The theory of evolution seemed puzzling, was counter intuitive and contradicted deeply held prejudices; but it has caused one of the major paradigm shifts in science. This seemingly simple theory whose only tool of operation is a simple mechanism called ‘natural selection’ has the ability...

The idea of the ICTS of the Tata Institute of Fundamental Research, naturally grew out of a strongly felt need in the Indian scientific community to enhance the research and education eco-system of Indian science. There is a need in India today, to create an institution...

1. Introduction Fixed point theory is very simple, but is based on fundamentals in Mathematics. For any continuous function $$f:Xrightarrow X$$ a fixed point of $$f$$ is a point $$xin X$$ satisfying the identity $$f(x)=x.$$ Two fundamental theorems concerning fixed points are Banach Theorem and Brouwer Theorem. Banach theorem states that if $$X$$ is a complete metric space and $$f$$ is a contraction then $$f$$ has a unique fixed point. In Brouwer theorem, $$X$$ must be the closed unit ball in a Euclidean space. Then any $$f$$ has a fixed point. But in this case, the set of fixed points is not necessarily a one-point set. In Banach theorem, a metric on $$X$$ is used in the crucial assumption that $$f$$ is a contraction. The unit ball in a Euclidean space is also a metric space and the metric topology determines the continuity of continuous functions, however the essence of Brouwer theorem is a topological property of the unit ball, namely the unit ball is compact and contractible. Banach theorem and Brouwer theorem tell us a difference between two major branches of fixed point theory, metric space fixed point theory and topological fixed point theory. It is impossible to distinguish two fixed point theories in an exact way, and it is not easy to determine a certain topics belong to which branch. In general, the fixed point theory is regarded as a branch of topology. But due to deep influence on topics related to nonlinear analysis or dynamic systems, many parts of the fixed point theory can be considered as a branch of analysis.

September 3, 2012, in Sydney (Ian Sloan) and Singapore (Peter Hall)   Introduction. Ian Hugh Sloan was born in Melbourne on June 17, 1938, and educated at Scotch College, Melbourne, and Ballarat College, before going on to undergraduate degrees in physics and mathematics at the University of Melbourne. Shortly after completing his BSc and BA (Hons) in late 1960 he joined the Colonial Sugar Refining Company. This might sound like an inauspicious start for a research mathematician, but by the early 1940s, CSR, as it is called today, had already diversified into building products and chemicals, and by the late 1950s had plans for a future based largely on scientific research. Thus, Ian was able to undertake a PhD in theoretical atomic physics at University College, London while receiving a salary from CSR. However, when Ian returned to Australia in 1964 he found a changed CSR. In particular, the research project on which he was supposed to work had collapsed, and his employer was more focused on short-term, rather than long-term, goals. So he left, and joined the University of New South Wales in 1965, and has been there ever since. Over the ensuing 48 years he has developed and fostered Australia’s premier numerical analysis programme.