Luca Rizzi - Keck Observatory

Luca Rizzi
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Luca Rizzi
Keck Observatory
United States

Pubs By Year

Pub Categories

Mathematics - Differential Geometry (16)
Mathematics - Optimization and Control (12)
Astrophysics (12)
Mathematics - Metric Geometry (8)
Astrophysics of Galaxies (6)
Mathematics - Analysis of PDEs (6)
Mathematics - Algebraic Geometry (5)
Cosmology and Nongalactic Astrophysics (4)
Mathematical Physics (3)
Mathematics - Mathematical Physics (3)
Quantum Physics (2)
Physics - General Physics (2)
Mathematics - Symplectic Geometry (2)
Mathematics - Probability (2)
Mathematics - Spectral Theory (2)
Solar and Stellar Astrophysics (2)
Instrumentation and Methods for Astrophysics (1)
General Relativity and Quantum Cosmology (1)
Mathematics - Dynamical Systems (1)

Publications Authored By Luca Rizzi

We prove that ideal sub-Riemannian manifolds (i.e., admitting no non-trivial abnormal minimizers) support interpolation inequalities for optimal transport. Read More

We prove an equivalence between the infinitesimal Torelli theorem for top forms on a hypersurface contained inside a Grassmannian $\mathbb G$ and the theory of adjoint volume forms presented in L. Rizzi, F. Zucconi, "Generalized adjoint forms on algebraic varieties", Ann. Read More

We prove that H-type Carnot groups of rank $k$ and dimension $n$ satisfy the $\mathrm{MCP}(K,N)$ if and only if $K\leq 0$ and $N \geq k+3(n-k)$. The latter integer coincides with the geodesic dimension of the Carnot group. The same result holds true for the larger class of generalized H-type Carnot groups introduced in this paper, and for which we compute explicitly the optimal synthesis. Read More

We solve the infinitesimal Torelli problem for $3$-dimensional quasi-smooth ${\mathbb{Q}}$-Fano hypersurfaces with at worst terminal singularities. We also find infinite chains of double coverings of increasing dimension which alternatively distribute themselves in examples and counterexamples for the infinitesimal Torelli claim and which share the analogue, and in some cases the same, Hodge-diagram properties as the length $3$ Gushel-Mukai chain of prime smooth Fanos of coindex $3$ and degree $10$. Read More

Two galaxies that lie deep within the Local Void provide a test of the expectation that voids expand. The modest (M_B~-14) HI bearing dwarf galaxies ALFAZOAJ1952+1428 and KK246 have been imaged with Hubble Space Telescope in order to study the stellar populations and determine distances from the luminosities of stars at the tip of the red giant branch. The mixed age systems have respective distances of 8. Read More

Affiliations: 1Caltech, 2W.M. Keck Observatory, 3INAF, 4Caltech, 5University of Tasmania, 6University of Tasmania, 7University of Minnesota, 8UC Berkeley

We present Keck/DEIMOS spectroscopy of individual stars in the relatively isolated Local Group dwarf galaxies Leo A, Aquarius, and the Sagittarius dwarf irregular galaxy. The three galaxies--but especially Leo A and Aquarius--share in common delayed star formation histories relative to many other isolated dwarf galaxies. The stars in all three galaxies are supported by dispersion. Read More

In this note, we study the cut locus of the free, step two Carnot groups $\mathbb{G}_k$ with $k$ generators, equipped with their left-invariant Carnot-Carath\'eodory metric. In particular, we disprove the conjectures on the shape of the cut loci proposed in [Myasnichenko - 2002] and [Montanari, Morbidelli - 2016], by exhibiting sets of cut points $C_k \subset \mathbb{G}_k$ which, for $k \geq 4$, are strictly larger than conjectured ones. While the latter were, respectively, smooth semi-algebraic sets of codimension $\Theta(k^2)$ and semi-algebraic sets of codimension $\Theta(k)$, the sets $C_k$ are semi-algebraic and have codimension $2$, yielding the best possible lower bound valid for all $k$ on the size of the cut locus of $\mathbb{G}_k$. Read More

We consider the quantum completeness problem, i.e. the problem of confining quantum particles, on a non-complete Riemannian manifold $M$ equipped with a smooth measure $\omega$, possibly degenerate or singular near the metric boundary of $M$, and in presence of a real-valued potential $V\in L^2_{\mathrm{loc}}(M)$. Read More

