The architecture of planetary systems is a key piece of information to our understanding of their formation and evolution. This information also allows us to place the Solar System in the exoplanet context. An important example is the impact of outer giant planets on the formation of inner super-Earths and sub-Neptunes. Radial velocity (RV) surveys aim at drawing statistical insights into the (anti-)correlations between giants and inner small planets, which remain unclear. These surveys are limited by the completeness of the systems, namely, the sensitivity of the data to planet detections. Here, we show that we can improve the completeness by accounting for orbital stability. We introduce the Algorithm for the Refinement of DEtection limits via N-body stability Threshold (ARDENT), an open-source Python package for detection limits that include the stability constraint. The code computes the classic data-driven detection limits, along with the dynamical limits via both analytical and numerical stability criteria. We present the code strategy and illustrate its performance on TOI-1736 using published SOPHIE RVs. This system contains an eccentric cold giant on a 570-day orbit and an inner sub-Neptune on a 7-day orbit. We demonstrate that no additional planet can exist in this system beyond 150 days due to the gravitational influence of the giant. This outcome allows us to significantly refine the system completeness and also carries implications for RV follow-ups. ARDENT is user-friendly and can be employed across a wide variety of systems to refine our understanding of their architecture.

Data analysis and machine learning have become an integrative part of the modern scientific methodology, offering automated procedures for the prediction of a phenomenon based on past observations, unraveling underlying patterns in data and providing insights about the problem. Yet, caution should avoid using machine learning as a black-box tool, but rather consider it as a methodology, with a rational thought process that is entirely dependent on the problem under study. In particular, the use of algorithms should ideally require a reasonable understanding of their mechanisms, properties and limitations, in order to better apprehend and interpret their results. Accordingly, the goal of this thesis is to provide an in-depth analysis of random forests, consistently calling into question each and every part of the algorithm, in order to shed new light on its learning capabilities, inner workings and interpretability. The first part of this work studies the induction of decision trees and the construction of ensembles of randomized trees, motivating their design and purpose whenever possible. Our contributions follow with an original complexity analysis of random forests, showing their good computational performance and scalability, along with an in-depth discussion of their implementation details, as contributed within Scikit-Learn. In the second part of this work, we analyse and discuss the interpretability of random forests in the eyes of variable importance measures. The core of our contributions rests in the theoretical characterization of the Mean Decrease of Impurity variable importance measure, from which we prove and derive some of its properties in the case of multiway totally randomized trees and in asymptotic conditions. In consequence of this work, our analysis demonstrates that variable importances [...].

Emission lines of FeI and NiI are commonly found in the coma of solar system comets, even at large heliocentric distances. These atoms are most likely released from the surface of the comet's nucleus or from a short-lived parent. The presence of these lines in cometary spectra is unexpected because the surface blackbody equilibrium temperature is too low to allow the sublimation of refractory minerals containing these metals. These lines were also found in the interstellar comet 2I/Borisov which has a NiI/FeI abundance ratio similar to that observed in solar system comets. On average, this ratio is one order of magnitude higher than the solar Ni/Fe abundance ratio. Here, we report observations of the new interstellar comet 3I/ATLAS, which were carried out with the ESO Very Large Telescope equipped with the UVES spectrograph. Spectra were obtained at six epochs, at heliocentric distances ranging from 3.14 to 2.14 au. NiI was detected at all epochs. FeI was only detected at heliocentric distances smaller than 2.64 au. We estimated the NiI and FeI production rates by comparing the observed line intensities with those produced by a fluorescence model. Comet 3I exhibits a high production rate of NiI atoms as well as a high NiI/FeI ratio, making it exceptional when compared to solar system comets and 2I/Borisov. Additionally, we found that the NiI/FeI ratio decreases rapidly with decreasing heliocentric distance, suggesting that comet 3I could soon become indistinguishable from solar system comets in this respect. We interpreted these observations assuming that the NiI and FeI atoms were released through the sublimation of Ni(CO)$_4$ and Fe(CO)$_5$ carbonyls, which supports the presence of these species in the cometary material.

