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Seminar Talks & Lectures

Title Speaker Affiliation Date

"A Categorical View of Completeness in Di-Uniform Texture Spaces" 


In the previous studies, it was shown that the ditopological texture spaces provide a unified setting for the study of topology, bitopology and fuzzy topology on Hutton algebras. Following that, a suitable uniformity theory in textures was constructed under the name di-uniformity, and this represented a generalization of classical quasi-uniformity. Therefore, by defining regular Cauchy difilters on a texture, the concept of dicompleteness as a natural counterpart of "completeness" in the sense of quasi-uniformity has been introduced for di-uniform texture spaces.

   Accordingly, in this work the following ideas will be taken up
  • It will be especially interested in categorical aspects of the connections between diuniformities and classical (quasi-)uniformities. Some results obtained by constructing isomorphic categories and using the connections between a (quasi-)uniformity and a di-uniformity are presented insofar as completeness is concerned.
  • Several types of completeness for di-uniform texture spaces, especially for complemented ones, that is di-uniform texture spaces endowed with a complementation mapping are considered.
  • Finally, the interrelations between the completeness for uniform spaces and those types of completeness for complemented di-uniform texture spaces are investigated in a categorical setting.
Prof Filiz Yildiz Hacettepe University, Turkey 16/09/2014

"Quasi Lattices"


Under certain conditions there are considerably more quasi-lattices than Banach lattices. For example, (within reason) nearly every finite dimensional ordered Banach space is a quasi-lattice, while there is essentially only one n-dimensional Banach lattice for each n.

We will show how certain properties carry over from Banach lattices to quasi-lattices and discuss some still open problems.

(Technical details are kept to a minimum, the talk should be accessible to students and non-analysts who know what a Banach space is).

Dr Miek Messerschmidt Potchefstroom campus of the North-West University, South Africa 06/06/2014
"High Order Finite Difference Approximations of Multi-physics Problems" Abstract

Great progress has been made for high order finite difference methods during the last 20 years. It is now rather straightforward to construct stable and high order accurate multi-block finite difference schemes in a building-block-like manner. In this talk we will discus new developments, new extensions, new fields of applications, share experience on the full scale use of the technique, and speculate about future trends. We present the theory by using simple model problems, and exemplify with complex multi-physics applications.

First we walk through the basic technique for a simple model problem where all the ingredients such as well-posedness, summation-by-parts operators, penalty techniques for boundary and interface conditions, and the energy method are explained. Next, we discuss the application of the theory to coupling techniques for conjugate heat transfer, earthquake simulations, fluid- solid interaction and simulation of potential propagation in neuronal branches. Finally we discuss new time-integration procedures, new boundary conditions for the Navier-Stokes equations and a new variance reduction technique for stochastic partial differential equations.

Professor Jan Nordeström Linköping University, Sweden 24/04/2014
"CRAG@65 Seminar on Topology and Category Theory" to celebrate Christopher Gilmour's many years of mathematical activity and his 65th birthday. Speakers University of Cape Town 08/04/2014
Stochastic Equations in Physics and Biology"
Abstract: I will give a very brief introduction into the framework of stochastic calculus, followed by a couple of examples borrowed from physics and biology. The first example is related to the transport of colloids through narrow nano-channels, the second example is concerned with the motion of the self-propelled particles, such as bacteria.
Dr. Andrey Pototski University of Cape Town 04/10/2012
Representation Theory of Symmetric Operators", Dr. Rob Martin University of Cape Town 27/09/2012
The Finite Element Method Dr Daya Reddy University of Cape Town 13/09/2012
Brian Hahn Memorial Lecture: Computationally linking the internal and external worlds of biological organisms.Granular flow modeling in tumbling mills University of Pretoria Professor Wayne Getz 20/07/2012
Granular flow modeling in tumbling mills Dr Indresan Govender University of Cape Town 31/05/2012
The Mathematics of "Fracking" Anthony Peirce University of British Columbia 15/05/2012
Combinatorics and Card Shuffling Sami Assaf University of Southern California 11/05/2012
Electrically-charged moving bodies of electrical propagation in the heart Sehun Chun AIMS, Muizenberg 09/02/2012
An invitation to sandpiles David Perkinson Reed College, Portland Oregon 08/02/2012
Parameters of integer partitions - a zoo of limit laws Stephan Wagner University of Stellenbosch 04/12/2011
Keep it simple stupid Greg Rose Qualcomm 24/10/2011
History of the Interplay between Mathematics and Chemistry Ivan Gutman University of Kragujevac 03/10/2011
Graph Theory as an Integral Part of Mathematics Peter Horak University of Washington 04/07/2011
Compact orbits and continuous group homomorphisms, constructively Douglas Bridges University of Canterbury 10/02/2011
Dark Energy and everyday Particle Physics Federico Urbano   18/02/2010
A Boundary Integral Based Hybrid Numerical Procedure for the Solution of Differential equations Okey Oseloka Onyejekwe   23/02/2010
A history of ideals in abstract algebra Professor Aldo Ursini University of Siena, Italy 04/03/2010
From thin liquid films to discrete stochastic systems Andrey Pototsky Loughborough University 17/05/2010
Cost effectiveness analysis of hospitalization and home-based care for people living with HIV/AIDS Senelani Dorothy Hove Musekwa National University of Science and Technology (NUST), Bulawayo 19/05/2010
Groups given by finite presentations Gilbert Baumslag City College of New York 18/11/2010
Hilbert's tenth problem, matrices and public key cryptography Gilbert Baumslag City College of New York 17/11/2010
Maths is sometimes fun Gilbert Baumslag City College of New York 16/11/2010
Partially hyperinvariant subspaces Robin Harte Trinity College, Dublin, Ireland 15/11/2010
Bringing teaching technology to the mathematical sciences...kicking and screaming. Jeff Murugan UCT MAM 02/11/2010
Optimizing the crossing number of a graphical representation of my mathematical genealogy using simulated annealing Elmar Teufl University of Tubingen  
Reflections on Hyderabad Kenneth Hughes UCT MAM 13/09/2010
What can we anticipate from Hyderabad? Kenneth Hughes UCT MAM 13/08/2010
The Hiring Problem and Permutations Conrado Martinez Universitat Politècnica de Catalunya 30/07/2010
Bows, Halos and Flashes: A Tour of Atmospheric Optics. Jonathan Shock The University of Santiago de Compostela 26/05/2010
Proof theory, topological dynamics and combinatorics Philipp Gerhardy University of Oslo 28/04/2010
Reproducing kernel Hilbert spaces and Sampling Theory Rob Martin University of California - Berkeley 28/04/2010
  Herve Enjieu Kadji Tohoku University 26/04/2010
On the solvability conditions for the diffusion equation with convection terms Vitali Vougalter University of Toronto 26/04/2010
Isoperimetric inequalities, eigenvalues, and related quantities Jesse Ratzkin University College Cork 26/04/2010
The Probabilistic Zeta Function of Finite and Profinite Groups Erika Damian University of East Anglia 30/03/2010
Pre- and Post-crisis Yield Curve Bootstrap Graeme West Financial Modelling Agency 30/03/2010
Asymptotic behaviour of a nonlinear differential equation in mathematical finance Cloud Makasu UWC 29/03/2010