Eventi
With the tools and perspective of Object Oriented Spatial Statistics, we analyze official daily data on mortality from all causes in the provinces and municipalities of Italy for the year 2020, the first of the COVID-19 pandemic. By comparison with mortality data from 2011 to 2019, we assess the local impact of the pandemic as perturbation factor of the natural spatio-temporal death process. For each Italian province and year, mortality data are represented by the densities of time of death during the calendar year. In this talk, the use of a density-on-density functional linear model, formulated to decouple temporal and spatial variability, will be firstly illustrated, followed by a spatial analysis focused on identifying the spatial correlation structure of the death process before and during the pandemic. An anomaly detection framework at the very granular scale of Italian municipalities will also be described.
This is a survey lecture about fractional diffusion. It describes its formulation via the integral Laplacian, the regularity of solutions on bounded domains and the approximation by finite element methods. It emphasizes recent research about Besov regularity on Lipschitz domains, BPX preconditioning, a priori error estimates in quasi-uniform and graded meshes, and local energy error estimates. It concludes with quasi-linear fractional problems.
Contatto: marco.verani@polimi.it
Ricardo H. Nochetto is professor at the University of Maryland (UMD), College Park. He has a dual affiliation with the Department of Mathematics and the Institute for Physical Science and Technology. He received his Ph.D. at the University of Buenos Aires (Argentina) in 1983, he was a postdoctoral fellow at the Istituto di Analisi Numerica (Pavia, Italy) from 1983 to 1986 and at the Institute for Mathematics and its Applications (Minneapolis, USA) from 1986 to 1987, before joining UMD in 1987. His research interests are on the numerical approximation of nonlinear PDEs (free boundary problems, shape optimization, geometric and fully nonlinear PDEs), fractional diffusion, and basic theory and applications of FEMs (error analysis, adaptivity, dG). R.H. Nochetto received the Sacchi-Landriani Prize in Numerical Analysis of Partial Differential Equations from the Istituto Lombardo (Accademia di Scienze e Lettere, Milan, Italy) in 1993, was invited speaker at the International Congress of Mathematicians in 2010 (Hyderabad, India) and plenary speaker at ICIAM (Beijing, China) in 2015, and is SIAM Fellow since 2011 and AMS Fellow since 2012. He was in the Scientific Advisory Board of ICERM, Brown University, 2016-2018, and is in the Board of Directors of Foundations of Computational Mathematics (FoCM), 2018-2022.
In questo seminario discutiamo un possibile approccio all'affronto di alcuni argomenti di Probabilità a livello di scuola secondaria di secondo grado. Esaminiamo alcune applicazioni in cui la Probabilità gioca un ruolo cruciale come strumento per modellizzare e gestire il rischio in ambiti in cui si studiano fenomeni in condizioni d'incertezza.
Ricardo H. Nochetto is professor at the University of Maryland (UMD), College Park. He has a dual affiliation with the Department of Mathematics and the Institute for Physical Science and Technology. He received his Ph.D. at the University of Buenos Aires (Argentina) in 1983, he was a postdoctoral fellow at the Istituto di Analisi Numerica (Pavia, Italy) from 1983 to 1986 and at the Institute for Mathematics and its Applications (Minneapolis, USA) from 1986 to 1987, before joining UMD in 1987. His research interests are on the numerical approximation of nonlinear PDEs (free boundary problems, shape optimization, geometric and fully nonlinear PDEs), fractional diffusion, and basic theory and applications of FEMs (error analysis, adaptivity, dG). R.H. Nochetto received the Sacchi-Landriani Prize in Numerical Analysis of Partial Differential Equations from the Istituto Lombardo (Accademia di Scienze e Lettere, Milan, Italy) in 1993, was invited speaker at the International Congress of Mathematicians in 2010 (Hyderabad, India) and plenary speaker at ICIAM (Beijing, China) in 2015, and is SIAM Fellow since 2011 and AMS Fellow since 2012. He was in the Scientific Advisory Board of ICERM, Brown University, 2016-2018, and is in the Board of Directors of Foundations of Computational Mathematics (FoCM), 2018-2022.
We consider a semi-linear integro-differential equation in dimension one associated to the half-Laplacian. This model describes the evolution of phase transitions associated to dislocations whose solution represents the atom dislocation in a crystal. The equation comprises the evolutive version of the classical Peierls-Nabarro model. We show that for a large number of dislocations, the solution, properly rescaled, converges to the solution of a well known equation called "the equation of motion of the dislocation continuum". The limit equation is a model for the macroscopic crystal plasticity with density of dislocations. In particular, we recover the so called Orowan's law which states that dislocations move at a velocity proportional to the effective stress. This is a joint paper with Tharathep Sangsawang.
