13 mai 2019

Tomasz Szarek (Université de Gdansk)
Random iterations of homeomorphisms on the interval and circle

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Lieu : salle 3L8

Résumé : The talk is concerned with the problem of ergodicity and limit theorems for iterated function systems defined on the interval or the circle. In particular we shall sketch the proof of the Central Limit Theorem for such systems. This is a survey of joint research with A.Zdunik and K.Czudek.

Random iterations of homeomorphisms on the interval and circle  Version PDF

Bruno Franchi (Dipartimento di Matematica, Università di Bologna)
Poincaré and Sobolev inequalities for differential forms in Euclidean spaces and Heisenberg groups (in collaboration with A. Baldi & P. Pansu)

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Lieu : IMO ; salle 3L8.

Résumé : In this talk we present endpoint Poincaré and Sobolev inequalities for the de Rham complex in Euclidean spaces as well as endpoint contact Poincaré and Sobolev inequalities in Heisenberg groups \mathbb{H}^n, where the word « contact » is meant to stress that de Rham’s exterior differential is replaced by the « exterior differential » d_c of the so-called Rumin’s complex (E_0^\bullet, d_c).
A crucial feature of Rumin’s construction is that d_c recovers the scale invariance of the « exterior differential » d_c under the group dilations associated with the stratification of the Lie algebra of \mathbb{H}^n. These inequalities provide a natural extension of the corresponding usual inequalities for functions in \mathbb{H}^n and are a quantitative formulation of the fact that d_c-closed forms are locally d_c-exact.

Poincaré and Sobolev inequalities for differential forms in Euclidean spaces and Heisenberg groups (in collaboration with A. Baldi & P. Pansu)  Version PDF

Xenia Spilioti (Fachbereich Mathematik, Universität Tübingen)
Dynamical zeta functions, trace formulae and applications

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Lieu : IMO ; salle 3L8.

Résumé : The dynamical zeta functions of Ruelle and Selberg are functions of a complex variable $s$ and are associated with the geodesic flow on the unit sphere bundle of a compact hyperbolic manifold. Their representation by Euler-type products traces back to the Riemann zeta function. In this talk, we will present trace formulae and Lefschetz formulae, and the machinery that they provide to study the analytic properties of the dynamical zeta functions and their relation to spectral invariants. In addition, we will present other applications of the Lefschetz formula, such as the prime geodesic theorem for locally symmetric spaces of higher rank.

Dynamical zeta functions, trace formulae and applications  Version PDF