 |
| index | speakers | video | art | registration | accommmodations |
| Som
Naimpally Topology and Applications It is not widely known that abstract pure mathematics has applications in daily life. There are many examples in mathematics but in this talk I wish to explain what is Topology and its applications. I’ll use simple examples from day to day life to illustrate the concepts. Topology deals with the concept of nearness at various levels. This concept was first formulated by the Hungarian Mathematician F. Riesz about 100 years ago in an address to the International Congress of Mathematicians in Rome ( 1908 ).. LEVEL 1 : Consider a typical family { Mother, Father, Son, Daughter }. We can say that a person is near the family if that person is blood related to the family. Of course, every member of the family is near the family and the family must first exist to talk about nearness ! Grandparents, aunts, uncles, cousins,… are persons near the family though they are not in the family. There are many other ways of having such nearness relations e. g. we can say that a person is near the family if the person helps the family in some way. In this definition the family doctor, the plumber, the mailman, … are near the family This concept is axiomatized with a few simple obvious conditions and we get the abstract concept of a topological space. This was first done by the Polish Mathematician K. Kuratowski in 1922. LEVEL 2: At this level we talk about nearness of two families, technically called a proximity space. This idea, already present in Riesz’s work, was thoroughly studied by the Soviet Mathematicians V. Efremovic around 1940 and published in 1951. This idea was further developed by the Soviet mathematician Yu. Smirnov Again this can happen in several ways : ( a ) two families can be near because a daughter from one family has married a son from another or ( b ) two families have a common friend ( i.e. a person near both families ) or ( c ) two families are interested in music and meet at a concert thus getting near each other. LEVEL 3 : Here we can talk of nearness of a number of families technically resulting in a uniform space discovered by the French Mathematician A. Weil in 1937. An example is that of the families of persons who work for the same company. Perhaps they get together for a picnic or a Christmas party. You can see that the subject is international and mathematicians from all over the world have worked on this topic. We work on this topic because the problems are interesting, challenging, or beautiful ! Sometimes problems come from other areas but there are many instances where applications were found later. Abstract topology has found applications in Theoretical computing, Quantum Mechanics, Relativity, Mathematical Economics, Optimization, Convex Analysis, Probability Theory, Theory of Capacities, Child Psychology, a model of our eyes etc. Biography Born 1931-08-31 in Mumbai ( Bombay ), India. Canadian Citizen. B. Sc. ( Honours ) Mathematics-Physics, University of Bombay, 1952. M. Sc. ( Honours ) Pure Mathematics, University of Bombay, 1954 M. Sc. ( Honours ) Applied Mathematics, University of Bombay, 1958 Ph. D. Mathematics ( Topology ), Michigan State University, 1964 Taught Mathematics in various colleges in University of Bombay ( 1952-1961 ), Michigan State University ( 1961-1964 ),Iowa State University ( 1964-1965 ), University of Alberta ( 1965-1969 ), Indian Institute of Technology, Kanpur ( 1969-1971 ), Lakehead University ( 1971-1988 ), Kuwait University ( 1988-1993 ) Visiting Professor: University of Regina, Indian Institute of Technology, Bombay, Southern Illinois Universty, Carbondale Invited addresses at 15 Topology Conferences in USA, India, Italy, Mexico Colloquium talks at various universities in Canada, USA, India, Japan, Hong Kong, Kuwait, Italy, Belgium Over 100 research articles published. One text book, three research-level monographs, one historical book on Mathematics. |