Zobrazeno 1 - 10
of 1 491
pro vyhledávání: '"P, Connes"'
Autor:
Connes, Alain, Kouneiher, Joseph
This article reflects on the life and mathematical contributions of Pierre Cartier, a distinguished figure in 20th- and 21st-century mathematics. As a key member of the Bourbaki collective, Cartier played a pivotal role in the formalization and moder
Externí odkaz:
http://arxiv.org/abs/2411.07409
We investigate the moment problem and Jacobi matrix associated -- by the operator theoretic framework of the semilocal trace formula -- to each finite set $S$ of places of $\mathbb Q$ containing the archimedean place. The measure is given by the abso
Externí odkaz:
http://arxiv.org/abs/2403.01247
Autor:
Connes, Alain
We compute the full asymptotic expansion of the heat kernel Trace$(\exp(-tD^2))$ where $D$ is, assuming RH, the self-adjoint operator whose spectrum is formed of the imaginary parts of non-trivial zeros of the Riemann zeta function. The coefficients
Externí odkaz:
http://arxiv.org/abs/2402.13082
Autor:
Connes, Alain, Consani, Caterina
We show that the scaling site $X_{\mathbb Q}$ and its periodic orbits $C_p$ of length $\log p$ offer a geometric framework for the well-known analogy between primes and knots. The role of the maximal abelian cover of $X_{\mathbb Q}$ is played by the
Externí odkaz:
http://arxiv.org/abs/2401.08401
We integrate in the framework of the semilocal trace formula two recent discoveries on the spectral realization of the zeros of the Riemann zeta function by introducing a semilocal analogue of the prolate wave operator. The latter plays a key role bo
Externí odkaz:
http://arxiv.org/abs/2310.18423
Autor:
Connes, Alain, Consani, Caterina
In the present paper, dedicated to Yuri Manin, we investigate the general notion of rings of $\mathbb S[\mu_{n,+}]$-polynomials and relate this concept to the known notion of number systems. The Riemann-Roch theorem for the ring $\mathbb Z$ of the in
Externí odkaz:
http://arxiv.org/abs/2307.06748
Autor:
Connes, Alain, Consani, Caterina
We show that by working over the absolute base $\mathbb S$ (the categorical version of the sphere spectrum) instead of $\mathbb S[\pm 1]$ improves our previous Riemann-Roch formula for $\overline{{\rm Spec\,}\mathbb Z}$. The formula equates the (inte
Externí odkaz:
http://arxiv.org/abs/2306.00456
Autor:
Benoit Champigneulle, François Caton, Landry Seyve, Émeric Stauffer, Aurélien Pichon, Julien V. Brugniaux, Michael Furian, Ivan Hancco, Blandine Deschamps, Lars Kaestner, Paul Robach, Philippe Connes, Pierre Bouzat, Benoit Polack, Raphael Marlu, Samuel Verges
Publikováno v:
Experimental Physiology, Vol 109, Iss 6, Pp 899-914 (2024)
Abstract Chronic mountain sickness is a maladaptive syndrome that affects individuals living permanently at high altitude and is characterized primarily by excessive erythrocytosis (EE). Recent results concerning the impact of EE in Andean highlander
Externí odkaz:
https://doaj.org/article/99763c63bddf425180094653fdd61574
Autor:
Connes, Alain, Consani, Caterina
We give a historical perspective on the role of the cyclic category in the development of cyclic theory. This involves a continuous interplay between the extension in characteristic one and in S-algebras, of the traditional development of cyclic theo
Externí odkaz:
http://arxiv.org/abs/2208.08339
Publikováno v:
Eur. Phys. J. Spec. Top. (2023)
We give an overview of the applications of noncommutative geometry to physics. Our focus is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting historically from the Heisenberg relations, we will explain how in ge
Externí odkaz:
http://arxiv.org/abs/2207.10901