Using the notion of generalized divisors introduced by Hartshorne, we adapt the theory of adjoint forms to the case of Gorenstein curves. We show an infinitesimal Torelli-type theorem for vector bundles on Gorenstein curves. We also construct explicit counterexamples to the infinitesimal Torelli claim in the case of a reduced reducible Gorenstein curve. Read More

We prove a full generalization of the Castelnuovo's free pencil trick. We show its analogies with the Adjoint Theorem; see L. Rizzi, F. Read More

We relate some basic constructions of stochastic analysis to differential geometry, via random walk approximations. We consider walks on both Riemannian and sub-Riemannian manifolds in which the steps consist of travel along either geodesics or integral curves associated to orthonormal frames, and we give particular attention to walks where the choice of step is influenced by a volume on the manifold. A primary motivation is to explore how one can pass, in the parabolic scaling limit, from geodesics, orthonormal frames, and/or volumes to diffusions, and hence their infinitesimal generators, on sub-Riemannian manifolds, which is interesting in light of the fact that there is no completely canonical notion of sub-Laplacian on a general sub-Riemannian manifold. Read More

We prove that any corank 1 Carnot group of dimension $k+1$ equipped with a left-invariant measure satisfies the $\mathrm{MCP}(K,N)$ if and only if $K \leq 0$ and $N \geq k+3$. This generalizes the well known result by Juillet for the Heisenberg group $\mathbb{H}_{k+1}$ to a larger class of structures, which admit non-trivial abnormal minimizing curves. The number $k+3$ coincides with the geodesic dimension of the Carnot group, which we define here for a general metric space. Read More

We present the Team Keck Redshift Survey 2 (TKRS2), a near-infrared spectral observing program targeting selected galaxies within the CANDELS subsection of the GOODS-North Field. The TKRS2 program exploits the unique capabilities of MOSFIRE, an infrared multi-object spectrometer which entered service on the Keck I telescope in 2012 and contributes substantially to the study of galaxy spectral features at redshifts inaccessible to optical spectrographs. The TKRS2 project targets 97 galaxies drawn from samples that include z~2 emission-line galaxies with features observable in the JHK bands as well as lower-redshift targets with features in the Y band. Read More

For a fat sub-Riemannian structure, we introduce three canonical Ricci curvatures in the sense of Agrachev-Zelenko-Li. Under appropriate bounds we prove comparison theorems for conjugate lengths, Bonnet-Myers type results and Laplacian comparison theorems for the intrinsic sub-Laplacian. As an application, we consider the sub-Riemannian structure of $3$-Sasakian manifolds, for which we provide explicit curvature formulas. Read More

In this paper we prove a sub-Riemannian version of the classical Santal\'o formula: a result in integral geometry that describes the intrinsic Liouville measure on the unit cotangent bundle in terms of the geodesic flow. Our construction works under quite general assumptions, satisfied by any sub-Riemannian structure associated with a Riemannian foliation with totally geodesic leaves (e.g. Read More

With the advent of modern multi-detector heterodyne instruments that can result in observations generating thousands of spectra per minute it is no longer feasible to reduce these data as individual spectra. We describe the automated data reduction procedure used to generate baselined data cubes from heterodyne data obtained at the James Clerk Maxwell Telescope. The system can automatically detect baseline regions in spectra and automatically determine regridding parameters, all without input from a user. Read More

In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like invariants. We show that these coefficients can be interpreted as the curvature of a canonical Ehresmann connection associated to the metric, first introduced in [Zelenko-Li]. We show why this connection is naturally nonlinear, and we discuss some of its properties. Read More

We compare different notions of curvature on contact sub-Riemannian manifolds. In particular we introduce canonical curvatures as the coefficients of the sub-Riemannian Jacobi equation. The main result is that all these coefficients are encoded in the asymptotic expansion of the horizontal derivatives of the sub-Riemannian distance. Read More

Tip of the red giant branch measurements based on Hubble Space Telescope and ground-based imaging have resulted in accurate distances to 29 galaxies in the nearby Centaurus A Group. All but two of the 29 galaxies lie in either of two thin planes roughly parallel with the supergalactic equator. The planes are only slightly tilted from the line-of-sight, leaving little ambiguity regarding the morphology of the structure. Read More

