540 research outputs found
Alain Connes - Boson de Higgs et structure fine de l'espace temps: Conférence grand public « MathEnVille » 2014
No full textDans sa conférence, Alain Connes parlera, de façon abordable, de la géométrie de l’espace-temps et du boson de Higgs. Cette particule élémentaire permet d’expliquer pourquoi certaines particules ont une masse et d’autres n’en ont pas.Alain Connes est un mathématicien de renommée mondiale. Membre de l’Académie des sciences, Professeur au Collège de France, à l’I.H.E.S. et à l’Université OSU, Columbus aux États-Unis, il a notamment reçu la Médaille Fields en 1982, le prix Crafoord en 2001 et la Médaille d’or du CNRS en 2004.Tout au long de sa carrière, Alain Connes s’est intéressé à la résolution des problèmes mathématiques soulevés par la physique quantique et la théorie de la relativité. Il a en particulier révolutionné la théorie des algèbres d’opérateurs et créé une nouvelle branche des mathématiques, la géométrie non-commutative
Alain Connes - Boson de Higgs et structure fine de l'espace temps: Conférence grand public « MathEnVille » 2014
No full textDans sa conférence, Alain Connes parlera, de façon abordable, de la géométrie de l’espace-temps et du boson de Higgs. Cette particule élémentaire permet d’expliquer pourquoi certaines particules ont une masse et d’autres n’en ont pas.Alain Connes est un mathématicien de renommée mondiale. Membre de l’Académie des sciences, Professeur au Collège de France, à l’I.H.E.S. et à l’Université OSU, Columbus aux États-Unis, il a notamment reçu la Médaille Fields en 1982, le prix Crafoord en 2001 et la Médaille d’or du CNRS en 2004.Tout au long de sa carrière, Alain Connes s’est intéressé à la résolution des problèmes mathématiques soulevés par la physique quantique et la théorie de la relativité. Il a en particulier révolutionné la théorie des algèbres d’opérateurs et créé une nouvelle branche des mathématiques, la géométrie non-commutative
The non-commutative standard model
No full textIn this work aspects of the classical Connes-Lott non-commutative standard model are examined. In particular the relationship between the chiral structure of the standard model and the condition of Poincaré Duality is investigated. Then the natural prediction of an additional force in the non-commutative standard model is explained and the consequences calculated. Finally the attempts at grand unification within the non-commutative framework are reviewed and extended
K-theory for group C*-algebras
No full textThese notes are based on a lecture course given by the first author in the Sedano Winter School on K-theory held in Sedano, Spain, on January 22-27th of 2007. They aim at introducing K-theory of C*-algebras, equivariant K-homology and KK-theory in the context of the Baum-Connes conjectur
The scaling site
No full textAbstractWe investigate the semi-ringed topos obtained from the arithmetic site A of [3,4], by extension of scalars from the smallest Boolean semifield B to the tropical semifield R+max. The obtained site [0,∞)⋊N× is the semi-direct product of the Euclidean half-line and the monoid N× of positive integers acting by multiplication. Its points are the same as the points A(R+max) of A over R+max and form the quotient of the adele class space of Q by the action of the maximal compact subgroup Zˆ⁎ of the idèle class group. The structure sheaf of the scaling topos endows it with a natural structure of tropical curve over the topos N׈. The restriction of this structure to the periodic orbits of the scaling flow gives, for each prime p, an analogue Cp of an elliptic curve whose Jacobian is Z/(p−1)Z. The Riemann–Roch formula holds on Cp and involves real-valued dimensions and real degrees for divisors
Compte rendu de Alain Connes : « La géométrie et le quantique »
No full textConnes (Alain), La géométrie et le quantique. – Paris : CNRS éditions ; De vive voix, 2019. – 73 p. – (Les grandes voix de la recherche). – 1 vol. broché de 12 × 18 cm. – 8,00 €. – isbn 978-2-271-12712-9
Noncommutative geometry
No full textThis English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathema
Symposium
No full textCERN scientists probe ever-deeper levels of matter and their interactions, but can we say that the patterns they see are truly fundamental? Does the universe obey the same laws throughout? Since mathematical constructions can be true in the absence of any relation to the physical world, is mathematics more fundamental than physics? Extraterrestrial life would probably look much different from that on Earth, but natural selection still be fundamental to their evolution?
Leading thinkers from a variety of subjects will explore the question of what is fundamental in a symposium at CERN. Richard Dawkins will speak on biology, Gerard ‘t Hooft will focus on physics, and Alain Connes will discuss mathematics; a leading computer scientist is also scheduled to speak.
Entrance free.
For more information on the speakers, see these Web sites:
Richard Dawkins:
http://www.world-of-dawkins.com/index.shtml
Gerard 't Hooft:
http://www.nobel.se/physics/laureates/1999/thooft-autobio.html
Alain Connes:
http://www.alainconnes.org</a
"Symposium" by Richard Dawkins, Gerard 't Hooft, Alain Connes
No full textRichard Dawkins will speak on biology, Gerard ât Hooft will focus on physics, and Alain Connes will discuss mathematics. CERN scientists probe ever-deeper levels of matter and their interactions, but can we say that the patterns they see are truly fundamental? Does the universe obey the same laws throughout? Since mathematical constructions can be true in the absence of any relation to the physical world, is mathematics more fundamental than physics? Extraterrestrial life would probably look much different from that on Earth, but natural selection still be fundamental to their evolution?<BR
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