29 mars 2018

Rhiannon Dougall (Université de Nantes)
Critical exponents for normal subgroups

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Lieu : Institut de Mathématique d’Orsay, salle 2L8

Résumé : Fix a cocompact group 𝚪_0 of isometries of a negatively curved, simply connected space X. We are interested in the dynamics of its normal subgroups 𝚪. Namely, we study the critical exponent 𝛅(𝚪), which is the exponential growth rate of the 𝚪-orbit of a point. We characterise the existence of a gap 𝛅(𝚪) < 𝛅(𝚪_0) uniform in a family of normal subgroups 𝚪, in terms of permutation representations given by the quotients 𝚪_0/𝚪.
The proof uses the symbolic dynamics for the geodesic flow, for which we obtain the analogous statements for countable state shifts obtained as group extensions of a finite state shift.

Notes de dernières minutes : Café culturel à 13h par Damien Thomine.

Critical exponents for normal subgroups  Version PDF

Daniel Yasumasa Takahashi (Princeton University)
Coupled oscillator dynamics of vocal turn-taking in monkeys

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Résumé : Much of human social interaction is mediated through conversation. These are speech exchanges between two individuals where smooth turn-taking occurs with no formal or explicit rules. Given its central importance in social interactions, it is natural to ask how turn-taking evolved and what might be its neural basis. To investigate these questions, we are using marmoset monkeys as a model system. Marmosets are a highly vocal primate species that often exchange vocalizations with conspecifics to maintain social contact. We show that marmosets, like humans, take turns during natural dyadic vocal exchanges and that the timing of exchanges is periodically coupled. This suggests that an oscillatory mechanism is responsible for the dynamics of turn-taking. Consistent with this idea, we show that marmosets entrain the timing of their vocal output during vocal exchanges, whereby faster (or slower) response intervals from one marmoset lead to faster (or slower) response intervals from the other marmoset. To explain these results, we built a stochastic dynamic systems model of two interacting oscillators. The model is based on the interactions among four neural structures (‘drive’, ‘motor’ and two ‘auditory’ nodes) with connectivity inspired by published physiological and anatomical data. We validate our model showing that it generates turn-taking dynamics nearly identical to that seen in natural marmoset vocal exchanges. We then use our model to predict that a self-monitoring mechanism is crucial for the correct timing of the vocal turn-taking.

Coupled oscillator dynamics of vocal turn-taking in monkeys  Version PDF

Matthieu Bonnivard (Université Paris Diderot)
Homogénéisation d’un modèle d’écoulement turbulent au voisinage d’une paroi rugueuse

Mihaela Ifrim (University of Wisconsin)
A Morawetz inequality for water waves

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Lieu : IMO, Salle 3L8

Résumé : We consider gravity and gravity/capillary water waves in two space dimensions. Assuming uniform energy bounds for the solutions, we prove local energy decay estimates. Our result is uniform in the infinite depth limit.
Joint work with Thomas Alazard and Daniel Tataru.

A Morawetz inequality for water waves  Version PDF