Dipartimento di Matematica e Informatica

Introduction to Complex Dynamics II | Prof. J.E.Fornaess (Throndheim University - Norway)

Rizzati Michele — 2020-11-27T09:19:36Z

The second seminar on Complex Dynamics, given by Prof. John Erik Fornaess (Throndheim University, Norway), and organized by Prof.ssa Cinzia Bisi.

on December 4th, 2020 at 5:00 pm

"Introduction to Complex Dynamics II"

To attend the seminar please go to the link:

meet.google.com/sry-dgqi-owb

Seminario di Geometria: Sul numero di modelli minimali di una threefold liscia

Rizzati Michele — 2015-02-26T14:33:29Z

Diletta Martinelli (Imperial College Londra)

Titolo: Sul numero di modelli minimali di una threefold liscia.

Abstract: Un'importante congettura afferma che il numero di modelli minimali di una varieta' complessa proiettiva sia finito modulo isomorfismi. Daro' una introduzione sulla congettura e sui risultati noti e parlero' di un work in progress sulla possibilita' di limitare il numero di modelli minimali di una threefold di tipo generale usando invarianti topologici.

Fractional operators: perimeters and related semilinear equations

Rizzati Michele — 2015-02-25T14:45:13Z

Diego PALLARA (Universita' del Salento)

"Fractional operators: perimeters and related semilinear equations”

Tutti gli interessati sono invitati a partecipare.

Scomposizioni e luoghi di Waring - Enrico Carlini (Politecnico di Torino)

Stumbo Fabio — 2016-01-26T08:59:09Z

SUNTO

Descrivere tutte le scomposizioni in forme di potenze di una forma F e' utile, interessante, ma difficile!

Le varieta' VSP(F) sono state introdotte allo scopo, ma sono spesso troppo astratte.

Esistono casi in cui riusciamo ad essere piu' espliciti, ad esempio se F e' una somma di forme in variabili disgiunte? La risposta e': spesso si, riusciamo, ma alrettanto spesso non riusciamo.

Riusciamo comunque a congetturare la risposta e introduciamo i luoghi di Waring che sono utili a raggiungere risultati intermedi.

Approximate current-vortex sheets near the onset of instability - Alessandro Morando (Università di Brescia)

Stumbo Fabio — 2017-11-14T11:31:05Z

Abstract:

This talk is concerned with the free boundary problem for 2D current-vortex sheets in ideal incompress-
ible magneto-hydrodynamics near the transition point between the linearized stability and instability. In
order to study the dynamics of the discontinuity near the onset of the instability, Hunter and Thoo [1]
have introduced an asymptotic quadratically nonlinear integro-di erential equation for the amplitude
of small perturbations of the planar discontinuity. We study such amplitude equation and prove its
nonlinear well-posedness under a stability condition given in terms of a longitudinal strain of the
fluid along the discontinuity. We first present the problem and discuss some known results about the stability
of current-vortex sheets; then we give some new results on the well-posedness of the Cauchy problem
associated to the amplitude equation.
This is a joint work with P. Secchi and P. Trebeschi.
[1]: Hunter, J. K. and Thoo, J. B., On the weakly nonlinear Kelvin-Helmholtz instability of tangential
discontinuities in MHD, J. Hyperbolic Di er. Equ., 8 (4), 2011, 691-726.

Modelli matematici di crescita e motilità cellulare - Luigi Preziosi (Politecnico di Torino)

Stumbo Fabio — 2016-03-07T11:09:46Z

Si è dimostrato ultimamente che le caratteristiche meccaniche della
cellula, del suo nucleo e dell'interazione con l'ambiente circostante
giocano un ruolo importante nella determinazione del comportamento e del
moto delle cellule in strutture fibrose reali e artificiali. Dal punto
di vista applicativo capire questo processo riveste una grande
importanza da una parte per descrivere il processo di diffusione di
metastasi tumorali e dall'altra per ottimizzare le metodologie di
crescita tissutale.
Dal punto di vista matematico, il problema può essere affrontato
utilizzando diversi modelli matematici, dalla scala microscopica
molecolare alla scala macroscopica tissutale. Anzi l'utilizzo di modelli
multiscala risulta essere una necessità intrinseca del problema
biomedico. Finalità del seminario è quindi quella di presentare diversi
modelli matematici sviluppati per descrivere i fenomeni di migrazione ed
aggregazione cellulare.

Piece-wise Constant Image Segmentation with a Deep Image Prior Approach

Rizzati Michele — 2024-05-16T08:54:49Z

La segmentazione di immagini è un tema di ricerca molto vivo in svariati ambiti di applicazione

(computer vision, image processing, medical imaging). Tale problema può essere formulato

attraverso la minimizzazione del funzionale di Mumford-Shah, uno degli approcci più utilizzati

in questo ambito. Negli anni recenti nuove tecniche sono state studiate, basate su approcci

di tipo Deep Learning. In questo seminario proponiano un approccio non supervisionato per la

segmentazione semantica basato sul framework Deep Image Prior: il funzionale di Mumford Shah

viene riparametrizzato attraverso i pesi di una rete convolutoria. I primi esperimenti, eseguiti su

immagini "naturali" e mediche mostrano come questo approccio fornisca risultati molto affidabili,

anche in presenza di rumore. Porremmo anche le basi per l'estensione al modello di Ambrosio-Tortorelli.

Tutti gli interessati sono invitati a partecipare.

