Talks

Let Sg be a closed surface of genus g ≥ 2. The curve graph corresponding to Sg, denoted by C(Sg), is a 1-dimensional simplicial complex whose vertices are isotopy classes of essential closed curves on Sg and two vertices share an edge if they represent mutually disjoint curves. Little is known about curves which are at a distance n ≥ 4 apart in C(Sg). This is primarily because the local infinitude of the vertices in C(Sg) hinders the calculation of distances in C(Sg).

In this talk, we will look at a family of pairs of curves on Sg which are at a distance 4 apart in C(Sg). These curves are created using Dehn twists. As an application, we will deduce an upper bound on the minimal intersection number of curves at a distance 4 apart in C(Sg). Finally, we will look at an example of a pair of curves on S2 which are at a distance 5 apart in C(S2).

In this talk I will briefly review the mapping of the MW disk and bulge and then focus on the complexities that have been unveiled recently thanks to the combination of different precise datasets (astrometry, photometry, spectroscopy, asteroseismology).The history of the MW starts to be clearer once ages are obtained for large samples of stars and other stellar population tracers (e.g. globular clusters and RR Lyrae). I will show recent results that unveil the complex history of the Milky Way discs.Finally, I will discuss some remaining challenges and how we plan to address these in the future.

The 3-body problem poses a longstanding challenge in physics and celestial mechanics. Despite the impossibility of obtaining general analytical solutions, statistical theories have been developed based on the ergodic principle. This assumption is justified by chaos, which is expected to fully mix the accessible phase space of the 3-body problem.We probed the presence of regular (i.e. non-chaotic) trajectories within the 3-body problem and assessed their impact on statistical escape theories.Our analysis reveals that regular trajectories occupy up to 37% of the phase space, and their outcomes defy the predictions of statistical escape theories. Our findings underscore the challenges in applying statistical escape theories to astrophysical problems, as they may bias results by excluding the outcome of regular trajectories. This is particularly important in the context of formation scenarios of gravitational wave mergers, where biased estimates of binary eccentricity can significantly impact estimates of coalescence efficiency and detectable eccentricity.Based on 2403.03247

A random walk on a Fuchsian group (that is, a lattice in SL(2,R)) gives a random walk in the hyperbolic plane. Under mild conditions, a typical sample path for such a walk converges to the circle at infinity. The distribution of the limits of sample paths define a stationary measure on the circle. This talk will survey the landscape of results related to the study of such stationary measures on the circle and in analogous contexts.