Dipartimento di Matematica e Informatica

Alcuni Spunti di Matematica Pura per l'Orientamento Nelle Scuole Superiori

Rizzati Michele — 2020-11-18T11:43:10Z

Il seminario nasce da un'esperienza personale dello studente Matteo Misurati, il quale si è dedicato ad attività di orientamento nelle classi terminali della scuola secondaria ed ha osservato che spesso in tali attività si tende a dare esempi di matematica applicata per coinvolgere maggiormente gli studenti. Questo però non soddisfa coloro che, come lui, amano la matematica pura. Da qui il desiderio di strutturare un breve percorso che possa essere utilizzato da chiunque per presentare la bellezza della matematica pura.

Siete tutti invitati a partecipare, questo il link di Meet dal quale sarà possibile seguire il seminario.

meet.google.com/tga-cktm-pgx

Alcuni risultati di statica e dinamica per sistemi elasticamente accoppiati di tipo trave-trave e cavo-trave - Claudio Giorgi (Università di Brescia)

Stumbo Fabio — 2018-10-30T09:15:55Z

Abstract:

Si presenteranno risultati di esistenza dell’attrattore globale per la dinamica asintotica di sistemi meccanici dissipativi costituiti da due travi elastiche estensibili (secondo il modello non lineare di Woinowski-Krieger) o da una trave di W-K ed un cavo (corda vibrante) quando l’accoppiamento elastico è lineare e distribuito lungo la loro lunghezza. Oltre ad un’analisi completa delle soluzioni stazionarie nei due problemi, si evidenzia che per particolari valori dei parametri elastici strutturali sorgono fenomeni di risonanza associati a infinite soluzioni statiche con due o tre modi fondamentali sovrapposti

Seminario di Geometria Algebrica: Mori Dream Spaces obtained by blowing-up points in projective spaces (Massarenti)

Foschi Damiano — 2014-12-11T16:44:45Z

speaker: Alex Massarenti (IMPA, Rio de Janeiro)

title: Mori Dream Spaces obtained by blowing-up points in projective spaces.

abstract:

The goal of the minimal model program is to construct a birational model of any complex projective variety which is as simple as possible in a suitable sense. This subject has its origins in the classical birational geometry of surfaces studied by the Italian school. In 1988 S. Mori extended the concept of minimal model to 3-folds by allowing suitable singularities on them. In 2010 there was a great breakthrough in the minimal model theory when C. Birkar, P. Cascini, C. Hacon and J. McKernan proved the existence of minimal models for varieties of log general type.

Mori Dream Spaces, introduced by Y. Hu and S. Keel in 2002, form a class of algebraic varieties that behave very well from the point of view of Mori's minimal model program. They can be algebraically characterized as varieties whose total coordinate ring, called the Cox ring, is finitely generated.

In addition to this algebraic characterization there are several algebraic varieties characterized by some positivity property of the anti-canonical divisor, such as weak Fano and log Fano varieties, that tourn out to be Mori Dream Spaces. In this talk, I will show how to obtain log Fano varieties and Mori Dream Spaces by blowing-up projective spaces in a certain number of general points.

Theory and applications of shearlets - Demetrio Labate (University of Houston - Texas)

Stumbo Fabio — 2015-11-24T11:23:18Z

Theory and applications of shearlets - Demetrio Labate (University of Houston - Texas)

Abstract

Several advanced multiscale representations, most notably curvelets and shearlets, were introduced during the last decade to overcome known limitations of wavelets and other traditional methods. In fact, even though wavelets are very efficient to handle signals with point singularities, they are suboptimal when dealing with edges and those distributed singularities which typically dominate multidimensional data. Shearlets, in particular, are specially designed to combine the power of multiscale analysis with ability to handle directional information efficiently. As a result, they offer very useful microlocal properties and optimally efficient representations, in a precise sense, for a large class of multivariate functions.
In this talk, I will illustrate the construction of shearlet frames and give a brief overview of their sparse approximation properties. Next, I will present and discuss several results illustrating the unique ability of the shearlet transform to provide a precise geometric characterization of singularities. These properties provide the theoretical underpinning for several state-of-the-art applications from signal processing and inverse problems, including data restoration, edge detection and feature extraction.

Il seminario, pur di ambito applicativo, include argomenti trasversali di analisi armonica e teoria dell'approssimazione.

Elliptic threefolds - Singularities and non-Kodaira fibres -- Andrea Cattaneo (Università di Parma)

Stumbo Fabio — 2016-01-04T16:44:52Z

Abstract.

Kodaira's classification of the singular fibres in an elliptic surface no
longer applies in the case of elliptic threefolds or higher dimensional
elliptic fibrations. In fact, the classification problem of the singular
fibres for a general elliptic fibration is sill open.