Ricardo H. Nochetto is professor at the University of Maryland (UMD), College Park. He has a dual affiliation with the Department of Mathematics and the Institute for Physical Science and Technology. He received his Ph.D. at the University of Buenos Aires (Argentina) in 1983, he was a postdoctoral fellow at the Istituto di Analisi Numerica (Pavia, Italy) from 1983 to 1986 and at the Institute for Mathematics and its Applications (Minneapolis, USA) from 1986 to 1987, before joining UMD in 1987. His research interests are on the numerical approximation of nonlinear PDEs (free boundary problems, shape optimization, geometric and fully nonlinear PDEs), fractional diffusion, and basic theory and applications of FEMs (error analysis, adaptivity, dG). R.H. Nochetto received the Sacchi-Landriani Prize in Numerical Analysis of Partial Differential Equations from the Istituto Lombardo (Accademia di Scienze e Lettere, Milan, Italy) in 1993, was invited speaker at the International Congress of Mathematicians in 2010 (Hyderabad, India) and plenary speaker at ICIAM (Beijing, China) in 2015, and is SIAM Fellow since 2011 and AMS Fellow since 2012. He was in the Scientific Advisory Board of ICERM, Brown University, 2016-2018, and is in the Board of Directors of Foundations of Computational Mathematics (FoCM), 2018-2022.
Utilizzeremo il caso delle teorie elettromagnetiche di James Clerk Maxwell per illustrare il ruolo dei modelli e dell' analogia nella produzione di nuova conoscenza fisica.
In particolare, discuteremo di come il modello dei vortici nel suo articolo 'On Physical Lines of Forces' (1861-62) e l'utilizzo del ragionamento analogico abbiano avuto un ruolo centrale nella formulazione delle famose equazioni elettromagnetiche.
Come evidenziato da diversi studi, descrivere gli aspetti storici ed epistemologici di episodi centrali nella storia della scienza è importante dal punto di vista didattico, dal momento che contribuisce ad una migliore comprensione da parte degli studenti del ruolo chiave dei modelli nella ricerca scientifica e allo sviluppo di competenze modellistiche.
Ricardo H. Nochetto is professor at the University of Maryland (UMD), College Park. He has a dual affiliation with the Department of Mathematics and the Institute for Physical Science and Technology. He received his Ph.D. at the University of Buenos Aires (Argentina) in 1983, he was a postdoctoral fellow at the Istituto di Analisi Numerica (Pavia, Italy) from 1983 to 1986 and at the Institute for Mathematics and its Applications (Minneapolis, USA) from 1986 to 1987, before joining UMD in 1987. His research interests are on the numerical approximation of nonlinear PDEs (free boundary problems, shape optimization, geometric and fully nonlinear PDEs), fractional diffusion, and basic theory and applications of FEMs (error analysis, adaptivity, dG). R.H. Nochetto received the Sacchi-Landriani Prize in Numerical Analysis of Partial Differential Equations from the Istituto Lombardo (Accademia di Scienze e Lettere, Milan, Italy) in 1993, was invited speaker at the International Congress of Mathematicians in 2010 (Hyderabad, India) and plenary speaker at ICIAM (Beijing, China) in 2015, and is SIAM Fellow since 2011 and AMS Fellow since 2012. He was in the Scientific Advisory Board of ICERM, Brown University, 2016-2018, and is in the Board of Directors of Foundations of Computational Mathematics (FoCM), 2018-2022.
As it is well known, the Clifford algebras have numerous applications. In the present talk, we will explain how the Clifford algebras and their representation can build two-step nilpotent Lie algebras. They received the name Heisenberg type Lie algebras, due to the fact that the classical Heisenberg algebra is the simplest example in this construction.
A special class of Heisenberg type Lie algebras was introduced by A. Kaplan in 1980 to study hypoelliptic partial differential operators and their fundamental solutions. The Heisenberg type Lie algebras admit rational structural constants, that lead to the existence of lattices on the corresponding Lie groups according to the Malcev theorem. The factor of Heisenberg type Lie groups by the lattices gives rise to a chain of examples of nilmanifolds that are isospectral but non-diffeomorphic.
In the talk, we will explain the construction of the Heisenberg type Lie algebras and give examples. We also will discuss the classification of the constructed Lie algebras and their group of automorphisms.
