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Concept# General relativity

Summary

General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of second order partial differential equations.
Newton's law of universal gravitation, which describes classical gravity, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity, however, are beyond Newton's law of universal gravitation in classica

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PHYS-402: Astrophysics IV : observational cosmology

Cosmology is the study of the structure and evolution of the universe as a whole. This course describes the principal themes of cosmology, as seen
from the point of view of observations.

PHYS-427: Relativity and cosmology I

Introduce the students to general relativity and its classical tests.

PHYS-101(g): General physics : mechanics

Le but du cours de physique générale est de donner à l'étudiant les notions de base nécessaires à la compréhension des phénomènes physiques. L'objectif est atteint lorsque l'étudiant est capable de prévoir quantitativement les conséquences de ces phénomènes avec des outils théoriques appropriés.

We define and study in terms of integral IwahoriâHecke algebras a new class of geometric operators acting on the Bruhat-Tits building of connected reductive groups over p-adic fields. These operators, which we call U-operators, generalize the geometric notion of "successors" for trees with a marked end. The first main contributions of the thesis are:
(i) the integrality of the U-operator over the spherical Hecke algebra using the compatibility between Bernstein and Satake homomorphisms,
(ii) in the unramified case, the U-operator attached to a cocharacter is a right root of the corresponding Hecke polynomial.
In the second part of the thesis, we study some arithmetic aspects of special cycles on (products of) unitary Shimura varieties, these cycles are expected to yield new results towards the BlochâBeilinson conjectures. As a global application of (ii), we obtain:
(iii) the horizontal norm relations for these GGP cycles for arbitrary n, at primes where the unitary group splits.
The general local theory developed in the first part of the thesis, has the potential to result in a number of global applications along the lines of (iii) (involving other Shimura varieties and also vertical norm relations) and offers
new insights into topics such as the BlasiusâRogawski conjecture as well.

2006

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