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Université de Neuchâtel

Large scale geometry of box spaces

Delabie, Thiebout ; Valette, Alain (Dir.) ; Khukhro, Ana (Codir.)

Thèse de doctorat : Université de Neuchâtel, 2018.

Box spaces are metric space that are constructed using group. They are useful as examples of metric spaces with exceptional large scale geometric properties. In this thesis we further investigate box space.

Université de Neuchâtel

Isoperimetric inequalities for Laplace and Steklov problems on Riemannian manifolds

Pétiard, Luc ; Colbois, Bruno (Dir.)

Thèse de doctorat : Université de Neuchâtel, 2019.

This thesis is about the spectra of the Laplacian and of the Dirichlet-to-Neumann operators on a compact Riemannian manifold. Both problems have physical interpretations that can be found in [Eva 1998] and [Ban 1980]. We focused on finding upper bounds for the eigenvalues, based on the geometry of the manifold. More precisely, we consider if it is possible to obtain upper bounds in which the...

Université de Fribourg

The diffeomorphism type of small hyperplane arrangements is combinatorially determined

Gallet, Matteo ; Saini, Elia

In: Advances in Geometry, 2019, vol. 19, no. 1, p. 89–100

It is known that there exist hyperplane arrangements with the same underlying matroid that admit non-homotopy equivalent complement manifolds. Here we show that, in any rank, complex central hyperplane arrangements with up to 7 hyperplanes and the same underlying matroid are isotopic. In particular, the diffeomorphism type of the complement manifold and the Milnor fiber and fibration of these...

Université de Neuchâtel

Action selectors without Floer-Homology

Haug, Carsten ; Schlenk, Felix (Dir.)

Thèse de doctorat : Université de Neuchâtel, 2018.

Hamiltonian systems on symplectic manifolds tend to have many periodic orbits. The “actions” of these orbits form an invariant for the Hamiltonian system. The set of actions can be very large, however. To get useful invariants, one selects for each Hamiltonian function just one action value by some minimax procedure: A so-called action selector associates with every compactly supported...

Université de Fribourg

Chromatic numbers of spheres

Prosanov, Roman

In: Discrete Mathematics, 2018, vol. 341, no. 11, p. 3123–3133

The chromatic number of a subset of Euclidean space is the minimal number of colors sufficient for coloring all points of this subset in such a way that any two points at the distance 1 have different colors. We give new upper bounds on chromatic numbers of spheres. This also allows us to give new upper bounds on chromatic numbers of any bounded subsets.

Université de Fribourg

Universality for the random-cluster model on isoradial graphs

Duminil-Copin, Hugo ; Li, Jhih-Huang ; Manolescu, Ioan

In: Electronic Journal of Probability, 2018, vol. 23, p. -

We show that the canonical random-cluster measure associated to isoradial graphs is critical for all q≥1. Additionally, we prove that the phase transition of the model is of the same type on all isoradial graphs: continuous for 1≤q≤4 and discontinuous for q>4. For 1≤q≤4, the arm exponents (assuming their existence) are shown to be the same for all isoradial graphs. In particular,...

Université de Fribourg

The phase transitions of the random-cluster and Potts models on slabs with $q \geq 1$ are sharp

Manolescu, Ioan ; Raoufiï, Aran

In: Electronic Journal of Probability, 2018, vol. 23, p. -

We prove sharpness of the phase transition for the random-cluster model with q≥1 on graphs of the form S:=G×S, where G is a planar lattice with mild symmetry assumptions, and S a finite graph. That is, for any such graph and any q≥1, there exists some parameter pc=pc(S,q), below which the model exhibits exponential decay and above which there exists a.s. an infinite cluster. The result...

Université de Fribourg

A note on the Petersen-Wilhelm conjecture

González-Álvaro, David ; Radeschi, Marco

In: Proceedings of the American Mathematical Society, 2018, vol. 146, no. 10, p. 4447–4458

In this note we consider submersions from compact manifolds, homotopy equivalent to the Eschenburg or Bazaikin spaces of positive curvature. We show that if the submersion is nontrivial, the dimension of the base is greater than the dimension of the fiber. Together with previous results, this proves the Petersen-Wilhelm conjecture for all the known compact manifolds with positive curvature.

Université de Neuchâtel

Properties and constructions of codes with the rank and the subspace metric

Ravagnani, Alberto ; Gorla, Elisa (Dir.)

Thèse de doctorat : Université de Neuchâtel, 2016.

In 2000 Ahlswede, Cai, Li, and Yeung discovered that employing coding techniques in network transmissions at the intermediate nodes of the network may give substantial gains in information throughput. These results originated a new research field, called network coding, concerned with efficiency and reliability of communications over networks. Network coding started to draw the attention...