COLÓQUIO MAP
Information Theory for All
Prof. Olivier Rioul (Telecom ParisTech - França)
17 de junho, sexta-feira, Auditório Antonio Gilioli - Sala 247/262 - Bloco A, IME-USP, das 16 às 17h Café às 15h30, na sala 265 A (Chefia do MAP)
Abstract:
2016 is the centenary of the birth of Claude Shannon, an American mathematician and engineer considered the "father of the Information Age". Hollywood has glorified other scientific heroes like Alan Turing and John Nash. Shannon, in comparison, he had a quiet and modest life. Adept of the unicycle and of juggling, he had fun building more or less crazy machines. At the same time, he made decisive theoretical advances in many diverse areas such as logic, cryptography, artificial intelligence, stock investment, wearable computing… and information theory. In his 1948 seminal article - A Mathematical Theory of Communication - the revolutionary theory brings together so many fundamental advances and strokes of genius that Shannon has become the hero of thousands of researchers, praised almost as a deity. One can say without exaggeration that Shannon's theorems are the mathematical theorems which have made possible the digital world as we know it today. We describe in more detail his most outstanding contributions: Shannon's paradigm; probabilistic aspects; Shannon's logarithmic unit; Shannon's limits of performance; Shannon's entropy and relative entropy; Shannon's definition of information; Shannon's random coding method; and Shannon's capacity formula. We go all the way to sketch Shannon's proofs of his first and second coding theorems using only elementary mathematical tools. The material presented here is part of a book chapter and a presentation at Institut Henri Poincaré, Paris on the occasion of Shannon's centenary. Bio: Olivier Rioul (PhD, HDR) is professor at Telecom ParisTech and Ecole Polytechnique, France. His research interests (http://perso.telecom-paristech.fr/~rioul/research.html) are in applied mathematics and include various, sometimes unconventional, applications of information theory such as inequalities in statistics, hardware security, and experimental psychology. He has been teaching information theory at various French universities for almost twenty years and has published a textbook which has become a classical French reference in the field. A Brazilian edition of the book is scheduled to be published by Editora da Unicamp in the near future.
