— In this survey article, we recall some facts about split Kac-Moody groups as defined by J. Tits, describe their main properties and then propose an analogue of Borel-Tits theory for a non-split version of them. The main result is a Galois descent theorem, i.e., the persistence of a nice combinatorial structure after passing to rational points. We are also interested in the geometric point of ...

We prove that there exists an integer p0 such that X split (p)(Q) is made of cusps and CM-points for any prime p > p0. Equivalently, for any non-CM elliptic curve E over Q and any prime p > p0 the image of the Galois representation ρE,p is not contained in the normalizer of a split Cartan subgroup. This gives a partial answer to an old question of Serre.

A simple relaxation of two rows of a simplex tableau is a mixed integer set consisting of two equations with two free integer variables and non-negative continuous variables. Recently Andersen et al. [2] and Cornu ́ejols and Margot [13] showed that the facet-defining inequalities of this set are either split cuts or intersection cuts obtained from lattice-free triangles and quadrilaterals. Throu...

The pathways by which dislocations, line defects within the lattice structure, overcome microstructural obstacles represent a key aspect in understanding the main mechanisms that control mechanical properties of ductile crystalline materials. While edge dislocations were believed to change their glide plane only by a slow, non-conservative, thermally activated motion, we suggest the existence o...

GLI-Split is a new addressing and routing architecture for the Internet. It splits the functionality of current IP addresses into a global locator, a local locator, and an identifier, and encodes them in IPv6 addresses. It implements the locator/identifier split and makes routing in the core of the Internet more scalable. GLI-Split can be incrementally deployed and it is backward-compatible wit...