Related papers: The level 1 weight 2 case of Serre's conjecture
In this note I provide two extensions of a particular case of the classical Poncelet theorem.
We give an elementary proof of low rank cases of the conjecture that the tensor product of two semistable Euclidean lattices is again semistable.
This is a Bourbaki's seminar text. We introduce the combinatorial Kashiwara-Vergne conjecture on the Baker-Campbell-Hausdorff serie. After recalling previous results and consequences, we explain the Alekseev-Meinrenken's proof…
The Surface Group Conjectures are statements about recognising surface groups among one-relator groups, using either the structure of their finite-index subgroups, or all subgroups. We resolve these conjectures in the two generator case.…
We recall the history of the proof of Seifert fibre space conjecture, as well as it motivations and its several generalisations.
We give a new approach for the local class field theory of Serre and Hazewinkel. We also discuss two-dimensional local class field theory in this framework.
We prove a counterpart of the log-convex density conjecture in the hyperbolic plane.
This is a survey on Kawaguchi-Silverman conjecture.
A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)
We prove that a certain conjecture holds true and the conjecture states a relationship between the zeta function of a finite category and the Euler characteristic of a finite category.
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
This note presents an elementary and direct proof for the convexity of the Choquet integral when the corresponding set function is submodular.
Frechet bounds of the 1-st kind for sets of events and its main properties are considered. The lemma on not more than two nonzero values of lower Frechet-bounds of the 1-st kind for a set of half-rare events is proved with the corollary on…
We generalize a result of Serre's to show that if every vertex of some fixed type of a convex subcomplex of an irreducible spherical building has an opposite, then the subcomplex is completely reducible.
We prove some extensions of Andrews inequality.
Motivated by two Legendre-type formulas for overpartitions, we derive a variety of their companions as Legendre theorems for overpartition pairs. This leads to equalities of subclasses of overpartitions and overpartition pairs.
We prove a general result on the existence of local solutions of any second order quasi-linear elliptic system with arbitrary 1-jet at a point.
We give an elementary and constructive proof for a theorem of de Smit et Lenstra. Note: In version 1, was missing the proof that "completely secant" implies "1-secant"
The study of the additive volume of sets can be reduced to the case of one-dimensional sets. The exact values of the volume of extremal sets are given as a conjecture.
Nous rappelons l'historique de la demonstration de la conjecture des fibres de Seifert, ainsi que ses motivations et ses diverses generalisations. ----- We recall the history of the proof of the Seibert fiber space conjecture, as well as…