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2017 International Conference on Mathematical Methods & Computational Techniques in Science & Engineering
University of Cambridge, UK, February 24-26, 2017

The Infinity Computer and numerical computations with infinities and infinitesimals

Professor Yaroslav D. Sergeyev, Ph.D., D.Sc., D.H.C.
Distinguished Professor, Head of Numerical Calculus Laboratory University of Calabria, Rende, Italy
E-mail: yaro@dimes.unical.it


The lecture presents a recent methodology allowing one to execute numerical computations with finite, infinite, and infinitesimal numbers on a new type of a computer – the Infinity Computer – patented in EU and USA. The new approach is based on the principle ‘The whole is greater than the part’ (Euclid’s Common Notion 5) that is applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). The new methodology (that is not related to non-standard analysis) evolves ideas of Cantor and Levi-Civita in a more applied way and, among other things, introduces new infinite integers that possess both cardinal and ordinal properties as usual finite numbers. The new methodology has been successfully used in a number of pure and applied areas of mathematics and computer science: measuring infinite sets, studying divergent series, hyperbolic geometry, Turing machines, lexicographic ordering, cellular automata, percolation and biological processes, optimization, numerical differentiation and ODEs, fractals, etc. The Infinity Calculator using the Infinity Computer technology is presented during the talk. More information about the new supercomputer at the internet page http://www.theinfinitycomputer.com

Brief Biography of the Speaker:
Yaroslav D. Sergeyev, Ph.D., D.Sc., D.H.C. is Distinguished Professor at the University of Calabria, Italy (professorship awarded by the Italian Government) and Head of Numerical Calculus Laboratory at the same university. His research interests include numerical analysis, global optimization (since 2016 he is Vice-President of the International Society of Global Optimization), infinity computing and calculus, philosophy of computations, set theory, number theory, fractals, parallel computing, and interval analysis. Prof. Sergeyev was awarded several research prizes (Pythagoras International Prize in Mathematics, Italy, 2010; EUROPT Fellow, 2016; Outstanding Achievement Award from the 2015 World Congress in Computer Science, Computer Engineering, and Applied Computing, USA; Honorary Fellowship, the highest distinction of the European Society of Computational Methods in Sciences, Engineering and Technology, 2015; The 2015 Journal of Global Optimization (Springer) Best Paper Award; Lagrange Lecture, Turin University, Italy, 2010; MAIK Prize for the best scientific monograph published in Russian, Moscow, 2008, etc.). His list of publications contains more than 200 items (among them 5 books). He is a member of editorial boards of 6 international journals. He delivered more than 50 plenary and keynote lectures at prestigious international congresses. Software developed under his supervision is used in more than 40 countries of the world. For more information see his web page http://wwwinfo.deis.unical.it/~yaro


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