In mathematics, the Riemann hypothesis, proposed by Bernhard Riemann (1859), is a conjecture about the distribution of the zeros of the Riemann zeta function which states that all non-trivial zeros have real part 1/2. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields.
The Riemann hypothesis implies results about the distribution of prime numbers that are in some ways as good as possible. Along with suitable generalizations, it is considered by some mathematicians to be the most important unresolved problem in pure mathematics (Bombieri 2000). The Riemann hypothesis is part of Problem 8, along with the Goldbach conjecture, in Hilbert's list of 23 unsolved problems, and is also one of the Clay Mathematics Institute Millennium Prize Problems. Since it was formulated, it has withstood concentrated efforts from many outstanding mathematicians. In 1973, Pierre Deligne proved an analogue of the Riemann Hypothesis for zeta functions of varieties defined over finite fields. The full version of the hypothesis remains unsolved, although modern computer calculations have shown that the first 10 trillion zeros lie on the critical line.
The Riemann zeta function ζ(s) is defined for all complex numbers s ≠ 1. It has zeros at the negative even integers (i.e. at s = −2, −4, −6, ...). These are called the trivial zeros. The Riemann hypothesis is concerned with the non-trivial zeros, and states that:
The real part of any non-trivial zero of the Riemann zeta function is 1/2.
Thus the non-trivial zeros should lie on the critical line, 1/2 + it, where t is a real number and i is the imaginary unit.

through Riemann's eyes | electronics | 2009

Born in 1974 in Nantes (France), Benoit Granier is a Professor, Composer, (ethno) Musicologist, Visual and sonic artist, Philosopher, and life long believer in collaborative works within the arts. After completing a Ph.D. in computer music and composition at Trinity College Dublin, Ireland, he moved to Beijing, China, to teach at central conservatory of Music, and developped strong relationships between China and other countries, mainly in Europe and the USA.

In 2008, he founded in Beijing the Timi Modern Music Ensemble, a cultural encounter between western instruments and traditional Chinese instruments. Among the pieces premiered by the Timi were works by emerging composers such as Tony Deritis, John Mallia and his personal pieces.

One of Dr. Granier's particularity as a composer is to use traditional instruments in modern electro-acoustic music (Asian, Irish, Celtic instruments...). He is also renowned for composing for "controlled improvisation", offering wide possibilities to the performing musicians.

As a composer he was commissioned for large orchestras (Vienna Chamber Orchestra, the Beijing International Chamber Orchestra, Shenzhen Symphony Orchestra) and for solo instruments (Patrick de Ritis, Hong Kong New Music Ensemble, Korean artist Gamin, flutist Orlando Cela, Les Temps Modernes in Lyon, Les Percussions de Strasbourg, Percussions Claviers de Lyon, American jazz musician Demetrius Spaneas...).

His pieces have been performed in prestigious places such as the China National Center for Performing arts, Beijing Modern Music Festival, Washington Smithsonian museum, Harvard University, New York's Carnegie Hall, the Performing Arts Center (Tokyo), Seoul National University, Espacio Cultural el tanque (Spain), Bourges International Electronic Music and Arts Festival, Strasbourg International Saxophone Festival Congress.

He taught in many recognized institutions such as The National University of Singapore, Peking University, and Beijing Film Academy, where he delivered courses in electronic music, orchestration, sound design, film music, acoustics and recording.

As a composer for a movie soundtrack, he was part of the second orchestration on major projects such as The Lord of the Rings: the fellowship of the ring and Kung Fu Panda 3.

He has also done extensive work for Mixed Media and pure electronics.

He is currently working on a new piece based on Dante's Divine Comedy, with with visual 3D creation and surround sound. This ambitious music piece will be performed by French ensemble Proxima Centauri. The piece will also feature a  brand new hyper-instrument. It will be touring Asia in Fall 2018, France and USA in 2019.

through Riemann's eyes | electronics | 2009

benoit granier