Direttore Vicario: Prof. Gabriele Grillo
Responsabile Gestionale: Dr.ssa Franca Di Censo

### Seminari

 Selezionare una sezione Tutte Algebra e Informatica Teorica Analisi Analisi Numerica Calcolo delle variazioni Dipartimento FDS Finanza Quantitativa Fisica Matematica Geometria Lezioni Leonardesche Matematica Discreta MOX Probabilità Quantistica Probabilità e Statistica Matematica Seminario Matematico e Fisico Seminari di Cultura Matematica Tomografia e Applicazioni Parola da cercare

### Seminari Passati

• Zero-dimensional symmetry, or locally profinite groups
George Willis, University of Newcastle, Australia
giovedì 21 novembre 2019 alle ore 16:00, Aula U5-3014 (Edificio 5, terzo piano) del Dipartimento di Matematica e Applicazioni dell'Università di Milano-Bicocca, in Via Cozzi 55
ABSTRACT
Automorphism groups of discrete structures such as graphs carry a totally disconnected topology: both the groups and the structures they act on are thus zero-dimensional. The group topology is often non-discrete, and it has been found in recent years that there is a strong interplay between the algebraic and topological properties of these groups.
Totally disconnected locally compact groups are, it turns out, locally profinite and have a rich structure theory which has parallels with the theory of Lie groups, although it is more complicated.
This theory is still being developed and, in addition to Lie theory, draws on results about finite groups and from geometric group theory.
Summarising progress so far, an analysis of the locally profinite structure of the groups corresponds to the local theory of Lie groups, and a canonical form for group elements corresponds to eigendecomposition in the Lie algebra of a Lie group. A decomposition theory separates the cases of discrete and profinite groups, which are treated as negligible, from cases which are not negligible such as simple Lie groups over $p$-adic or function fields and automorphism groups of regular trees.
The techniques developed have been applied so far to answer questions about ergodic theory, random walks and arithmetic groups.
• Geometrie non Euclidee e Teorie Fisiche
Marco Pedroni, Università di Bergamo
mercoledì 20 novembre 2019 alle ore 15:00, Sala Consiglio - piano 7° - edificio 14
ABSTRACT
Dopo aver introdotto il concetto di geodetica su una superficie e aver brevemente discusso le geometrie non euclidee, si passerà a una descrizione della relatività (ristretta e generale). Lo scopo è quello di mostrare che in relatività generale avviene una fusione tra geometria e fisica: lo spazio non si può più concepire come un palcoscenico immutabile nel quale vengono poi introdotti i corpi, come nelle teorie classiche. In conclusione, se il tempo lo permetterà, si accennerà all'osservazione delle onde gravitazionali
• Construction and Validation of Subject-Specific Biventricular Finite-Element Models of Healthy and Failing Swine Hearts From High-Resolution Diffusion Tensor MRI
Julius Guccione, Surgery Division of Adult Cardiothoracic Surgery, University of California San Francisco (UCSF)
martedì 19 novembre 2019 alle ore 15:00, aula consiglio VII piano
ABSTRACT
What if physicians and surgeons could virtually analyze their patients’ health and plan therapies and surgeries using the same advanced modeling and simulation technology that the automotive, aerospace, energy and hi-tech industries rely on to test their product before they are built? As early as 1906, researchers first began suggesting the solution of continuum mechanics problems by modeling the body with a lattice of elastic bars and employing frame analysis methods. In 1941, Courant recognized piecewise polynomial interpolation over triangular subregions as a Rayleigh-Ritz solution of variational problems. Since there were no computers at the time, neither approach was practical and Courant’s work was largely forgotten until engineers had independently developed it. By 1953, structural engineers were solving matrix stiffness equations with digital computers. The widespread use of finite element methods in engineering began with the classic papers by Turner et al. and Argyris and Kelsey. The name “finite element” was coined in 1960, and the method began to be recognized as mathematically rigorous by 1963. The creation of subject-specific biventricular finite element models has been a long-term endeavor within the biomedical engineering community. Using high resolution (0.3 × 0.3 × 0.8 mm) ex-vivo data, we constructed precise fully subject-specific biventricular finite-element models of healthy and failing swine hearts. Each model includes fully subject-specific geometries, myofiber architecture and, in the case of the failing heart, fibrotic tissue distribution. Each model was calibrated using subject-specific experimental data and compared with independent in-vivo strain data obtained from echocardiography. Our methods produced highly detailed representations of swine hearts that function mechanically in a remarkably similar manner to the in-vivo subject-specific strains on a global and regional comparison. The degree of subject-specificity included in the models represents a milestone for modeling efforts that captures realism of the whole heart. This study establishes a foundation for future computational studies that can apply these validated methods to advance cardiac mechanics research.