On a sub-Riemannian manifold we define two type of Laplacians. The \emph{macroscopic Laplacian} $\Delta_\omega$, as the divergence of the horizontal gradient, once a volume $\omega$ is fixed, and the \emph{microscopic Laplacian}, as the operator associated with a sequence of geodesic random walks. We consider a general class of random walks, where \emph{all} sub-Riemannian geodesics are taken in account. Read More

Affiliations: 1Caltech, 2Irvington High School, 3The Harker School, 4Harvard, 5Caltech, 6UC Santa Cruz, 7McDonald Observatory, 8Chungnam National University, 9Keck Observatory

We present carbon abundances of red giants in Milky Way globular clusters and dwarf spheroidal galaxies (dSphs). Our sample includes measurements of carbon abundances for 154 giants in the clusters NGC 2419, M68, and M15 and 398 giants in the dSphs Sculptor, Fornax, Ursa Minor, and Draco. This sample doubles the number of dSph stars with measurements of [C/Fe]. Read More

Let $\pi\colon\mathcal{X}\to B$ be a family over a smooth connected analytic variety $B$, not necessarily compact, whose general fiber $X$ is smooth of dimension $n$, with irregularity $\geq n+1$ and such that the image of the canonical map of $X$ is not contained in any quadric of rank $\leq 2n+3$. We prove that if the Albanese map of $X$ is of degree $1$ onto its image then the fibers of $\pi\colon\mathcal{X}\to B$ are birational under the assumption that all the $1$-forms and all the $n$-forms of a fiber are holomorphically liftable to $\mathcal{X}$. Moreover we show that generic Torelli holds for such a family $\pi\colon \mathcal{X}\to B$ if, in addition to the above hypothesis, we assume that the fibers are minimal and their minimal model is unique. Read More

We investigate the number of geodesics between two points $p$ and $q$ on a contact sub-Riemannian manifold M. We show that the count of geodesics on $M$ is controlled by the count on its nilpotent approximation at $p$ (a contact Carnot group). For contact Carnot groups we make the count explicit in exponential coordinates $(x,z) \in \mathbb{R}^{2n} \times \mathbb{R}$ centered at $p$. Read More

In this paper, we extend the use of the tip of the red giant branch (TRGB) method to near-infrared wavelengths from previously-used $I$-band, using the \textit{Hubble Space Telescope (HST)} Wide Field Camera 3 (WFC3). Upon calibration of a color dependency of the TRGB magnitude, the IR TRGB yields a random uncertainty of $\sim 5%$ in relative distance. The IR TRGB methodology has an advantage over the previously-used ACS $F606W$ and $F814W$ filter set for galaxies that suffer from severe extinction. Read More

We prove sectional and Ricci-type comparison theorems for the existence of conjugate points along sub-Riemannian geodesics. In order to do that, we regard sub-Riemannian structures as a special kind of variational problems. In this setting, we identify a class of models, namely linear quadratic optimal control systems, that play the role of the constant curvature spaces. Read More

Motivated by the study of linear quadratic optimal control problems, we consider a dynamical system with a constant, quadratic Hamiltonian, and we characterize the number of conjugate times in terms of the spectrum of the Hamiltonian vector field $\vec{H}$. We prove the following dichotomy: the number of conjugate times is identically zero or grows to infinity. The latter case occurs if and only if $\vec{H}$ has at least one Jordan block of odd dimension corresponding to a purely imaginary eigenvalue. Read More

Cosmicflows-2 is a compilation of distances and peculiar velocities for over 8000 galaxies. Numerically the largest contributions come from the luminosity-linewidth correlation for spirals, the TFR, and the related Fundamental Plane relation for E/S0 systems, but over 1000 distances are contributed by methods that provide more accurate individual distances: Cepheid, Tip of the Red Giant Branch, Surface Brightness Fluctuation, SNIa, and several miscellaneous but accurate procedures. Our collaboration is making important contributions to two of these inputs: Tip of the Red Giant Branch and TFR. Read More

The curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. Our construction of the curvature is direct and naive, and it is similar to the original approach of Riemann. Read More

For an equiregular sub-Riemannian manifold M, Popp's volume is a smooth volume which is canonically associated with the sub-Riemannian structure, and it is a natural generalization of the Riemannian one. In this paper we prove a general formula for Popp's volume, written in terms of a frame adapted to the sub-Riemannian distribution. As a first application of this result, we prove an explicit formula for the canonical sub-Laplacian, namely the one associated with Popp's volume. Read More

