Rota’s universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In articular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

Courbe de rotation de la galaxie à partir de la photométrie d'amas situés à la périphérie du disque

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Analytic Torsion, the Eta Invariant, and Closed Differential Forms on Spaces of Metrics

The central idea of this dissertation is to interpret certain invariants constructed from Laplace spectral data on a compact Riemannian manifold as regularized integrals of closed differential forms on the space of Riemannian metrics, or more generally on a space of metrics on a vector bundle. We apply this idea to both the Ray-Singer analytic torsion

and the eta invariant, explaining their dependence on the metric used to define them with a Stokes' theorem argument. We also introduce analytic multi-torsion, a generalization of analytic torsion, in the context of certain manifolds with local product structure; we prove that it is metric independent in a suitable sense.

Courbe de rotation de la galaxie à partir de la photométrie d'amas situés à la périphérie du disque

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Siblings’ Sex is linked to Mental Rotation Performance in Males but not Females

Research has consistently found sex differences in mental rotation. Twin research has suggested that females with male co-twins perform better than females with female co-twins on mental rotation. Because twins share both pre-natal and post-natal environments, it is not possible to test whether this advantage is due to in-uterine transmission of testosterone from males to females or due to socialisation processes. The present study explored whether the advantage of females with brothers can be observed in non-twin siblings. Participants (N = 1799) were assessed on mental rotation. The observed group differences were overall small: males performed significantly better than females; females with sisters performed similarly to females with brothers; importantly, males with brothers performed significantly better than both female groups. The results suggest that sex differences in mental rotation are driven by the group of males with brothers.

On the rotation of co-orbital bodies in eccentric orbits

We investigate the resonant rotation of co-orbital bodies in eccentric and planar orbits. We develop a simple analytical model to study the impact of the eccentricity and orbital perturbations on the spin dynamics. This model is relevant in the entire domain of horseshoe and tadpole orbit, for moderate eccentricities. We show that there are three different families of spin-orbit resonances, one depending on the eccentricity, one depending on the orbital libration frequency, and another depending on the pericenter's dynamics. We can estimate the width and the location of the different resonant islands in the phase space, predicting which are the more likely to capture the spin of the rotating body. In some regions of the phase space the resonant islands may overlap, giving rise to chaotic rotation.