In this talk, we want to study the case of threefolds in detail: after
making some examples of non-Kodaira fibres, we will focus on the link
between the fibration and its Weierstrass model and, using some
singularity theory, we will prove a structure result for non-Kodaira
fibres for a class of elliptic threefolds which is much considered in the
applications.

Finally, we will briefly discuss some aspects concerning this
classification problem in general and how it is possible to extend the
previous results (this is still a work in progress).

Seminario di Analisi Matematica - Non occurrence of the Lavrentiev gap for multidimensional autonomous problems

Rizzati Michele — 2022-02-24T09:59:44Z

NON OCCURRENCE OF THE LAVRENTIEV GAP FOR
MULTIDIMENSIONAL AUTONOMOUS PROBLEMS

PIERRE BOUSQUET

We establish that the Lavrentiev phenomenon does not occur for autonomous

problems in the multiple integrals Calculus of Variations, provided that the inte-
grand is convex with respect to the gradient variable. The main novelty is that

no other (artificial) restriction is assumed on the integrand or on the domain. The
core of the proof is based on a new approximation result for a parametric version
of the variational problem.

CalVaFer - Calculus of Variations in Ferrara

Brasco Lorenzo — 2024-03-05T08:24:54Z

List of Speakers:

- Veronica Felli (Milano Bicocca)

- Giuseppe Mingione (Parma)

- Alessandra Pluda (Pisa)

- Berardo Ruffini (Bologna)

- Firoj Sk (Oldenburg)

- Giorgio Tortone (Pisa)

Per maggiori informazioni potete consultare https://sites.google.com/unife.it/calvafer/home-page

Tutti gli interessati sono i benvenuti a partecipare, previa registrazione on-line all'indirizzo sopra indicato.

Dimension Lifting for Quantum Computation of partial differential equations and related problems

Rizzati Michele — 2024-03-05T08:18:58Z

Giovedì 7 marzo 2024, ore 16.30

Aula C1 (Palazzo Manfredini)

Shi Jin (Shangai Jiao Tong University)

"Dimension Lifting for Quantum Computation of partial differential equations and related problems"

Abstract

Quantum computers have the potential to gain algebraic and even up to exponential speed up compared with its classical counterparts, and can lead to technology revolution in the 21st century. Since quantum computers are designed based on quantum mechanics principle, they are most suitable to solve the Schrodinger equation, and linear PDEs (and ODEs) evolved by unitary operators. The most efficient quantum PDE solver is quantum simulation based on solving the Schrodinger equation. It will be interesting to explore what other problems in scientific computing, such as ODEs, PDEs, and linear algebra that arise in both classical and quantum systems, can be handled by quantum simulation.
We will present a systematic way to develop quantum simulation algorithms for general differential equations. Our basic framework is dimension lifting, that transfers nonlinear PDEs to linear ones, and linear ones to Schrodinger type PDEs. For non-autonomous PDEs and ODEs, or Hamiltonian systems with time-dependent Hamiltonians, we also add an extra dimension to transform them into autonomous PDEs that have only time-independent coefficients, thus quantum simulations can be done without using the cumbersome Dyson’s series and time-ordering operators. Our formulation allows both qubit and qumode (continuous-variable) formulations, and their hybridizations, and provides the foundation for analog quantum computing.

Biography
Prof. Shi Jin is the Director of Institute of Natural Sciences, and Chair Professor of Mathematics, at Shanghai Jiao Tong University. He is also a co-director of the Shanghai Center of Applied Mathematics. He was department chair and Vilas Distinguished Achievement Professor at University of WisconsinMadison, Chair of Department of Mathematics at Shanghai Jiao Tong University. He received a Feng Kang Prize of Scientific Computing in 2001 and a Morningside Silver Medal of Mathematics at the International Congress of Chinese Mathematicians in 2007. He is an inaugural Fellow of the American Mathematical Society (AMS) (2012), a Fellow of Society of Industrial and Applied Mathematics (SIAM) (2013), an inaugural Fellow of the China Society for Industrial and Applied Mathematics (CSIAM) (2020), and an Invited Speaker at the International Congress of Mathematicians (ICM) in 2018.

Come gli animali usano la matematica - A. Foà (Università di Ferrara)

Stumbo Fabio — 2020-01-15T10:41:09Z

Seminario Mathesis

Smoluchowski equation in perforamed domains: Homogenization and applications to mathematical models in medicine - Silvia Lorenzani (Politecnico di Milano)

Stumbo Fabio — 2018-11-20T08:13:22Z

Abstract:

In recent years, the Smoluchowski equation has been considered in biomedical research to model the aggregation and diffusion of beta-amyloid peptide in the cerebral tissue, a process thought to be associated with the development of Alzheimer's disease. In this work, we study the homogenization of a Smoluchowski system of discrete diffusion-coagulation equations with non-homogeneous Neumann boundary conditions, defined in a periodically perforated domain through a two scale convergence technique.

