Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 23-01-2023 al 29-01-2023
Lunedì 23 gennaio 2023
Ore 11:00, Aula B, Dipartimento di Matematica, Università di Roma `La Sapienza'
Corso di Dottorato
Dario Trevisan
Mathematical aspects of quantum information theory
Per informazioni, rivolgersi a: bertini@mat.uniroma1.it
Lunedì 23 gennaio 2023
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Gian Paolo Leonardi (Università degli Studi di Trento)
A vertex-skipping property for perimeter almost-minimizers in convex containers.
A crucial issue in capillarity-type problems is understanding the behavior of solutions near singular points in the boundary of the container. In the special case of the relative perimeter functional, we prove that the closure of the internal boundary of a perimeter almost-minimizer in a 3-dimensional convex container \(\Omega\) cannot contain vertices of \(\Omega\). As a byproduct of our study, we also prove a boundary monotonicity formula for perimeter almost-minimizers within a convex container of any dimension, without any extra regularity of the boundary but a suitable closeness to its tangent cones. This is joint work with Giacomo Vianello (Ph.D. UniTN).
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it
Martedì 24 gennaio 2023
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Geometria
Antonio Trusiani (Institut de Mathématiques de Toulouse)
A relative Yau-Tian-Donaldson conjecture and stability thresholds
In the first part of the talk the set of Kähler-Einstein metrics with prescribed singularities and a new relative K-stability notion will be introduced. A particular focus will be given to the motivations and intuitions, making a comparison with the log K-stability/log Kähler-Einstein metrics. The two notions mentioned above will then be related to each other through a Yau-Tian-Donaldson correspondence, which will be the core of the talk. An important role will be played by a valuative criterion, which can be also used to relate the prescribed singularities setting to the absolute setting. Indeed new estimates on the Fujita-Odaka δ-invariant and new information on the genuine K-stability will be deduced. Time permitting, a further discussion on some future developments will conclude the talk.
Martedì 24 gennaio 2023
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Elena Gaburro (Inria Center Bordeaux-Sud-Ouest)
Structure preserving high order Lagrangian schemes for the solution of hyperbolic equations: from fluid-dynamics to astrophysics
In this talk, we will present a novel family of high order accurate direct Arbitrary-Lagrangian-Eulerian (ALE) Discontinuous Galerkin (DG) schemes with a posteriori subcell Finite Volume (FV) limiter, on moving Voronoi tessellations that, at each time step, are regenerated in order to guarantee a high quality of the moving mesh. Remeshing may produce connectivity and topology changes: the main feature of our family of schemes is the capability of maintaining the high order of accuracy also in these situations. We achieve this result by a high order integration of the space-time conservation formulation of the governing hyperbolic PDE system not only over the extruded Voronoi elements, as in standard direct ALE schemes, but also over the sliver elements we build to fill the space–time holes originated where topology changes occur. This kind of schemes guarantee Galilean and rotational invariance and allow to better track contact discontinuities and moving material interfaces, thus they result very useful in multi-material applications and for the study of super/hyper-sonic objects in aerodynamics and astrophysics. In addition, astrophysical phenomena are characterized by the joint evolution of matter and spacetime which can be described by complex first order hyperbolic systems, like the Einstein field equations coupled with the general relativistic Euler equations. Here, in order to obtain stable and robust simulations, we have developed structure preserving schemes able to guarantee the exact preservation, up to machine precision, of equilibria and involution constraints. We will show some preliminary results for the simulation of neutron stars and accretion disks.
