Related papers: Un portrait kal\'eidoscopique du jeune Camille Jor…

The Jordan measure, the Jordan curve theorem, as well as the other generic references to Camille Jordan's (1838-1922) achievements highlight that the latter can hardly be reduced to the "great algebraist" whose masterpiece, the Trait\'e des…

This paper appeals to the figure of \'Evariste Galois for investigating the gates between mathematics and their "publics." The figure of Galois draws some lines of/within mathematics for/from the outside of mathematics and these lines in…

The paper surveys the history and state-of-the-art of the study of Jordan homomorphisms.

The study of arboreal Galois representations (that is, Galois groups arising from iteration of polynomial and rational functions) originated with work of Odoni in the 1980s. Beginning in the early 2000s it underwent a period of renewed…

As Jordan observed in 1870, just as univariate polynomials have Galois groups, so do problems in enumerative geometry. Despite this pedigree, the study of Galois groups in enumerative geometry was dormant for a century, with a systematic…

During the whole of 1874, Camille Jordan and Leopold Kronecker quar- relled vigorously over the organisation of the theory of bilinear forms. That theory promised a "general" and "homogeneous" treatment of numerous questions arising in…

We show that the Jordan decomposition of characters of finite reductive groups can be chosen so that if the centralizer of the relevant semisimple element in the dual group is connected, then the map is Galois-equivariant. Further, in this…

Several classes of baric algebras studied by different authors will be given a unified treatment, using the technique of gametization introduced by Mallol et al. Many of these algebras will be shown to be either Jordan algebras or to be…

In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of Galois groups with algebraic geometry, complex analysis and discrete subgroups of Lie…

What did "algebra" mean before the development of the algebraic theories of the 20th century ? This paper stresses the identities taken by the algebraic practices developped during the century long discussion around the equation around the…

We investigate automorphism groups of planar graphs. The main result is a complete recursive description of all abstract groups that can be realized as automorphism groups of planar graphs. The characterization is formulated in terms of…

The object of this paper is the study of a class of dessins d'enfants, the so-called diameter four trees. These objects, first introduced by G. Shabat, can be considered as the simplest non trivial example of etale covers of the projective…

This paper is meant to be an informal introduction to Quantum Groups, starting from its origins and motivations until the recent developments. We call in particular the attention on the newly descovered relationship among quantum groups,…

We throw a brief glance at Galois' life, on the occasion of his 200th anniversary (written in German).

The aim of this article is to start a study of Jordan derivations in finite endomorphism semirings.

This is a survey paper, on recent progress around lifting Galois representations. I focused on approaches that solely rely on Galois cohomology. Emphasis is laid on material I talked about, at the conference held in Ottawa in June 2024, to…

We state conjectures on the relationships between automorphic representations and Galois representations, and give evidence for them.

These notes were written following lectures I had the pleasure of giving on this subject at Keio University, during November and December 2004. The first part is about new applications of Jordan algebras to the geometry of Hermitian…

For each prime number $\ell$ and for each imaginary quadratic order of class number one or two, we determine all the possible $\ell$-adic Galois representations that occur for any elliptic curve with complex multiplication by such an order…

In this paper, we study dimensions of some varieties, that were introduced recently by Kisin in order to prove modularity of some Galois representations. In fact, we mainly consider a special case for which we obtain an estimation of the…