Sharp Quantitative Isocapacitary Inequality -- Ekaterina Mukoseeva (SISSA)

Brasco Lorenzo — 2019-03-26T14:58:56Z

Seminario di: Analisi Matematica

Proprietà dei minimi e continuità del costo per il problema di trasporto ottimo con molte marginali e costo Coulombiano.

Rizzati Michele — 2016-11-22T13:15:40Z

Introdurrò il problema di trasporto ottimo con molte marginali e costo repulsivo Coulombiano. Dopo aver presentato alcune motivazioni per lo studio di tale problema,
passerò all'analisi delle proprietà elementari dei minimi. Le proprietà dei minimi verranno poi utilizzate per studiare la continuità del costo.
(Lavoro in collaborazione con G. Buttazzo e T.Champion).

The infinite dimensional Gaussian random matching problem - Dario Trevisan (Università di Pisa)

Brasco Lorenzo — 2018-12-11T12:20:52Z

Abstract: The random matching problem consists of estimating the expected value of a transportation cost between the (random) empirical measure of independent identically distributed random variables, and their the common law, finding in particular asymptotic rates when the number of variables becomes large. Using a random PDE approach, M. Ledoux recently provided upper and lower bounds for the Wasserstein-Kantorovich cost in the case of standard Gaussian random variables, in any (but finite) dimension. In this seminar we will illustrate how a similar technique leads to some results in the infinite dimensional Gaussian setting, with applications e.g. the problem of matching samples of Brownian paths to the Wiener measure.

Seminario di Geometria: Anticanonical models and maps of Fano type varieties (Park)

Foschi Damiano — 2014-12-01T18:34:20Z

Il Dott. Jinhyung Park del KIAS (Seul) sara` ospite del nostro Dipartimento nel periodo 9-16 Dicembre.

L'invitato terra` due seminari:

Primo seminario, Martedi 9 Dicembre, ore 15.30-16.30, aula 1.

Geometric properties of projective manifolds of small degree

Secondo seminario, Giovedi 11 Dicembre, ore 11-12, aula 1.

Anticanonical models and maps of Fano type varieties

Abstract: The purpose of this talk is to present a generalization of Sakai’s work on anticanonical models of rational surfaces to varieties of Fano type. We first show a characterization of Fano type varieties using the singularities of anticanonical models. Secondly, we study the decomposition of the anticanonical map using the minimal model program. This is joint work with Dong Seon Hwang and Sung Rak Choi.

Tutti gli interessati sono invitati a partecipare.

Paltin Ionescu

Presentazione del Dipartimento di Matematica e Informatica

Rizzati Michele — 2022-11-28T10:53:26Z

Questa presentazione vuole inquadrare per gli studenti ma anche per i visitatori esterni alcuni dati e performance per chi vuole conoscere più da vicino cosa si studia e quali sono le attività scientifiche dei nostri docenti e ricercatori.

Per visionare la presentazione clicca qui (rimando alla pagina: http://www.dmi.unife.it/it/organizzazione/presentazione)

Dipartimento di Matematica e Informatica

Alcuni Spunti di Matematica Pura per l'Orientamento Nelle Scuole Superiori

Alcuni risultati di statica e dinamica per sistemi elasticamente accoppiati di tipo trave-trave e cavo-trave - Claudio Giorgi (Università di Brescia)

Seminario di Geometria Algebrica: Mori Dream Spaces obtained by blowing-up points in projective spaces (Massarenti)

Theory and applications of shearlets - Demetrio Labate (University of Houston - Texas)

Elliptic threefolds - Singularities and non-Kodaira fibres -- Andrea Cattaneo (Università di Parma)

Seminario di Analisi Matematica - Non occurrence of the Lavrentiev gap for multidimensional autonomous problems

NON OCCURRENCE OF THE LAVRENTIEV GAP FORMULTIDIMENSIONAL AUTONOMOUS PROBLEMSPIERRE BOUSQUET

CalVaFer - Calculus of Variations in Ferrara

Dimension Lifting for Quantum Computation of partial differential equations and related problems

Come gli animali usano la matematica - A. Foà (Università di Ferrara)

Smoluchowski equation in perforamed domains: Homogenization and applications to mathematical models in medicine - Silvia Lorenzani (Politecnico di Milano)

Sharp Quantitative Isocapacitary Inequality -- Ekaterina Mukoseeva (SISSA)

Proprietà dei minimi e continuità del costo per il problema di trasporto ottimo con molte marginali e costo Coulombiano.

The infinite dimensional Gaussian random matching problem - Dario Trevisan (Università di Pisa)

Seminario di Geometria: Anticanonical models and maps of Fano type varieties (Park)

Presentazione del Dipartimento di Matematica e Informatica

NON OCCURRENCE OF THE LAVRENTIEV GAP FOR
MULTIDIMENSIONAL AUTONOMOUS PROBLEMS

PIERRE BOUSQUET