Per informazioni, rivolgersi a: giuseppe.visconti@uniroma1.it
Martedì 24 gennaio 2023
Ore 16:00, Aula D'Antoni, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Analisi Matematica
Paolo Roselli (Università di Roma "Tor Vergata")
Il paradosso del piano tangente e il rapporto incrementale vettoriale di un piano secante
La retta tangente il grafico di una funzione sufficientemente regolare è la posizione limite di rette secanti il grafico. Ci si aspetterebbe che il piano tangente il grafico di una funzione a due variabili sufficientemente regolare sia la posizione limite di piani secanti il grafico in tre punti non collineari (a,f(a)), (b,f(b)) e (c,f(c)), ma così non è. Questo fenomeno paradossale è una versione locale del paradosso dell'area di una superficie curva (detto anche paradosso di Schwarz). In questo seminario visualizzerò il fenomeno paradossale, e mostrerò come il "coefficiente angolare vettoriale" di un piano secante possa esprimersi sia come combinazione vettoriale delle normali esterne al triangolo di vertici a, b e c, sia come rapporto vettoriale incrementale, quando il prodotto vettoriale è quello geometrico di Clifford. Se rimarrà tempo, accennerò anche a come modificare tale rapporto incrementale vettoriale per renderlo sempre convergente al gradiente di f.
Per informazioni, rivolgersi a: molle@mat.uniroma2.it
Mercoledì 25 gennaio 2023
Ore 10:30, In presenza in aula 116 al primo piano di via dei Taurini 19 a Roma e in streaming sul canale youtube dell'IAC: https://www.youtube.com/watch?v=ocqMICHqLpk, Istituto per le Applicazioni del Calcolo - Cnr
Seminario introduttivo
Massimo Bernaschi (IAC-Cnr)
Introduzione al quantum computing: terza parte
Terzo appuntamento introduttivo sul tema del Quantum Computing
Per informazioni, rivolgersi a: massimo.bernaschi@cnr.it
Mercoledì 25 gennaio 2023
Ore 14:30, In presenza all'IAC in via dei Taurini 19 a Roma, aula seminari 116, primo piano, e sul Canale Youtube dell'IAC https://www.youtube.com/watch?v=CeNtG_bzEeQ, Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche
Seminari Generali IAC 2023
Adriano Tiribocchi (Istituto per le Applicazioni del Calcolo “Mauro Picone” - Cnr)
Modeling the collective properties of multi-core emulsions under confinement
Multi-core emulsions are a class of soft fluids assembled from cluster configurations of deformable oil-water double droplets (cores), often employed as building-blocks for the realisation of devices of interest in biotechnology, drug delivery and tissue engineering. We use lattice Boltzmann simulations to study the physics of multi-core emulsions flowing in microfluidic channels and report numerical evidence of a surprisingly rich variety of driven non-equilibrium states, whose formation is caused by a dipolar fluid vortex triggered by the sheared structure of the flow carrier within the microchannel. If time permits, we will also discuss the translocation dynamics of emulsion drops with multiple close-packed inner droplets flowing within constrictions. Under such conditions, these liquid architectures display a number of non-trivial features, such as permanent shape deformations and memory-like effects, of particular relevance for the design of soft porous materials.
Per informazioni, rivolgersi a: maya.briani@cnr.it
Mercoledì 25 gennaio 2023
Ore 16:00, Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
seminario
Roberto Conti (Sapienza University of Rome)
Heat properties for groups
Somewhat motivated by the original approach of J.-B. Fourier to solve the heat equation on a bounded domain, we formulate some new properties of countable discrete groups involving certain completely positive multipliers of the reduced group C*-algebra and norm-convergence of Fourier series. The stronger "heat property" implies the Haagerup property, while the "weak heat property" is satisfied by a much larger class of groups. Examples will be provided to illustrate the various aspects. In perspective, a challenging goal would be to obtain yet another characterization of groups with Kazhdan's property (T). (Based on joint work with E. Bédos.)
