In the middle of the sixties, A. Lichnerowicz raised the following simple question: “Is the round sphere the only compact Riemannian manifold admitting a noncompact group of conformal transformations?” The talk will present the developments which arose from Lichnerowicz's question. It will be an opportunity to see diverse aspects of conformal dynamics in Riemannian, as well as Lorentzian geometry
We give an arithmetic version of the recent proof of the improved triangle removal lemma by Fox [Fox11], for the group $F_2^n$.
Resonances are complex analogs of eigenvalues for Laplacians on noncompact manifolds, arising in long time resonance expansions of linear waves. We prove a Weyl type asymptotic formula for the number of resonances in a strip, provided that the set of trapped geodesics is r-normally hyperbolic for large r and satisfies a pinching condition. Our dynamical assumptions are stable under small smooth perturbations and motivated by applications to black holes. We also establish a high frequency analog of resonance expansions.
An institution dating from antiquity whose formal recognition culminates with the 1951 Geneva Convention on Refugees, asylum has been confronted with a dramatic increase in applicants during the past century. However, this burden has been unevenly distributed worldwide: refugees are massively concentrated in camps of the global South, particularly Sub-Saharan Africa and Central Asia, whereas asylum seekers are selected via a form of casuistry in the global North, under the pressure of growing suspicion toward so-called bogus refugees.
Drawing on ten years of research, this lecture by Didier Fassin, James D. Wolfensohn Professor in the School of Social Science, examines the significant changes to the conception of the right to asylum in recent decades and the ordeal faced by applicants as they go through complex administrative and judiciary procedures in an attempt to have their status acknowledged. Beyond the study of the refugee problem, the analysis proposes an inquiry into the question of truth—that of the asylum seekers as well as that of contemporary societies in their endeavor to define and circumscribe the responsibility to protect the victims of violence.
The theorem of the title is that if the L-function L(E,s) of an elliptic curve E over the rationals vanishes to order r=0 or 1 at s=1 then the rank of the group of rational rational points of E equals r and the Tate-Shafarevich group of E is finite. This talk will describe an approach to the converse. The methods are mostly p-adic.