Ricardo H. Nochetto is professor at the University of Maryland (UMD), College Park. He has a dual affiliation with the Department of Mathematics and the Institute for Physical Science and Technology. He received his Ph.D. at the University of Buenos Aires (Argentina) in 1983, he was a postdoctoral fellow at the Istituto di Analisi Numerica (Pavia, Italy) from 1983 to 1986 and at the Institute for Mathematics and its Applications (Minneapolis, USA) from 1986 to 1987, before joining UMD in 1987. His research interests are on the numerical approximation of nonlinear PDEs (free boundary problems, shape optimization, geometric and fully nonlinear PDEs), fractional diffusion, and basic theory and applications of FEMs (error analysis, adaptivity, dG). R.H. Nochetto received the Sacchi-Landriani Prize in Numerical Analysis of Partial Differential Equations from the Istituto Lombardo (Accademia di Scienze e Lettere, Milan, Italy) in 1993, was invited speaker at the International Congress of Mathematicians in 2010 (Hyderabad, India) and plenary speaker at ICIAM (Beijing, China) in 2015, and is SIAM Fellow since 2011 and AMS Fellow since 2012. He was in the Scientific Advisory Board of ICERM, Brown University, 2016-2018, and is in the Board of Directors of Foundations of Computational Mathematics (FoCM), 2018-2022.
Online: mox.polimi.it/mox-seminars/?id_evento=2101
Gastrulation is a critical event in vertebrate morphogenesis, characterized by coordinated large-scale multi-cellular movements. One grand challenge in modern biology is understanding how spatio-temporal morphological structures emerge from cellular processes in a developing organism and vary across vertebrates. We derive a theoretical framework that couples tissue flows, stress-dependent myosin activity, and actomyosin cable orientation. Our model, consisting of a set of nonlinear coupled PDEs, predicts the onset and development of observed experimental patterns of wild-type and perturbations of chick gastrulation as a spontaneous instability of a uniform state. We use analysis and numerics to show how our model recapitulates the phase space of gastrulation morphologies seen across vertebrates, consistent with experiments. Altogether, this suggests that early embryonic self-organization follows from a minimal predictive theory of active mechano-sensitive flows. www.biorxiv.org/content/10.1101/2021.10.03.462928v2
Contatto: pasquale.ciarletta@polimi.it
Ricardo H. Nochetto is professor at the University of Maryland (UMD), College Park. He has a dual affiliation with the Department of Mathematics and the Institute for Physical Science and Technology. He received his Ph.D. at the University of Buenos Aires (Argentina) in 1983, he was a postdoctoral fellow at the Istituto di Analisi Numerica (Pavia, Italy) from 1983 to 1986 and at the Institute for Mathematics and its Applications (Minneapolis, USA) from 1986 to 1987, before joining UMD in 1987. His research interests are on the numerical approximation of nonlinear PDEs (free boundary problems, shape optimization, geometric and fully nonlinear PDEs), fractional diffusion, and basic theory and applications of FEMs (error analysis, adaptivity, dG). R.H. Nochetto received the Sacchi-Landriani Prize in Numerical Analysis of Partial Differential Equations from the Istituto Lombardo (Accademia di Scienze e Lettere, Milan, Italy) in 1993, was invited speaker at the International Congress of Mathematicians in 2010 (Hyderabad, India) and plenary speaker at ICIAM (Beijing, China) in 2015, and is SIAM Fellow since 2011 and AMS Fellow since 2012. He was in the Scientific Advisory Board of ICERM, Brown University, 2016-2018, and is in the Board of Directors of Foundations of Computational Mathematics (FoCM), 2018-2022.
We will present some new results for a class of free boundary systems associated to shape optimization problems (spectral and integral functionals). The new main point of these results is the analysis of the regular part of the free boundary based on a linearization argument that takes care of the vectorial attitude of the problem.
This is based on joint works with D. De Silva and with F.P. Maiale and B. Velichkov.
