Related papers: PC4 at Age 40
A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.
This paper is devoted to Poincar\'e's work in probability. Though the subject does not represent a large part of the mathematician's achievements, it provides significant insight into the evolution of Poincar\'e's thought on several…
On January 4, 2012, the centenary of Henri Poincar\'e's death, a colloquium was held in Nancy, France the subject of which was "Vers une biographie d'Henri Poincar\'e". Scholars discussed several approaches for writing a biography of…
The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…
The paper contains a proof of the Fontaine-Jannsen conjecture based on a crystalline version of the p-adic Poincar'e lemma (different proofs were found earlier by Faltings, Niziol and Tsuji).
The claim that a particle is an irreducible representation of the Poincar\'e group -- what I call \emph{Wigner's identification} -- is now, decades on from Wigner's (1939) original paper, so much a part of particle physics folklore that it…
Computer science would not be the same without personal computers. In the West the so called PC revolution started in the late '70s and has its roots in hobbyists and do-it-yourself clubs. In the following years the diffusion of home and…
We give a new proof of a_4\phi_3 summation due to G.E. Andrews and confirm another_4\phi_3 summation conjectured by him recently. Some variations of these two_4\phi_3 summations are also given.
This article gives a sketch of teachers and colleagues who have had strong influence on my becoming a particle physicist.
In the paper are proved theorems, which amplify the results of my paper "On the difference equation of Poincare type (Part 3)", Max-Plank-Institut fuer Mathematik, Bonn, Preprint Series, 2004, 09, 1-34.
We present some reflections concerning two papers by H. Poincar\'e concerning the theory of quanta.
(l) I have enough evidence to render the sentence S probable. (la) So, relative to what I know, it is rational of me to believe S. (2) Now that I have more evidence, S may no longer be probable. (2a) So now, relative to what I know, it is…
We highlight four points which have been ignored or underestimated before and which allow a better understanding of "Sur la dynamique de l'electron": (i) the use by Poincare of active Lorentz transformations (boosts); (ii) the necessity,…
A systematic study of non-trivial cubic extensions of the four-dimensional Poincar\'e algebra is undertaken. Explicit examples are given with various techniques (Young tableau, characters etc).
Here we outline a proof for the 4-dimensional smooth Poincare Conjecture.
The fortieth anniversary of the original construction of Supergravity provides an opportunity to combine some reminiscences of its early days with an assessment of its impact on the quest for a quantum theory of gravity.
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…
The Lonely Runner Conjecture originated in Diophantine approximation is turning 60. Even if the conjecture is still widely open, the flow of partial results, innovative tools and connections to different problems and applications has been…
This year, 2010, is the 40th anniversary of Physical Review C as a separate section of the Physical Review. We write here with a double purpose: first, to describe how PRC has evolved and to explore how this evolution has reflected changes…
The classical PCP theorem is arguably the most important achievement of classical complexity theory in the past quarter century. In recent years, researchers in quantum computational complexity have tried to identify approaches and develop…