Stellar surface inhomogeneities such as spots and faculae introduce Doppler variations that challenge exoplanet detection via the radial velocity method. While their impact on disc-integrated spectra is well established, detailed studies of the underlying local line profiles have so far been limited to the Sun. We present an observational campaign targeting the active star WASP-85 A during transits of its hot Jupiter companion. The transits span two stellar rotation periods, allowing us to probe the evolution of active regions. From ground-based photometry we identify seven active regions, six containing dark spots. Using simultaneous ESPRESSO transit spectroscopy, we spatially resolve these regions on the stellar surface by using the planet as a probe. We detect significant bisector shape changes, line broadening, and net redshifts during spot occultations, with velocity shifts of 108-333 m/s (mean uncertainty 50 m/s). The observed broadening is consistent with the Zeeman effect, implying magnetic field strengths (Stokes $I$) $B$ = 2.7-4.4 kG (mean uncertainty 0.6 kG), comparable to solar umbrae. Combined with our photometric spot model, this yields lower limits to the disc-integrated field $Bf = 16 \pm 3$ G and $61 \pm 9$ G for the two hemispheres probed -- at least three times higher than Sun-as-a-star values. We also measure centre-to-limb variations in FWHM, line depth, equivalent width, and convective blueshift, which broadly agree with solar observations and 3D MHD models. This work demonstrates a new way to characterise the surfaces of exoplanet host stars, paving the way for future analyses incorporating synthetic line profiles from 3D MHD simulations.

The distribution of close-in exoplanets is shaped by the interplay between atmospheric and dynamical processes. The Neptunian Desert, Ridge, and Savanna illustrate the sensitivity of these worlds to such processes, making them ideal to disentangle their roles. Determining how many Neptunes were brought close-in by early disk-driven migration (DDM; maintaining primordial spin-orbit alignment) or late high-eccentricity migration (HEM; generating large misalignments) is essential to understand how much atmosphere they lost. We propose a unified view of the Neptunian landscape to guide its exploration, speculating that the Ridge is a hot spot for evolutionary processes. Low-density Neptunes would mainly undergo DDM, getting fully eroded at shorter periods than the Ridge, while denser Neptunes would be brought to the Ridge and Desert by HEM. We embark on this exploration via ATREIDES, which relies on spectroscopy and photometry of 60 close-in Neptunes, their reduction with robust pipelines, and their interpretation through internal structure, atmospheric, and evolutionary models. We carried out a systematic RM census with VLT/ESPRESSO to measure the distribution of 3D spin-orbit angles, correlate its shape with system properties and thus relate the fraction of aligned-misaligned systems to DDM, HEM, and atmospheric erosion. Our first target, TOI-421c, lies in the Savanna with a neighboring sub-Neptune TOI-421b. We measured their 3D spin-orbit angles (Psib = 57+11-15 deg; Psic = 44.9+4.4-4.1 deg). Together with the eccentricity and possibly large mutual inclination of their orbits, this hints at a chaotic dynamical origin that could result from DDM followed by HEM. ATREIDES will provide the community with a wealth of constraints for formation and evolution models. We welcome collaborations that will contribute to pushing our understanding of the Neptunian landscape forward.

The Gaia Galactic survey mission is designed and optimized to obtain astrometry, photometry, and spectroscopy of nearly two billion stars in our Galaxy. Yet as an all-sky multi-epoch survey, Gaia also observes several million extragalactic objects down to a magnitude of G~21 mag. Due to the nature of the Gaia onboard selection algorithms, these are mostly point-source-like objects. Using data provided by the satellite, we have identified quasar and galaxy candidates via supervised machine learning methods, and estimate their redshifts using the low resolution BP/RP spectra. We further characterise the surface brightness profiles of host galaxies of quasars and of galaxies from pre-defined input lists. Here we give an overview of the processing of extragalactic objects, describe the data products in Gaia DR3, and analyse their properties. Two integrated tables contain the main results for a high completeness, but low purity (50-70%), set of 6.6 million candidate quasars and 4.8 million candidate galaxies. We provide queries that select purer sub-samples of these containing 1.9 million probable quasars and 2.9 million probable galaxies (both 95% purity). We also use high quality BP/RP spectra of 43 thousand high probability quasars over the redshift range 0.05-4.36 to construct a composite quasar spectrum spanning restframe wavelengths from 72-100 nm.

We investigate the existence of densities for finite-dimensional distributions of Hermite processes of order $q \ge 1$ and self-similarity parameter $H\in(\frac12,1)$. Whereas the Gaussian case $q=1$ (fractional Brownian motion) is well understood, the non-Gaussian situation has not yet been settled. In this work, we extend the classical three-step approach used in the Gaussian case: factorization of the determinant into conditional terms, strong local nondeterminism, and non-degeneracy. We transport this strategy to the Hermite setting using Malliavin calculus. Specifically, we establish a determinant identity for the Malliavin matrix, prove strong local nondeterminism at the level of Malliavin derivatives, and apply the Bouleau-Hirsch criterion. Consequently, for any distinct times $t_1,\dots,t_n$, the vector $(Z^{H,q}_{t_1},\dots,Z^{H,q}_{t_n})$ of a Hermite process admits a density with respect to the Lebesgue measure. Beyond the result itself, the main contribution is the methodology, which could extend to other non-Gaussian models.

