Dipartimento di Matematica e Informatica

Seminario di Analisi: Trasformata di Wigner, utilizzo in analisi tempo-frequenza e applicazioni alle equazioni differenziali (Oliaro)

Foschi Damiano — 2014-11-18T18:42:07Z

Cari colleghi,

il giorno lunedi 24 novembre 2014 alle ore 11.30
il Dott. Alessandro Oliaro terrà in aula 3 un seminario dal titolo:

"Trasformata di Wigner: utilizzo in analisi tempo-frequenza
e applicazioni alle equazioni differenziali"

Si tratta di un seminario introduttivo sulla trasformata di Wigner, sieti quindi tutti caldamente invitati a partecipare.

Cordialmente,
Chiara Boiti

seminario di Algebra: The Homology of Graded (Co)rings (Stefan)

Foschi Damiano — 2014-11-10T11:26:56Z

Il Prof. Dragos STEFAN dell'Università di Bucarest (Romania) sarà ospite del nostro Dipartimento dal 17 Novembre al 23 Novembre 2014. In tale periodo il Prof. Stefan terrà un ciclo di seminari su "On the (co)homology of graded (co)rings".

Il primo seminario avrà luogo Martedì 18 novembre alle ore 16 in aula 1. Seguono titolo e Abstract.

1. The Homology of Graded (Co)rings

We shall review the basic properties of Ext and Tor functors of a graded R-ring, where R denotes a semisimple ring. A key tool in our investigation will be played by the bar resolution of R. The dual case, corresponding to a graded $R$-coring, will also be discussed.

Il secondo seminario avrà luogo Giovedì 20 novembre alle ore 16 in aula 2. Seguono titolo e Abstract.

2. Koszul (co)rings.

Koszul rings were introduced by Beilinson, Ginzburg and Soergel, as natural generalization of Koszul algebras, which play a fundamental role in Representation Theory. Our aim is to present the most important properties of this class of rings, using a new method which based on the so called Koszul pairs. By duality, Koszul corings are introduced and investigated. Several examples and applications will be presented.

Tutti gli interessati sono invitati a partecipare.

Si sottolinea inoltre che Il Prof. Stefan, durante il suo periodo di visita al Dipartimento, sarà disponibile ad interagire scientificamente con tutti gli interessati.

Claudia Menini

Categorical representability and rationality - Marcello Bernadara (Tolosa)

Stumbo Fabio — 2016-02-29T14:59:29Z

This talk is aimed at introducing the notion of categorical representability and some examples and motivations that let us conjecture it to provide an obstruction to rationality.

In particular, we will focus on some motivic motivation and on birational properties of geometrically rational surfaces, which were studied in a joint work with A.Auel.

We will end by considering some threefold and fourfold examples under this perspective.

Seminario di Algebra: Lifting via cocycle deformation (Agustín García Iglesias)

Ferrari Michele — 2014-02-20T11:02:06Z

Lifting via cocycle deformation

Agustín García Iglesias (Universidad Nacional de Córdoba, Argentina)

Abstract: We develop a strategy to compute all liftings of a Nichols
algebra over a finite dimensional cosemisimple Hopf algebra. We produce
them as cocycle deformations of the bosonization of these two. The
process also produces new examples of (infinite dimensional) Hopf
algebras, as well as bi-Galois objects associated to bosonizations of
(pre-)Nichols algebras and their liftings.

Seminario di Algebra: Doubly transitive groups and quandles (Leandro Vendramin)

Ferrari Michele — 2014-02-20T10:57:37Z

Doubly transitive groups and quandles

Leandro Vendramin (Universidad de Buenos Aires, Argentina)

Abstract: We prove that for n>2 there exists a quandle of cyclic type of size n
if and only if n is a power of a prime number. This establishes a
conjecture of S. Kamada, H. Tamaru and K. Wada. As a corollary, every
finite quandle of cyclic type is an Alexander quandle. We also prove
that finite doubly transitive quandles are of cyclic type. This
establishes a conjecture of H. Tamaru.

Mathematical and numerical analysis of non-standard mathematical models for flow in porous media -- Iuliu Sorin Pop (Hasselt University)

Brasco Lorenzo — 2019-01-08T15:50:13Z

Commonly used models for flow in porous media assume that quantities like saturation, phase pressure differences, or relative permeability are related by monotone, algebraic relationships. These relationships are determined experimentally, assuming that the involved quantities have reached a local equilibrium. Under such assumptions, the solutions of the resulting mathematical models have properties like stability in various norms, and satisfy the maximum principle. In particular, such standard models rule out effects like saturation overshoot or the formation of finger profiles, which have been evidenced experimentally. This contradiction is the main motivation when considering non-standard models, where dynamic effects and hysteresis are included in the above mentioned relationships. The resulting models are nonlinear evolution systems of (pseudo-)parabolic and possibly degenerate equations, and may involve differential inclusions. In this contribution we discuss the behaviour of the solutions to such models based on the travelling wave analysis, and analyze different numerical schemes (multipoint flux approximation, discontinuous Galerkin) for approximating the solutions. In particular, we present the rigorous convergence analysis of the numerical solution to the weak solution of the model. Also, we analyze different linear iterative methods for approximating the numerical solution to the nonlinear, fully discrete problems encountered at each time step.

Joint work with C.J. van Duijn, K. Mitra (Eindhoven University of Technology), X. Cao (York University), S. Karpinski (ESPRiT Engineering GmbH), F.A. Radu (University of Bergen), S. Lunowa (Hasselt University).