We analyze the quantum-mechanical behavior of a system described by a one-dimensional asymmetric potential constituted by a step plus (i) a linear barrier or (ii) an exponential barrier. We solve the energy eigenvalue equation by means of the integral representation method, classifying the independent solutions as equivalence classes of homotopic paths in the complex plane. We discuss the structure of the bound states as function of the height U_0 of the step and we study the propagation of a sharp-peaked wave packet reflected by the barrier. Read More

Recent observations of UGC4879 with the Advanced Camera for Surveys on the Hubble Space Telescope confirm that it is a nearby isolated dwarf irregular galaxy. We measure a distance of 1.36+/-0. Read More

We analyze a toy model describing an empty spacetime in which the motion of a test mass (and the trajectories of photons) evidence the presence of a continuous and homogeneous distribution of matter; however, since the energy-momentum tensor vanishes, no real matter or energy distribution is present at all. Thus, a hypothetical observer will conclude that he is immersed in some sort of dark matter, even though he has no chance to directly detect it. This suggests yet another possibility of explaining the elusive dark matter as a purely dynamical effect due to the curvature of spacetime. Read More

We analyze the behavior of a quantum system described by a one-dimensional asymmetric potential consisting of a step plus a harmonic barrier. We solve the eigenvalue equation by the integral representation method, which allows us to classify the independent solutions as equivalence classes of homotopic paths in the complex plane. We then consider the propagation of a wave packet reflected by the harmonic barrier and obtain an expression for the interaction time as a function of the peak energy. Read More

Affiliations: 1Queen's University Belfast, UK, 2Queen's University Belfast, UK, 3Queen's University Belfast, UK, 4Imperial College London, UK, 5MPA Garching, 6Queen's University Belfast, UK, 7INAF Padova, 8INAF Padova, 9Queen's University Belfast, UK, 10Queen's University Belfast, UK, 11Pulkovo Central Astronomical Observatory, 12INAF Teramo, 13INAF Teramo, 14INAF Teramo, 15INAF Teramo, 16Spitzer Science Centre, 17Arhus University, 18Dark Cosmology Centre, 19University of Munich, 20Pulkovo Central Astronomical Observatory, 21Dark Cosmology Centre, 22MPA Garching, 23INAF Padova, 24University of Munich, 25University of Munich, 26JAC, Hawaii, 27Sternberg Astronomical Institute, 28INAF Padova, 29University of Munich

We present photometric and spectroscopic observations at optical and near-infrared wavelengths of the nearby type Ic SN 2007gr. These represent the most extensive data-set to date of any supernova of this sub-type, with frequent coverage from shortly after discovery to more than one year post-explosion. We deduce a rise time to B-band maximum of 11. Read More

Affiliations: 1INAF-OA Brera, 2INAF-OA Bologna, 3INAF-OA Padova, 4INAF-OA Bologna, 5Univ. of Michigan, 6INAF-OA Brera, 7JAC, 8INAF-OA Padova, 9INAF-OA Bologna
Category: Astrophysics

We have carried out an intensive survey of the northern region of the Fornax dwarf spheroidal galaxy with the aim of detecting the galaxy's short--period pulsating stars (P<0.25 days). Observations collected over three consecutive nights with the Wide Field Imager of the 2. Read More

Affiliations: 1ESO, 2ESO, 3OAPD, Italy, 4CEA, Paris, France, 5UCLA, USA, 6IfA, Honolulu, USA, 7JAC, Hilo, USA
Category: Astrophysics

(abridged) The present work is a first step to collect homogeneous abundances and near-infrared (NIR) luminosities for a sample of dwarf irregular (dIrr) galaxies, located in nearby groups. The use of NIR luminosities is intended to provide a better proxy to mass than the blue luminosities commonly used in the literature; in addition, selecting group members reduces the impact of uncertain distances. Accurate abundances are derived to assess the galaxy metallicity. Read More

We have obtained deep infrared $J$ and $K$ band observations of five fields located in the Large Magellanic Cloud (LMC) bar with the ESO New Technology Telescope equipped with the SOFI infrared camera. In our fields, 65 RR Lyrae stars catalogued by the OGLE collaboration were identified. Using different theoretical and empirical calibrations of the period-luminosity-metallicity relation, we find consistent LMC distance moduli values. Read More