We experimentally investigate the wake dynamics of a square cylinder rising through quiescent water over a range of Froude numbers ($\mathrm{Fr}$). Time-resolved Particle Image Velocimetry provides velocity and vorticity fields that enable pressure reconstruction and vortex characterization. Diagnostics based on swirl strength ($\lambda_{ci}$), the Okubo-Weiss parameter ($W$), and a shear-vortex interaction measure ($\Lambda$) reveal that the wake is governed by a persistent pair of counter-rotating vortices rather than by periodic shedding. Circulation exhibits a two-regime dependence on $\mathrm{Fr}$, with a sharp increase below $\mathrm{Fr}\approx 1$ and saturation above this threshold, mirroring entrainment force scaling reported previously. While vortex area remains nearly constant, swirl strength and negative-$W$ regions expand with $\mathrm{Fr}$, indicating that entrainment enhancement arises from intensified rotation rather than an enlarged vortex footprint. These findings provide new physical insight into vortex-free-surface interactions and enrich the understanding of entrainment mechanisms in unsteady wakes, with implications for multiphase flows and the hydrodynamic design of naval and offshore structures.

Deep learning has advanced weather forecasting, but accurate predictions first require identifying the current state of the atmosphere from observational data. In this work, we introduce Appa, a score-based data assimilation model generating global atmospheric trajectories at 0.25\si{\degree} resolution and 1-hour intervals. Powered by a 565M-parameter latent diffusion model trained on ERA5, Appa can be conditioned on arbitrary observations to infer plausible trajectories, without retraining. Our probabilistic framework handles reanalysis, filtering, and forecasting, within a single model, producing physically consistent reconstructions from various inputs. Results establish latent score-based data assimilation as a promising foundation for future global atmospheric modeling systems.

We present ExoMiner++, an enhanced deep learning model that builds on the success of ExoMiner to improve transit signal classification in 2-minute TESS data. ExoMiner++ incorporates additional diagnostic inputs, including periodogram, flux trend, difference image, unfolded flux, and spacecraft attitude control data, all of which are crucial for effectively distinguishing transit signals from more challenging sources of false positives. To further enhance performance, we leverage multi-source training by combining high-quality labeled data from the Kepler space telescope with TESS data. This approach mitigates the impact of TESS's noisier and more ambiguous labels. ExoMiner++ achieves high accuracy across various classification and ranking metrics, significantly narrowing the search space for follow-up investigations to confirm new planets. To serve the exoplanet community, we introduce new TESS catalog containing ExoMiner++ classifications and confidence scores for each transit signal. Among the 147,568 unlabeled TCEs, ExoMiner++ identifies 7,330 as planet candidates, with the remainder classified as false positives. These 7,330 planet candidates correspond to 1,868 existing TESS Objects of Interest (TOIs), 69 Community TESS Objects of Interest (CTOIs), and 50 newly introduced CTOIs. 1,797 out of the 2,506 TOIs previously labeled as planet candidates in ExoFOP are classified as planet candidates by ExoMiner++. This reduction in plausible candidates combined with the excellent ranking quality of ExoMiner++ allows the follow-up efforts to be focused on the most likely candidates, increasing the overall planet yield.

The AU Microscopii planetary system is only 24 Myr old, and its geometry may provide clues about the early dynamical history of planetary systems. Here, we present the first measurement of the Rossiter-McLaughlin effect for the warm sub-Neptune AU Mic c, using two transits observed simultaneously with the European Southern Observatory's (ESO's) Very Large Telescope (VLT)/Echelle SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observations (ESPRESSO), CHaracterising ExOPlanet Satellite (CHEOPS), and Next-Generation Transit Survey (NGTS). After correcting for flares and for the magnetic activity of the host star, and accounting for transit-timing variations, we find the sky-projected spin-orbit angle of planet c to be in the range $\lambda_c=67.8_{-49.0}^{+31.7}$\,degrees (1-$\sigma$). We examine the possibility that planet c is misaligned with respect to the orbit of the inner planet b ($\lambda_b=-2.96_{-10.30}^{+10.44}$\,degrees), and the equatorial plane of the host star, and discuss scenarios that could explain both this and the planet's high density, including secular interactions with other bodies in the system or a giant impact. We note that a significantly misaligned orbit for planet c is in some degree of tension with the dynamical stability of the system, and with the fact that we see both planets in transit, though these arguments alone do not preclude such an orbit. Further observations would be highly desirable to constrain the spin-orbit angle of planet c more precisely.

