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30 November 2021 | Story Leonie Bolleurs | Photo Supplied
Prof Johan Meyer, Senior Professor in the Department of Mathematics and Applied Mathematics, says he is looking forward to learning from others in the field during this collaboration.

What do trees, black holes, earthquakes, and time structures have in common? 

The answer to this question is that these, in one way or the other, form the focus of some of the abstracts delivered during the Annual Congress of the South African Mathematical Society. The society has as its main objective the advancement of mathematics in South Africa. 

The Department of Mathematics and Applied Mathematics at the University of the Free State (UFS), in conjunction with the South African Mathematical Society (SAMS 2021), is hosting the 64th Annual Congress of the society this week (29 November to 1 December 2021).

Prof Johan Meyer, Senior Professor in the department, says the congress, which is being conducted online, is focusing on all aspects of mathematics research, including history and teaching.

Learning from others in the field

The congress, which aims to share the latest research results in mathematics, will be attended by staff and students from universities across South Africa as well as abroad. “Anyone from the public is, of course, welcome to attend or even share their results if they are also involved in mathematics research,” adds Prof Meyer. 

He says that he is looking forward to learning from others in the field during this collaboration. 

The congress will include discussions on more than 120 abstracts, covering category theory, algebra, topology, logic; functional analysis and operator theory; finite groups and combinatorial structures; graph theory and combinatorics; lie symmetries and nonlinear differential equations; and applied and numerical mathematics.

Array of interesting topics presented

“It is important in many areas of science and engineering to predict and to simulate rare, random events, the occurrence of which may have negative or even catastrophic consequences. Examples include internet server overflows, mechanical breakdowns, floods, and financial crashes. Rare events can also have a positive effect, triggering for example chemical reactions or driving genetic evolution via random mutations.” Prof Hugo Touchette from Stellenbosch University will be shedding some light on this interesting topic in his presentation on Predicting and simulating rare events.

Prof Jeandrew Brink, Associate Professor in the Department of Mathematics and Applied Mathematics at the UFS, is presenting a plenary session on the topic Determining the geometry of strong field space-times in spite of tacitly assuming the answer during every measurement. In South Africa, state-of-the art pulsar timing data from the MeerKAT telescope will make a considerable contribution to conducting GR orbital tests. Prof Brink comments on how pulsar timing tests differ from tests using gravitational wave detectors, as well as what we can learn from the framework already employed to perform pulsar timing measurements.

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Inaugural lecture: Prof. Phillipe Burger
2007-11-26

 

Attending the lecture were, from the left: Prof. Tienie Crous (Dean of the Faculty of Economic and Management Sciences at the UFS), Prof. Phillipe Burger (Departmental Chairperson of the Department of Economics at the UFS), and Prof. Frederick Fourie (Rector and Vice-Chancellor of the UFS).
Photo: Stephen Collet

 
A summary of an inaugural lecture presented by Prof. Phillipe Burger on the topic: “The ups and downs of the South African Economy: Rough seas or smooth sailing?”

South African business cycle shows reduction in volatility

Better monetary policy and improvements in the financial sector that place less liquidity constraints on individuals is one of the main reasons for the reduction in the volatility of the South African economy. The improvement in access to the financial sector also enables individuals to manage their debt better.

These are some of the findings in an analysis on the volatility of the South African business cycle done by Prof. Philippe Burger, Departmental Chairperson of the University of the Free State’s (UFS) Department of Economics.

Prof. Burger delivered his inaugural lecture last night (22 November 2007) on the Main Campus in Bloemfontein on the topic “The ups and downs of the South African Economy: Rough seas or smooth sailing?”

In his lecture, Prof. Burger emphasised a few key aspects of the South African business cycle and indicated how it changed during the periods 1960-1976, 1976-1994 en 1994-2006.

With the Gross Domestic Product (GDP) as an indicator of the business cycle, the analysis identified the variables that showed the highest correlation with the GDP. During the periods 1976-1994 and 1994-2006, these included durable consumption, manufacturing investment, private sector investment, as well as investment in machinery and non-residential buildings. Other variables that also show a high correlation with the GDP are imports, non-durable consumption, investment in the financial services sector, investment by general government, as well as investment in residential buildings.

Prof. Burger’s analysis also shows that changes in durable consumption, investment in the manufacturing sector, investment in the private sector, as well as investment in non-residential buildings preceded changes in the GDP. If changes in a variable such as durable consumption precede changes in the GDP, it is an indication that durable consumption is one of the drivers of the business cycle. The up or down swing of durable consumption may, in other words, just as well contribute to an up or down swing in the business cycle.

A surprising finding of the analysis is the particularly strong role durable consumption has played in the business cycle since 1994. This finding is especially surprising due to the fact that durable consumption only constitutes about 12% of the total household consumption.

A further surprising finding is the particularly small role exports have been playing since 1960 as a driver of the business cycle. In South Africa it is still generally accepted that exports are one of the most important drivers of the business cycle. It is generally accepted that, should the business cycles of South Africa’s most important trade partners show an upward phase; these partners will purchase more from South Africa. This increase in exports will contribute to the South African economy moving upward. Prof. Burger’s analyses shows, however, that exports have generally never fulfil this role.

Over and above the identification of the drivers of the South African business cycle, Prof. Burger’s analysis also investigated the volatility of the business cycle.

When the periods 1976-1994 and 1994-2006 are compared, the analysis shows that the volatility of the business cycle has reduced since 1994 with more than half. The reduction in volatility can be traced to the reduction in the volatility of household consumption (especially durables and services), as well as a reduction in the volatility of investment in machinery, non-residential buildings and transport equipment. The last three coincide with the general reduction in the volatility of investment in the manufacturing sector. Investment in sectors such as electricity and transport (not to be confused with investment in transport equipment by various sectors) which are strongly dominated by the government, did not contribute to the decrease in volatility.

In his analysis, Prof. Burger supplies reasons for the reduction in volatility. One of the explanations is the reduction in the shocks affecting the economy – especially in the South African context. Another explanation is the application of an improved monetary policy by the South African Reserve Bank since the mid 1990’s. A third explanation is the better access to liquidity and credit since the mid 1990’s, which enables the better management of household finance and the absorption of financial shocks.

A further reason which contributed to the reduction in volatility in countries such as the United States of America’s business cycle is better inventory management. While the volatility of inventory in South Africa has also reduced there is, according to Prof. Burger, little proof that better inventory management contributed to the reduction in volatility of the GDP.

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