Mercoledì 25 gennaio 2023
Ore 16:00, sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Corentin Le Bihan (ENS, Lyon)
Dynamical correlation of the Gibbs measure of a gas in a low density scaling
We consider a gas of \(N\) particles in a box of dimension 3, interacting pairwise with a potential \(\alpha V(r/\varepsilon)\). We want to understand the behavior of the system in the limit \(N\to\infty\), with a suitable scaling for \(\alpha\) and \(\varepsilon\). If we choose \(\varepsilon=1\), \(\alpha=1/N\), it is the mean field limit: particles interact weakly at long distance. We are interested in the low density limit \(\varepsilon = N-1/2\), \(\alpha=1\). Then the distance crossed by a particle is constant. This limit is well understood since the work of Lanford: the empirical law of the system converges to a solution of the Boltzmann equation. It is a kind of Law of Large Numbers. Sadly this convergence occurs only for a short time. In order to go to longer times, we study the fluctuations around the equilibrium, which follow a linearized version of the Boltzmann equation. The talk will present the idea of the proof of Bodineau, Gallagher, Saint Raymond and Simonella for hard sphere potentials and the idea of an improvement in case of realistic interaction potentials.
Giovedì 26 gennaio 2023
Ore 14:00, aula H, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Storia della Matematica
Benedetto Scoppola (Università di Roma Tor Vergata)
Aritmetica Euclidea e Filosofia Stoica
Si mostra come il problema dell'irrazionalità delle radici n-esime dei numeri interi fosse risolto negli Elementi di Euclide, e che probabilmente questo risultato è legato all'interazione tra Euclide e i logici che lo hanno preceduto, specialmente Filone dialettico.
Giovedì 26 gennaio 2023
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
P(n)/N(p) : Problemi differenziali nonlineari/Nonlinear differential problems
Antonio Greco (Università di Cagliari)
Three problems on elliptic equations
In this talk I will informally report on three problems I have recently had the opportunity to work on in collaboration with L. Cadeddu (Cagliari), F. Gladiali (Sassari), B. Mebrate (Wollo, Ethiopia) and G. Viglialoro (Cagliari). Problem 1 arises from civil engineering and is modeled by an elliptic equation with a second-order boundary condition of Ventsel type. Problem 2 deals with the symmetries of solutions with low Morse index to a mixed problem in a cylindrical sector. Problem 3 is overdetermined by prescribing both a Dirichlet and a (non autonomous) Neumann boundary condition, and we prove that the domain of the problem (unknown at the beginning) must be radially symmetric for a solution to exist.
Per informazioni, rivolgersi a: galise@mat.uniroma1.it
Venerdì 27 gennaio 2023
Ore 11:00, Aula G, Dipartimento di Matematica, Università di Roma `La Sapienza'
Corso di Dottorato
Dario Trevisan
Mathematical aspects of quantum information theory
Per informazioni, rivolgersi a: bertini@mat.uniroma1.it
Venerdì 27 gennaio 2023
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario MoMA
Laura Palagi (Sapienza Università di Roma)
From black forests to interpretable trees: an overview and recent development on Optimal classification trees
In recent years there has been a growing attention to machine learning models which are able to give explanatory insights on the decisions made by the algorithm. Thanks to their interpretability, decision trees have been intensively studied for classification tasks, and, due to the remarkable advances in Mixed-Integer Programming (MIP), various approaches have been proposed to formulate the Optimal Classification Tree (OCT) problem as a MIP model starting from the seminal paper [Bertsimas D. and J. Dunn. "Optimal classification trees." Machine Learning 106.7 (2017)]. In this talk, we will make an overview on classification trees and random forests and on the optimal tree classification formulation. First, we present a novel formulation for binary classification using OCT and exploiting the generalization capabilities of another well know machine learning classifiers which are Support Vector Machines [Cortes C. , and V. Vapnik. "Support vector machine." Machine learning 20.3 (1995)]. In particular, the maximum MARGin Optimal Classification Tree (MARGOT) uses at each node of the decision tree a regularized Linear SVM to define a linear classifiers with maximum margin in a tree structure. The resulting model is a Mixed Integer Quadratic Programming problem. The model can also include feature selection constraints which allows to define a hierarchy on the subsets of features which mostly affect the outcome. We further present an OCT for approximating random forests with a single tree following a similar modelling approach. Numerical results on benchmark dataset are reported. Joint work with: Giulia Di Teodoro, Marta Monaci, Federico D'onofrio, Giorgio Grani
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