We present the results of time-resolved photometry, abundance analysis and Doppler imaging of an Ap star, HD 100357. The {\it TESS} photometry revealed rotational modulation with a period of 1.6279247 days. Upon inspecting the residuals after removing the rotational period and its harmonics, we found additional frequencies around 15.8054 d$^{-1}$ which we later confirmed with ground-based observations as originating from a nearby star. Using high-resolution spectroscopy, we identified HD 100357 as an Ap Si/He-wk star exhibiting rotational modulation caused by surface abundance spots. The stellar parameters of HD 100357 were determined as $T_{\rm eff}$ = 11,850 K, $\log g$ = 4.57, $\upsilon\sin i$ = 60 km\,s$^{-1}$, and an inclination angle $i$ = 72$^{\circ}$. The detailed abundance analysis revealed strongly overabundant stratified silicon, an overabundance of iron-peak elements and rare earth elements combined with remarkably deficient helium. Mapping of Fe and Cr abundances revealed the existence of ring-shaped regions with a lower concentration of the elements. Their geometry might reflect the orientation of the hypothetical magnetic field of the star, oriented $\sim$90$^{\circ}$ to the rotational axis. HD 100357, with its strong chemical peculiarities and indications of possible magnetic fields, represents an interesting candidate for follow-up spectropolarimetric observations aimed at investigating its magnetic field topology and stellar activity.

Gravitational waves from black-hole merging events have revealed a population of extra-galactic BHs residing in short-period binaries with masses that are higher than expected based on most stellar evolution models - and also higher than known stellar-origin black holes in our Galaxy. It has been proposed that those high-mass BHs are the remnants of massive metal-poor stars. Gaia astrometry is expected to uncover many Galactic wide-binary systems containing dormant BHs, which may not have been detected before. The study of this population will provide new information on the BH-mass distribution in binaries and shed light on their formation mechanisms and progenitors. As part of the validation efforts in preparation for the fourth Gaia data release (DR4), we analysed the preliminary astrometric binary solutions, obtained by the Gaia Non-Single Star pipeline, to verify their significance and to minimise false-detection rates in high-mass-function orbital solutions. The astrometric binary solution of one source, Gaia BH3, implies the presence of a 32.70 \pm 0.82 M\odot BH in a binary system with a period of 11.6 yr. Gaia radial velocities independently validate the astrometric orbit. Broad-band photometric and spectroscopic data show that the visible component is an old, very metal-poor giant of the Galactic halo, at a distance of 590 pc. The BH in the Gaia BH3 system is more massive than any other Galactic stellar-origin BH known thus far. The low metallicity of the star companion supports the scenario that metal-poor massive stars are progenitors of the high-mass BHs detected by gravitational-wave telescopes. The Galactic orbit of the system and its metallicity indicate that it might belong to the Sequoia halo substructure. Alternatively, and more plausibly, it could belong to the ED-2 stream, which likely originated from a globular cluster that had been disrupted by the Milky Way.

The quasar main sequence (QMS), characterized by the Eigenvector 1 (EV1), serves as a unifying framework for classifying type-1 active galactic nuclei (AGNs) based on their diverse spectral properties. Although a fully self-consistent physical interpretation has long been lacking, our physically motivated 2.5D FRADO (Failed Radiatively Accelerated Dusty Outflow) model naturally predicts that the Eddington ratio ($\dot{m}$) is the primary physical driver of the QMS, with black hole mass ($M_{\rm BH}$) and inclination ($i$) acting as secondary contributors. We employed a dense grid of FRADO simulations of the geometry and dynamics of the broad-line region (BLR), covering a representative range of $M_{\rm BH}$ and $\dot{m}$. For each simulation, we computed the full width at half maximum (FWHM) of the H$\beta$ line under different $i$. The resulting FWHM--$\dot{m}$ diagram closely resembles the characteristic trend observed in the EV1 parameter space. This establishes the role of $\dot{m}$ as the true proxy for the Fe II strength parameter ($R_{\rm Fe}$), and vice versa. Our results suggest that $\dot{m}$ can be regarded as the sole underlying physical tracer of $R_{\rm Fe}$ and should therefore scale directly with it. The $M_{\rm BH}$ accounts for the virial mass-related scatter in FWHM, while $i$ acts as a secondary driver modulating $R_{\rm Fe}$ and FWHM for a given $\dot{m}$ and $M_{\rm BH}$.