On a degenerate problem in the Calculus of Variations - Pierre Bousquet (Università di Tolosa, FRANCIA)

Stumbo Fabio — 2016-05-20T16:30:05Z

Abstract : We present a scalar problem in the multiple integrals 
calculus of variations with a convex  Lagrangian which is neither smooth 
nor strictly convex. We describe the regularity of the solutions and we 
address the uniqueness problem. This is a  joint work with Guy Bouchitté 
and Cedric Galusinski.

Seminari di Analisi @ Unife - Wavefronts for degenerate diffusion-convection reaction equations

Rizzati Michele — 2021-04-26T09:46:21Z

Title: Wavefronts for degenerate diffusion-convection reaction equations

Abstract: We deal with wavefront solutions to a scalar parabolic equation in one spatial dimension.
The equation consists of a convective term, a reaction term (typically of monostable type) and
a vanishing diffusivity. Wavefronts are traveling waves whose profile is globally defined,
non-constant and monotone. The main topic of this talk concerns the existence of such solutions,
their regularity and related properties. In particular, about the regularity, it is highlighted the behaviour
where the diffusivity vanishes.
All results are based on joint work with Corli (Ferrara) and Malaguti (Modena and Reggio Emilia).

Giovedì 29 aprile 2021
Ore 16.00
Diego Berti (Università di Modena e Reggio Emilia)

Il seminario si terra’ in modalità’ telematica e il codice meet per collegarsi e’

https://meet.google.com/dif-qrmm-bgy

Seminario: On the root uncertainty principle

Ferrari Michele — 2016-10-03T09:18:01Z

Speaker: prof. Diogo Oliveira e Silva (Università di Bonn)

Title: On the root uncertainty principle.

Abstract:

This talk will focus on a recent result of Bourgain, Clozel and Kahane. One of its versions states that a real-valued function which equals its Fourier transform and vanishes at the origin necessarily has a root which is larger than c>0, where the best constant c satisfies 0.41

preprint: https://arxiv.org/abs/1602.03366

Transmission conditions arising by homogenisation of Neumann problems - Giovanni Franzina (Indam, Firenze)

Stumbo Fabio — 2018-05-09T15:07:46Z

Seminario di: Analisi Matematica

Descent cohomology - Bachi Mesablishvili (Razmadze Mathematical Institute of Tbilisi State University - Georgia)

Stumbo Fabio — 2016-07-01T11:28:24Z

We introduce and investigate descent cohomology of (co)monads

on arbitrary base category with coefficients in (co)algebras over the (co)monad.

Some homomorphisms between groups of birational transformations - Christian Urech (Univ. di Basilea)

Stumbo Fabio — 2016-07-01T11:24:28Z

To a projective variety X one can associate Bir(X), its group of birational transformations. In this talk we will look at the question, how one can embed Bir(P^n) into groups of birational transformations in higher dimensions.
In particular, I will describe geometrical properties of an example of an embedding of Bir(P^2) into Bir(P^5) by Gizatullin and I will give a classification of certain embeddings of Bir(P^n) into Bir(X), where X is a variety of dimension n+1.

Picard groups of moduli of curves and polarized K3 surfaces - Andrea Di Lorenzo

Stumbo Fabio — 2019-09-30T09:19:43Z

Abstract: The Picard group of a variety, i.e. the group of line bundles that live over it, is an interesting and much studied invariant in algebraic geometry. In particular, the Picard groups of moduli spaces of objects (e.g. smooth curves of fixed genus, quasi-polarized K3 surfaces of fixed degree) have been the subject of a large amount of research in the past thirty years.
In this talk, I will explain how techniques of equivariant intersection theory, applied to certain moduli spaces of complete intersections, can shed some light on two specific questions:
(1) Suppose that the base field has positive characteristic. Is the Picard group of the moduli stack of smooth curves of fixed genus freely generated by the Hodge line bundle?
(2) Do the Noether-Lefschetz elliptic divisors freely generate the integral Picard group of moduli stack of polarized K3 surfaces?
Time permitting, I will show how the same methods can be used in order to compute the classes of some geometrically meaningful divisors on these moduli spaces in terms of the generators of the Picard groups.

Equazioni e soluzioni nell’analisi ‘comune’ cartesiana e nella ‘nuova’ analisi leibniziana - Prof. Niccolò Guicciardini (Università di Bergamo)

Rizzati Michele — 2018-06-28T12:26:14Z

During the seventeenth century, the advent of what were known as the ‘common’ and the ‘new analyses’, changed the mathematical landscape of European mathematics in a deep way. The narrative which is widely accepted is that the seventeenth-century analyses (algebra and calculus), mostly due respectively to Descartes and Leibniz, promoted a transition from geometrical to symbolical methods, from Euclidean proportion theory to equations. It is this change that would have allowed the advent of a more abstract way of practicing mathematics, a way that culminated in the eighteenth century with the algebraic approach to calculus and mechanics promoted by Leonhard Euler and Joseph-Louis Lagrange. In this lecture, I will show that, contrary to the accepted narrative [1], for Descartes, Leibniz and their immediate followers, geometrical interpretation and mechanical constructions still played a crucial role. This is revealed by the way in which they handled equations and how they sought their solutions.

[1] One can read in Morris Kline’s influential, and still fundamental, textbook: ‘Whereas from Greek times until about 1600 geometry dominated mathematics and algebra was subordinate, after 1600 algebra became the basic mathematical subject; in this transposition of roles the calculus was the decisive factor’. Morris Kline, Mathematical Thought from Ancient to Modern Times, New York, Oxford University Press, 1972, p. 323.