modelling and Numerical Analysis. He has been to many regional and international Mathematics conferences, in particular, the International Congress of Mathematicians (ICM) which he has been attending since 2006. He has held short-term research fellowships at WITS, NWU (South Africa) and Kyushu University (Japan). He received the TWAS Young Scientist National Award in 2011 and his PhD thesis was awarded the Rand Merchant Bank Gold Medal in 2010.
Mathematical Models of Reaction-Diffusion-Convection
Different mathematical models with applications in reaction-diffusion-convection processes are considered, namely, a nonlinear reaction-diffusion-convection equation [3], a system of singular reaction-diffusion equations [2] and a system comprising reaction-diffusion equation and shallow water equation [1]. The various forms of the model parameters are specified through the Lie symmetry approach. Each form yields a submodel the Lie point symmetries of which are employed for derivation of exact solutions.
References
[1] Khatebe L. and Molati M., Group classification of a system of reaction-diffusion and shallow water equations, Preprint.
[2] Maseela T. and Molati M., Symmetry analysis of a coupled system of singular reactiondiffusion equations modelling isothermal autocatalysis, Preprint.
[3] Molati M. and Murakawa H., Exact solutions of nonlinear diffusion-convection-reaction equation: A Lie symmetry analysis approach, Commun. Nonlinear Sci. Numer. Simul., 67, 253-263, 2019.
Massamba, Fortuné
Massamba, Fortuné
Fortuné Massamba is a Professor in the School of Mathematics, Statistics and Computer Science at the University of KwaZulu-Natal, where he has been since May 2013. During 2009-2015, he was a Regular Associate at The Abdus Salam International Centre for Theoretical Physics (Trieste, Italy). He was a visiting research scholar at international institutes such as Max-Planck Institute for Mathematics in the Sciences (Leipzig, Germany), Berlin Mathematical School (Berlin, Germany), Institut des Hautes Etudes Scientifiques (Bures-Sur-Yvette, France), etc. In 2018 and 2019, he received an International Mathematical Union - Simons Africa Fellowship award and a DVC Senior Tertiary award for the College of Agriculture, Engineering and Science of the UKZN, respectively.
He has supervised a lot of postgraduate students across the continent (Botswana, Namibia, Togo, Guinea, Chad, Nigeria, Burundi, Congo, DR Congo, Uganda, Mauritania, South Africa). More precisely, he supervised more than ten MSc students and five PhD students. He has been invited as a key speaker in many conferences and workshops and lectured differential geometry and related topics to Master and Doctoral students to Universities and Institutes like (but not limited to) AIMS Cameroun, AIMS Senegal, University of Botswana, University of Namibia, International Chair in Mathematical Physics and Applications, Institute of Mathematics and Physical Sciences, etc.
His research interests span both topology and differential geometry, and he has published more than 50 papers in international reputable journals.
A Class of Almost Kähler Manifolds
A Class of Almost Kähler Manifolds
We present a class of locally conformal almost Kähler manifolds. Prove that there exist leaves in such manifolds which are hypersurfaces with mean curvature vector fields proportional to the Lee vector field and minimalities coinciding with the incompressibility of the Lee vector field.
Razafimandimby, Paul
Razafimandimby, Paul
Paul Razafimandimby did all his undergraduate studies in Madagascar and did his PhD studies at the University of Pretoria. After a one year postdoctoral fellowship at the University of Pretoria, he was awarded a Lise Meitner fellowship from the Austria Science Fund (Fonds zur Förderung der wissenschaftlichen Forschung, FWF) at the University of Leoben, Austria from 2012-2015. He joined the University of Pretoria as a Lecturer in 2016. In 2019, he was awarded a Marie Curie Individual Fellowship from the European Union and spent two years at the University of York, UK. He is currently an Assistant Professor Above the Bar at Dublin City University. Paul’s main research interest is the Theory of Stochastic/Deterministic PDEs and its applications.
On the Strong Solutions to the 2D Stochastic Ericksen-Leslie System:
A Ginzburg-Landau Approximation Approach
Zdzislaw Brzézniak, University of York, United Kingdom
Gabriel Deugoué, University of Dschang, Cameroon
Paul Razafimandimby∗, Dublin City University, Ireland
Motivated by the importance of noise in the dynamics of nematic liquid crystals, we consider a nonlinear and constrained stochastic PDEs modelling the dynamics of 2-dimensional nematic liquid crystals under random perturbation. This system is coupling of the Navier-Stokes and the Heat Flow of Harmonic maps and is known as the stochastic Ericksen-Leslie equations (SELEs). We discuss the existence of local strong solution to the stochastic Ericksen-Leslie equations. In particular, we study the convergence of the stochastic Ginzburg-Landau approximation of SELEs, and prove that the SELEs with initial data in H1 ×H2 has at least a martingale, local solution which is strong in PDEs sense.
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