Professor Peter Beelen gives his inaugural lecture "From al-Khwarizmi to error-correcting codes: Aspects of algebra and its applications", November 28, 2014, 14:00, Building 101 - meeting room S01.
DTU Compute would like to invite you to welcome our new professor in mathematics Peter Beelen, and engage in an afternoon of inspiring talks and discussions. There will be a reception in the foyer outside meeting room S01 following the lecture.
From al-Khwarizmi to error-correcting codes: Aspects of algebra and its applications:
Around the year 800 a Persian scholar named al-Khwarizmi wrote a treatise on how to solve polynomial equations of degree one and two in one variable. A modern translation of the original title is "The compendious book on calculation by completion and balancing". The word algebra originates from this, since in Europa it became known under the latinized title "Liber algebrae et almucabola". More precisely, the word algebra corresponds to the word completion, by which al-Kwarizmi meant an operation to simplify a polynomial equation. The word algebra therefore had originally a very concrete algorithmic meaning. Also in this lecture algorithmic aspects of algebra play an important role.
Since the arrival of computers, algorithms in algebra and its applications have become more and more feasible and have helped to find technological solutions to engineering challenges. An example is in the way a Blu-ray player handles scratches on the surface of a Blue-ray disc. Such scratches give rise to errors that need to be corrected using what is known as an error-correcting code. The idea is simply to add redundancy to the data in such a way that it can be used to correct such errors. Adding redundancy results in an increase of error-tolerance, but also in a loss of data density depending on the rate of the code.
In this lecture the essential ingredients that are used in algebraic error-correction codes will be explained. Also it will be indicated how existing algebraic error-correcting codes (such as the well-known Reed-Solomon codes) can be generalized. This generalization gives rise to what became known as algebraic geometry codes (AG codes). Briefly put AG codes are constructed using algebraic curves, whereas Reed-Solomon codes can be seen as coming from the simplest possible curve: a line. Compared to Reed-Solomon codes, AG codes have the advantage that significantly more errors can be corrected without any further loss of rate. However, using the currently known algorithmic approaches, a competitive performance in the actual error-correction cannot be achieved. As will be shown, recent progress is starting to close this gap. A further algorithmic problem is that the construction of the algebraic curves needed to construct families of good AG codes, is far from trivial. However, as will be explained, also in this area recent progress has been made using a mix of explicit methods and advanced algebraic tools.
Prof. Peter Beelen was born in Kampen, the Netherlands, on May 5, 1973. He studied mathematics at the university of Utrecht (the Netherlands), where he got his Master’s degree in 1996. In 2001 he obtained a Ph.D. degree in mathematics at the Technical University of Eindhoven (the Netherlands) on the thesis ”Algebraic geometry and coding theory”. From September 2001 till September 2002 he was a post-doc at the same university in Eindhoven and from September 2002 till August 2004, he was a post-doc at the university of Essen (Germany). He came to DTU in October 2004, where he worked as an assistant professor till January 2007 and as associate professor till August 2014. Currently he is professor in applied algebra at the department of applied mathematics and computer science and head of the section for mathematics. His research interests include various aspects of algebra and its applications, such as algebraic curves, boolean functions, coding theory, and function field theory. He has published more than 25 peer-reviewed papers in international journals and is internationally recognized as an expert in the applications of algebraic curves in coding theory.