One dimensional optimal reinforcements of elastic structures - Giuseppe Buttazzo (Pisa)

Stumbo Fabio — 2018-01-25T10:58:46Z

Il problema che si intende studiare è quello del rinforzo di una membrana elastica, fissata al bordo, mediante una struttura unidimensionale. Il risultato principale è l'esistenza di un rinforzo ottimo nella classe degli insiemi unidimensionali connessi di lunghezza totale prefissata. La struttura ottima può presentare zone di molteplicità, cioè in cui possono esserci sovrapposizioni. Questo viene mostrato anche da alcune simulazioni numeriche, che illustrano la crescente complessità delle strutture ottime al crescere della lunghezza totale.

Lagrangian numerical schemes for continuum mechanics

Rizzati Michele — 2020-11-09T08:12:14Z

The behavior of a continuum is mathematically described by systems of nonlinear hyperbolic partial differential equations (PDE). Both fluids and solids are modelled by balance laws which are based on first physical principles like conservation of mass, momentum and total energy. A wide range of applications are involved in continuum mechanics, such as environmental and meteorological flows, hydrodynamic and thermodynamic problems, plasma flows as well as the dynamics of many industrial and mechanical processes, namely high energetic interactions of metals involving fluidization, melting and solidification in metallurgy, complex flows like granular flows and flows of viscoplastic fluids (yield stress fluids), which exhibit properties of both elastic solids and viscous fluids. The numerical solution of the discrete governing equations constitutes nowadays a challenging task, thus being a very active research field in the context of applied mathematics. Lagrangian algorithms, in which the computational mesh moves with the material velocity, have become very popular in the last decades due to the excellent properties achieved by these numerical methods in the resolution of moving material interfaces and contact waves. Since the computational mesh is moving with the local fluid velocity, Lagrangian methods are typically affected by much less numerical dissipation compared to classical Eulerian approaches on fixed grids, hence obtaining a more accurate approximation of the solution.
This series of lectures aims at introducing the governing equations for continuum mechanics and at providing an overview of the state-of-the-art numerical methods for the numerical solution of the PDE in the Lagrangian framework.

Date
1st – 3rd December 2020.
Venue
Online seminar on Google Meet platform.
Registration and contacts
Please register by email to walter.boscheri@unife.it before 15th November 2020.
Note
PhD students will be granted 1 CFU for attending the entire series of lectures.

Program
1st December, 9:00 – 11:00 am
Governing equations and models for continuum mechanics Ilya Peshkov
2nd December, 9:00 – 11:00 am
Lagrangian and ALE numerical methods. Raphaël Loubère
3rd December, 9:00 – 11:00 am
ALE and structure-preserving numerical schemes for fluids and solids. Walter Boscheri

Locandina

The story of a fish in a turbulent ocean: how to survive and how to return home - Eugene Stepanov (San Pietroburgo)

Stumbo Fabio — 2018-01-12T11:50:07Z

Abstract:

Can a fish with limited velocity capabilities reach any point in the (possibly unbounded) ocean? In a recent paper by D. Burago, S. Ivanov and A. Novikov, "A survival guide for feeble fish", an affirmative answer has been given under the condition that the fluid velocity field is incompressible, bounded and has vanishing mean drift. This brilliant result extends some known point-to-point global controllability theorems though being substantially non constructive. We will give a fish a different recipe of how to survive in a turbulent ocean, and show how this is related to structural stability of dynamical systems by providing a constructive way to change slightly a divergence free vector field with vanishing mean drift to produce a non dissipative dynamics. This immediately leads to closing lemmas for dynamical systems, in particular to C. Pugh's closing lemma, saying also that the fish can eventually return home.
Joint work with Sergey Kryzhevich (Nova Gorica and St. Petersburg).

Convegno "Matematica e Storia" nel Liceo Matematico

Rizzati Michele — 2020-12-09T20:25:00Z

Il convegno su “Matematica e Storia” è uno dei convegni tematici del progetto “Liceo Matematico”, che secondo le linee guida del progetto, presenta temi interdisciplinari tra matematica e storia, per tutti i cicli di istruzione, rivolti agli insegnanti di scuola e ai ricercatori in didattica e storia della matematica ( https://www.liceomatematico.it/ ). Questa edizione del convegno ha un focus particolare sulle applicazioni della matematica.

Organizzato dal Dipartimento di Matematica e Informatica dell’Università di Ferrara, in collaborazione con il Dipartimento di Matematica di Salerno, si svolge nelle giornate del 10 e 11 dicembre 2020 in modalità telematica, e si articola in conferenze e in laboratori.

Comitato scientifico: Maria Teresa Borgato, Alessandra Fiocca, Emilia Florio Erika Luciano, Francesco Saverio Tortoriello.

Comitato organizzatore: Maria Teresa Borgato, Maria Giulia Lugaresi, Elisa Patergnani.,

Locandina e il programma del convegno.

Per iscriversi bisogna compilare l’apposito modulo di Google reperibile al seguente link:

https://docs.google.com/forms/d/1h90yeUYFbSzEcc77QWEwZdQUJZvTiJJkk820deB83Iw/edit

Successivamente verrà inviata una mail con il link per accedere all'aula virtuale di Google Meet.

Link per partecipare all'evento in live streaming:

https://stream.meet.google.com/stream/6a8157e2-e448-49a4-a57c-7466074cc1eb

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).