We present the discovery and characterization of TOI-4364\,b, a young mini-Neptune in the tidal tails of the Hyades cluster, identified through TESS transit observations and ground-based follow-up photometry. The planet orbits a bright M dwarf ($K=9.1$\,mag) at a distance of 44\,pc, with an orbital period of 5.42\,days and an equilibrium temperature of $488^{+4}_{-4}$\,K. The host star's well-constrained age of 710\,Myr makes TOI-4364\,b an exceptional target for studying early planetary evolution around low-mass stars. We determined a planetary radius of $2.01^{+0.1}_{-0.08}$\,Earth radii, indicating that this planet is situated near the upper edge of the radius valley. This suggests that the planet retains a modest H/He envelope. As a result, TOI-4364\,b provides a unique opportunity to explore the transition between rocky super-Earths and gas-rich mini-Neptunes at the early stages of evolution. Its radius, which may still evolve as a result of ongoing atmospheric cooling, contraction, and photoevaporation, further enhances its significance for understanding planetary development. Furthermore, TOI-4364\,b possesses a moderately high Transmission Spectroscopy Metric of 44.2, positioning it as a viable candidate for atmospheric characterization with instruments such as JWST. This target has the potential to offer crucial insights into atmospheric retention and loss in young planetary systems.

Detecting unmodeled gravitational wave (GW) bursts presents significant challenges due to the lack of accurate waveform templates required for matched-filtering techniques. A primary difficulty lies in distinguishing genuine signals from transient noise. Machine learning approaches, particularly convolutional neural networks (CNNs), offer promising alternatives for this classification problem. This paper presents a CNN-based pipeline for detecting short GW bursts (duration < 10~\mathrm{s}), adapted from an existing framework designed for longer-duration events. The CNN has been trained on core-collapse supernova (CCSN) gravitational waveform models injected into simulated Gaussian noise. The network successfully identifies these signals and generalizes to CCSN waveforms not included in the training set, showing the potential of U-Net architectures for detecting short-duration gravitational wave transients across diverse astrophysical scenarios.

We produce a clean and well-characterised catalogue of objects within 100\,pc of the Sun from the \G\ Early Data Release 3. We characterise the catalogue through comparisons to the full data release, external catalogues, and simulations. We carry out a first analysis of the science that is possible with this sample to demonstrate its potential and best practices for its use. The selection of objects within 100\,pc from the full catalogue used selected training sets, machine-learning procedures, astrometric quantities, and solution quality indicators to determine a probability that the astrometric solution is reliable. The training set construction exploited the astrometric data, quality flags, and external photometry. For all candidates we calculated distance posterior probability densities using Bayesian procedures and mock catalogues to define priors. Any object with reliable astrometry and a non-zero probability of being within 100\,pc is included in the catalogue. We have produced a catalogue of \NFINAL\ objects that we estimate contains at least 92\% of stars of stellar type M9 within 100\,pc of the Sun. We estimate that 9\% of the stars in this catalogue probably lie outside 100\,pc, but when the distance probability function is used, a correct treatment of this contamination is possible. We produced luminosity functions with a high signal-to-noise ratio for the main-sequence stars, giants, and white dwarfs. We examined in detail the Hyades cluster, the white dwarf population, and wide-binary systems and produced candidate lists for all three samples. We detected local manifestations of several streams, superclusters, and halo objects, in which we identified 12 members of \G\ Enceladus. We present the first direct parallaxes of five objects in multiple systems within 10\,pc of the Sun.

