Borelian subgroups of simple Lie groups

We prove that in a simple real Lie group, there is no Borel measurable dense subgroup of intermediate Hausdorff dimension.Comment: 26 pages, no figur

A Product Theorem in simple Lie groups

We prove a discretized Product Theorem for general simple Lie groups, in the spirit of Bourgain's Discretized Sum-Product Theorem.Comment: 27 page

Birds of a feather or by note? Ideological nationalization of local electoral manifestos in Belgium

Until now, scholars trying to unravel the phenomenon of nationalization have seldom considered the local policy layer or the ideological dimension as their main subject. This paper, however, studies the ideological nationalization of Flemish local party branches. It applies the method of content analysis of electoral manifestos to the local elections and examines the programmatic overlaps between the party headquarter and its local branches. An innovative nationalization measure is introduced and subsequently included in an explanatory regression model. The results show that ideological similarities are ubiquitous and especially prevailing among leftist parties, in majority-participating party branches and in large municipalities

A spectral gap theorem in simple Lie groups

We establish the spectral gap property for dense subgroups generated by algebraic elements in any compact simple Lie group, generalizing earlier results of Bourgain and Gamburd for unitary groups.Comment: 20 page

Rational approximation on quadrics: a simplex lemma and its consequences

We give elementary proof of stronger versions of several recent results on intrinsic Diophantine approximation on rational quadric hypersurfaces $X\subset \mathbb{P}^n(\mathbb{R})$. The main tool is a refinement of the simplex lemma, which essentially says that rational points on $X$ which are sufficiently close to each other must lie on a totally isotropic rational subspace of $X$.Comment: 15 page