The peculiar velocity of the Local Group of galaxies manifested in the Cosmic Microwave Background dipole is found to decompose into three dominant components. The three components are clearly separated because they arise on distinct spatial scales and are fortuitously almost orthogonal in their influences. The nearest, which is distinguished by a velocity discontinuity at ~7 Mpc, arises from the evacuation of the Local Void. Read More

The luminosity of the Tip of the Red Giant Branch (TRGB) provides an excellent measure of galaxy distances and is easily determined in the resolved images of nearby galaxies observed with Hubble Space Telescope. There is now a large amount of archival data relevant to the TRGB methodology and which offers comparisons with other distance estimators. Zero-point issues related to the TRGB distance scale are reviewed in this paper. Read More

Accurate distances to galaxies can be determined from the luminosities of stars at the Tip of the Red Giant Branch (TRGB). We use a Maximum Likelihood algorithm to locate the TRGB in galaxy color-magnitude diagrams. The algorithm is optimized by introducing reliable photometric errors and a completeness characterization determined with artificial star experiments. Read More

Affiliations: 1IfA, Hawaii, USA, 2IfA, Hawaii, USA, 3IfA, Hawaii, USA, 4Concepcion, Chile, 5Concepcion, Chile
Category: Astrophysics

We have used the Advanced Camera for Surveys on board the Hubble Space Telescope to obtain deep photometry of the NGC 300 spiral galaxy in the Sculptor group. The results have been used to derive an accurate distance determination based on the Tip of the Red Giant Branch distance estimator. Both edge-detection and maximum likelihood methods have been applied, to derive a distance modulus (m-M)_0=26. Read More


We report on the recent developments of our long-term investigation of the near-IR luminosity-metallicity relation for dwarf irregular galaxies in nearby groups. A very well-defined relation is emerging from our observational database, and a preliminary discussion of its implications is given. Read More

Affiliations: 1Osservatorio Astronomico di Padova, INAF, 2Osservatorio Astronomico di Padova, INAF, 3Osservatorio Astronomico di Bologna, INAF, 4Osservatorio Astronomico di Bologna, INAF, 5Osservatorio Astronomico di Padova, INAF, 6Osservatorio Astronomico di Roma, INAF
Category: Astrophysics

We have obtained intermediate-resolution VLT spectroscopy of 75 globular cluster candidates around the Sa galaxy M104 (NGC4594). Fifty-seven candidates out to ~ 40 kpc in the halo of the galaxy were confirmed to be bona-fide globular clusters, 27 of which are new. A first analysis of the velocities provides only marginal evidence for rotation of the cluster system. Read More

Affiliations: 1Osservatorio Astronomico di Padova, INAF, 2Osservatorio Astronomico di Padova, INAF, 3Osservatorio Astronomico di Padova, INAF, 4Osservatorio Astronomico di Roma, INAF, 5Osservatorio Astronomico di Bologna, INAF, 6Osservatorio Astronomico di Bologna, INAF
Category: Astrophysics

We present preliminary results of a wide field study of the globular cluster system of NGC4594, the Sombrero galaxy. The galaxy was observed in B, V, and R using the Wide Field Imager on the ESO 2.2m telescope. Read More

We present and discuss the photometric and spectroscopic evolution of the peculiar SN1998bw, associated with GRB980425, through an analysis of optical and near IR data collected at ESO-La Silla. The spectroscopic data, spanning the period from day -9 to day +376 (relative to B maximum), have shown that this SN was unprecedented, although somewhat similar to SN1997ef. Maximum expansion velocities as high as 3x10^4 km/s to some extent mask its resemblance to other Type Ic SNe. Read More

Affiliations: 1UniPD, Italy, 2OAPD, Italy, 3UniPD, Italy, 4OAPD, Italy
Category: Astrophysics

Recent results on the detection of substructure in dwarf spheroidal galaxies are discussed. In most cases they show that, when a galaxy experiences multiple SF episodes, the intermediate age population is more centrally concentrated than the old population, and that the recent SF is even more concentrated towards the central regions. Moreover, it appears that the spatial distribution of stars becomes more and more irregular as younger and younger subpopulations are considered. Read More