Ricardo H. Nochetto is professor at the University of Maryland (UMD), College Park. He has a dual affiliation with the Department of Mathematics and the Institute for Physical Science and Technology. He received his Ph.D. at the University of Buenos Aires (Argentina) in 1983, he was a postdoctoral fellow at the Istituto di Analisi Numerica (Pavia, Italy) from 1983 to 1986 and at the Institute for Mathematics and its Applications (Minneapolis, USA) from 1986 to 1987, before joining UMD in 1987. His research interests are on the numerical approximation of nonlinear PDEs (free boundary problems, shape optimization, geometric and fully nonlinear PDEs), fractional diffusion, and basic theory and applications of FEMs (error analysis, adaptivity, dG). R.H. Nochetto received the Sacchi-Landriani Prize in Numerical Analysis of Partial Differential Equations from the Istituto Lombardo (Accademia di Scienze e Lettere, Milan, Italy) in 1993, was invited speaker at the International Congress of Mathematicians in 2010 (Hyderabad, India) and plenary speaker at ICIAM (Beijing, China) in 2015, and is SIAM Fellow since 2011 and AMS Fellow since 2012. He was in the Scientific Advisory Board of ICERM, Brown University, 2016-2018, and is in the Board of Directors of Foundations of Computational Mathematics (FoCM), 2018-2022.
We prove the existence of ground states, i.e. minimizers of the energy at fixed mass, for the focusing, subcritical Nonlinear Schroedinger equation in two dimensions, with a linear point interaction, or defect. Ground states turn out to be positive up to a phase, and to show a logaritmico singularity at the defect. The analogous problem has been widely treated in the one dimensional setting, including the case of graphs. The two dimensional version is more complicated because of the structure of the energy space, that is larger than the standard one. This result opens the way to the study of nonlinear hybrids. This is a joint work with Filippo Boni, Raffaele Carlone, and Lorenzo Tentarelli.
Ricardo H. Nochetto is professor at the University of Maryland (UMD), College Park. He has a dual affiliation with the Department of Mathematics and the Institute for Physical Science and Technology. He received his Ph.D. at the University of Buenos Aires (Argentina) in 1983, he was a postdoctoral fellow at the Istituto di Analisi Numerica (Pavia, Italy) from 1983 to 1986 and at the Institute for Mathematics and its Applications (Minneapolis, USA) from 1986 to 1987, before joining UMD in 1987. His research interests are on the numerical approximation of nonlinear PDEs (free boundary problems, shape optimization, geometric and fully nonlinear PDEs), fractional diffusion, and basic theory and applications of FEMs (error analysis, adaptivity, dG). R.H. Nochetto received the Sacchi-Landriani Prize in Numerical Analysis of Partial Differential Equations from the Istituto Lombardo (Accademia di Scienze e Lettere, Milan, Italy) in 1993, was invited speaker at the International Congress of Mathematicians in 2010 (Hyderabad, India) and plenary speaker at ICIAM (Beijing, China) in 2015, and is SIAM Fellow since 2011 and AMS Fellow since 2012. He was in the Scientific Advisory Board of ICERM, Brown University, 2016-2018, and is in the Board of Directors of Foundations of Computational Mathematics (FoCM), 2018-2022.
The optimal matching problem is one of the classical random optimization problems. While the asymptotic behavior of the expected cost is well understood only little is known for the asymptotic behavior of the optimal couplings - the solutions to the optimal matching problem. In this talk we show that at all mesoscopic scales the displacement under the optimal coupling converges in suitable Sobolev spaces to a Gaussian field which can be identified as the curl-free part of a vector Gaussian free field. Based on joint work with Michael Goldman.
Ricardo H. Nochetto is professor at the University of Maryland (UMD), College Park. He has a dual affiliation with the Department of Mathematics and the Institute for Physical Science and Technology. He received his Ph.D. at the University of Buenos Aires (Argentina) in 1983, he was a postdoctoral fellow at the Istituto di Analisi Numerica (Pavia, Italy) from 1983 to 1986 and at the Institute for Mathematics and its Applications (Minneapolis, USA) from 1986 to 1987, before joining UMD in 1987. His research interests are on the numerical approximation of nonlinear PDEs (free boundary problems, shape optimization, geometric and fully nonlinear PDEs), fractional diffusion, and basic theory and applications of FEMs (error analysis, adaptivity, dG). R.H. Nochetto received the Sacchi-Landriani Prize in Numerical Analysis of Partial Differential Equations from the Istituto Lombardo (Accademia di Scienze e Lettere, Milan, Italy) in 1993, was invited speaker at the International Congress of Mathematicians in 2010 (Hyderabad, India) and plenary speaker at ICIAM (Beijing, China) in 2015, and is SIAM Fellow since 2011 and AMS Fellow since 2012. He was in the Scientific Advisory Board of ICERM, Brown University, 2016-2018, and is in the Board of Directors of Foundations of Computational Mathematics (FoCM), 2018-2022.
Seminari Matematici al
Politecnico di Milano
- Analisi
- Cultura Matematica
- Seminari FDS
- Geometria e Algebra
- Probabilità e Statistica Matematica
- Probabilità Quantistica