Contatto: alfio.quarteroni@polimi.it

This seminar is organized within the ERC-2016-ADG Research project iHEART - An Integrated Heart Model for
the simulation of the cardiac function, that has received funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 740132)

• La retromarcia in Matematica: invertire formule, funzioni, operatori
Anna Salvadori, Primo Brandi, Università di Perugia
mercoledì 13 novembre 2019 alle ore 15:00, Sala Consiglio - piano 7° - edificio 14
ABSTRACT
Scopo dell’intervento è presentare il percorso didattico innovativo, in continuità fra vari ordini scolastici, sul tema dell’invertibilità. Partendo dalle formule inverse delle funzioni elementari, l’argomento sottende la soluzione delle equazioni elementari ed è la chiave per affrontare i modelli differenziali.
Il tema sarà trattato in interazione dinamica fra Realtà e Matematica.

Nota: questo seminario sarà una lezione-laboratorio e avrà durata un’ora e mezzo.
• On the highly compressible limit for the Navier-Stokes-Korteweg model with density dependent viscosity
Matteo Caggio, Università degli Studi dell'Aquila
martedì 12 novembre 2019 alle ore 14:30, Aula seminari 3° piano
ABSTRACT
We investigate the regime of high Mach number flows for compressible barotropic fluids with density dependent viscosity. The Korteweg model as an isothermal model of capillary and quantum compressible fluids is considered. A weak-strong uniqueness analysis is also discussed.
• Sharp concentration estimates near criticality for sign-changing solutions of Dirichlet and Neumann problems
martedì 12 novembre 2019 alle ore 15:30, Aula seminari 3° piano
ABSTRACT
Consider the slightly subcritical problem $-\Delta u_\varepsilon = |u_\varepsilon|^{\frac{4}{n-2}-\varepsilon}u_\varepsilon$ either on $\mathbb{R}^n$ ($n\geq 3$) or in a ball $B$ satisfying Dirichlet or Neumann boundary conditions. For radial solutions, we provide sharp rates and constants describing the asymptotic behavior (as $\varepsilon\to 0$) of all local minima and maxima of $u_\varepsilon$ as well as its derivative at roots. As corollaries, we complement a known asymptotic approximation of the Dirichlet nodal solution in terms of a tower of bubbles and present a similar formula for the Neumann problem.
Moreover, we analyse the nonradial case with Neumann boundary conditions, namely the existence of least energy solutions and their dependence on the exponent $p$ up to the Sobolev critical exponent.
These are joint works with Alberto Saldaña and Massimo Grossi.
• Quantum Hydrodynamics: physical models and mathematical theory
Piero Marcati, DISIM, Università de L' Aquila & Gran Sasso Science Institute (GSSI)
lunedì 4 novembre 2019 alle ore 14:15, aula Saleri VI piano
ABSTRACT
: The first part of the talk will provide a self-contained introduction to the formal deduction of the quantum hydrodynamics (QHD) in the form of an Euler Dispersive Irrotational compressible fluid system.
We will then introduce in a possible simple way the a macroscopic approach to various related to superfluids due to the Russian school by Landau, Khalaktikov and other important models in superconductivity and semiconductor devices.
Then we show important mathematical difficulties related to the presence of vacuum and explain their physical counterpart, even in relation with quantum vortices and Bose Einstein condensation. We also will relate our analysis to the Gross-Pitaevskii model.
We will show how to develop a mathematical theory in 2-D and 3-D, consistent with the physics for the problem of large data weak solutions, in the energy norm. All the theory, including irrotationality, is formulated by using observable quantities (density and linear momentum), avoiding the need of defining the velocity fields. The methods are based on a ad hoc" polar factorization, dispersive analysis and local smoothing. The initial data are restricted to be momenta of a wave funtiona.
It has been recently developed a large data 1-D theory purely hydrodynamical of weal solutions with strong stability.
In conclusion we will just mention several other related problems connected to quantum vortices, dispersive shocks and the presence of magnetic fields.

Contatto: paola.antonietti@polimi.it

• Maths goes social: usare i meme per fare matematica in classe
Giulia Bini, Università degli Studi di Torino
mercoledì 30 ottobre 2019 alle ore 15:00, Sala Consiglio - piano 7° - edificio 14 - via Ponzio 31/p
ABSTRACT
Questo seminario vuole condividere i primi risultati di un lavoro di ricerca sui significati e i possibili usi didattici dei meme matematici. I meme sono oggetti digitali – tipicamente di natura umoristica – creati dagli utenti e condivisi in modo virale nel web: essi vengono dal pianeta social, ma recenti ricerche mostrano che possano dare un contributo alla didattica della matematica, facendo leva su ciò che gli studenti conoscono. Nel seminario sarà prima proposto un costrutto teorico per identificare gli elementi che compongono il sistema di significati veicolati da un meme e verranno condivisi esempi ed esperienze didattiche.