Lionel Nguyen Van Thé

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In 2005, Kechris, Pestov and Todorčević provided a powerful tool to compute an invariant of topological groups known as the universal minimal flow, immediately leading to an explicit representation of this invariant in many concrete cases. More recently, the framework was generalized allowing for further applications, and the purpose of this paper is to(More)
The distinguishing number of a graph G is the smallest positive integer r such that G has a labeling of its vertices with r labels for which there is no non-trivial automorphism of G preserving these labels. In early work, Michael Albertson and Karen Collins computed the distinguishing number for various finite graphs, and more recently Wilfried Imrich,(More)
We prove that if the universalminimal flow of a Polish groupG ismetrizable and contains a Gδ orbit G · x0, then it is isomorphic to the completion of the homogeneous space G/Gx0 and show how this result translates naturally in terms of structural Ramsey theory. We also investigate universal minimal proximal flows and describe concrete representations of(More)
8 We investigate infinite versions of vector and affine space partition 9 results, and thus obtain examples and a counterexample for a parti10 tion problem for relational structures. In particular we provide two 11 (related) examples of an age indivisible relational structure which is 12 not weakly indivisible. 13
We study finite dimensional partition properties of the countable homogeneous dense local order (a directed graph closely related to the order structure of the rationals). Some of our results use ideas borrowed from the partition calculus of the rationals and are obtained thanks to a strengthening of Milliken’s theorem on trees.
We study the oscillation stability problem for the Urysohn sphere, an analog of the distortion problem for l2 in the context of the Urysohn space U. In particular, we show that this problem reduces to a purely combinatorial problem involving a family of countable ultrahomogeneous metric spaces with finitely many distances.