We present the discovery of 11 new transiting brown dwarfs and low-mass M-dwarfs from NASA's TESS mission: TOI-2844, TOI-3122, TOI-3577, TOI-3755, TOI-4462, TOI-4635, TOI-4737, TOI-4759, TOI-5240, TOI-5467, and TOI-5882. They consist of 5 brown dwarf companions and 6 very low mass stellar companions ranging in mass from $25 M_{\rm J}$ to $128 M_{\rm J}$. We used a combination of photometric time-series, spectroscopic, and high resolution imaging follow-up as a part of the TESS Follow-up Observing Program (TFOP) in order to characterize each system. With over 50 transiting brown dwarfs confirmed, we now have a large enough sample to directly test different formation and evolutionary scenarios. We provide a renewed perspective on the transiting brown dwarf desert and its role in differentiating between planetary and stellar formation mechanisms. Our analysis of the eccentricity distribution for the transiting brown dwarf sample does not support previous claims of a transition between planetary and stellar formation at $\sim42$ $M_{\rm J}$. We also contribute a first look into the metallicity distribution of transiting companions in the range $7 - 150$ $M_{\rm J}$, showing that this too does not support a $\sim42$ $M_{\rm J}$ transition. Finally, we also detect a significant lithium absorption feature in one of the brown dwarf hosts (TOI-5882) but determine that the host star is likely old based on rotation, kinematic, and photometric measurements. We therefore claim that TOI-5882 may be a candidate for planetary engulfment.

On 29 May 2023, the LIGO Livingston observatory detected the gravitational-wave signal GW230529_181500 from the merger of a neutron star with a lower mass-gap compact object. Its long inspiral signal provides a unique opportunity to test General Relativity (GR) in a parameter space previously unexplored by strong-field tests. In this work, we performed parameterized inspiral tests of GR with GW230529_181500. Specifically, we search for deviations in the frequency-domain GW phase by allowing for agnostic corrections to the post-Newtonian coefficients. We performed tests with the Flexible Theory Independent (FTI) and Test Infrastructure for General Relativity (TIGER) frameworks using several quasi-circular waveform models that capture different physical effects (higher modes, spins, tides). We find that the signal is consistent with GR for all deviation parameters. Assuming the primary object is a black hole, we obtain particularly tight constraints on the dipole radiation at $-1$PN order of $|\delta\hat{\varphi}_{-2}| \lesssim 8 \times 10^{-5}$, which is a factor $\sim17$ times more stringent than previous bounds from the neutron star--black hole merger GW200115_042309, as well as on the 0.5PN and 1PN deviation parameters. We discuss some challenges that arise when analyzing this signal, namely biases due to correlations with tidal effects and the degeneracy between the 0PN deviation parameter and the chirp mass. To illustrate the importance of GW230529_181500 for tests of GR, we mapped the agnostic $-1$PN results to a class of Einstein-scalar-Gauss-Bonnet (ESGB) theories of gravity. We also conducted an analysis probing the specific phase deviation expected in ESGB theory and obtain an upper bound on the Gauss-Bonnet coupling of $\ell_{\rm GB} \lesssim 0.51~\rm{M}_\odot$ ($\sqrt{\alpha_{\rm GB}} \lesssim 0.28$ km), which is better than any previously reported constraint.

On 2017 August 17, the gravitational-wave event GW170817 was observed by the Advanced LIGO and Virgo detectors, and the gamma-ray burst (GRB) GRB 170817A was observed independently by the Fermi Gamma-ray Burst Monitor, and the Anticoincidence Shield for the Spectrometer for the International Gamma-Ray Astrophysics Laboratory. The probability of the near-simultaneous temporal and spatial observation of GRB 170817A and GW170817 occurring by chance is $5.0\times 10^{-8}$. We therefore confirm binary neutron star mergers as a progenitor of short GRBs. The association of GW170817 and GRB 170817A provides new insight into fundamental physics and the origin of short gamma-ray bursts. We use the observed time delay of $(+1.74 \pm 0.05)\,$s between GRB 170817A and GW170817 to: (i) constrain the difference between the speed of gravity and the speed of light to be between $-3\times 10^{-15}$ and $+7\times 10^{-16}$ times the speed of light, (ii) place new bounds on the violation of Lorentz invariance, (iii) present a new test of the equivalence principle by constraining the Shapiro delay between gravitational and electromagnetic radiation. We also use the time delay to constrain the size and bulk Lorentz factor of the region emitting the gamma rays. GRB 170817A is the closest short GRB with a known distance, but is between 2 and 6 orders of magnitude less energetic than other bursts with measured redshift. A new generation of gamma-ray detectors, and subthreshold searches in existing detectors, will be essential to detect similar short bursts at greater distances. Finally, we predict a joint detection rate for the Fermi Gamma-ray Burst Monitor and the Advanced LIGO and Virgo detectors of 0.1--1.4 per year during the 2018-2019 observing run and 0.3--1.7 per year at design sensitivity.