Dipartimento di Matematica

Prossimi Seminari

Seminar
Vieta Formula, Distributions, and Lemniscate
Ahmed Sebbar, Chapman University
mercoledì 21 aprile 2021 alle ore 17:00
On line

ABSTRACT

ABSTRACT
We give two extensions of the classical Vieta (or Viète) formula.
The first extension leads to the classical Fabius function, an infinitely differentiable function that is nowhere analytic. The second extension discusses the corresponding formula for
the elliptic curves with complex multiplication $y^2=x^3 -Dx$, $y^2=x^3-D$.
Seminar
Machine Learning as an inverse problem
Ernesto De Vito, Università di Genova
lunedì 3 maggio 2021 alle ore 16:00
On line

ABSTRACT

ABSTRACT
The talk is devoted to a mathematical introduction to Machine Learning
from the point of view of inverse problems. In the presentation, we focus on
supervised learning problems in the framework of kernel methods.
Seminar
La delta di Dirac: storia di un mostro
Marco Bramanti , Politecnico di Milano
mercoledì 5 maggio 2021 alle ore 12:15
online: tiny.cc/fdsCM2021
Seminar
The DPG Method for Convection-Reaction Problems
Leszek Demkowicz, Oden Institute, The University of Texas at Austin
lunedì 10 maggio 2021 alle ore 17:00
On line

ABSTRACT

ABSTRACT
We present a progress report on the development of Discontinuous
Petrov-Galerkin methods for the convection-reaction problem in
context of time-stepping and space-time discretizations of Boltzmann
equations [1].
The work includes a complete analysis for both conforming (DPGc)
and non-nonconforming (DPGd) versions of the DPG method employing
either globally continuous or discontinuous piece-wise polynomials to
discretize the traces.
The results include construction of a local Fortin operator for
the case of constant convection and a global discrete stability
analysis for both DPGc and DPGd methods.
The theoretical findings are illustrated with numerous numerical
experiments in two space dimensions.

This is a joint work with Nathan Roberts from Sandia National Laboratories.

[1] L. Demkowicz, N. Roberts, ``The DPG Method for the
Convection–Reaction Problem Revisited'', submitted.
Seminar
The Schrödinger equation as inspiration of beautiful mathematics
Gigliola Staffilani , MIT Mathematics, Cambridge, MA, US
lunedì 10 maggio 2021 alle ore 16:00
online

ABSTRACT

ABSTRACT
In the last two decades great progress has been made in the study of dispersive and wave equations. Over the years the toolbox used in order to attack highly nontrivial problems related to these equations has developed to include a collection of techniques: Fourier and harmonic analysis, analytic number theory, math physics, dynamical systems, probability and symplectic geometry. In this talk I will introduce a variety of results using as model problem mainly the periodic 2D cubic nonlinear Schrodinger equation. I will start by giving
a physical derivation of the equation from a quantum many-particles
system, I will introduce periodic Strichartz estimates along with some remarkable connections to analytic number theory, I will move on the concept of energy transfer and its connection to dynamical systems, and I will end with some results on the derivation of a wave kinetic equation.
Seminar
"L'amor che move il sole e l'altre stelle". Il cielo nella Divina Commedia
Fabio Peri , Civico Planetario U. Hoepli di Milano
mercoledì 12 maggio 2021 alle ore 12:15
online: tiny.cc/fdsCM2021
Seminar
Design and Health
Stefano Capolongo , Politecnico di Milano
mercoledì 19 maggio 2021 alle ore 12:15
online: tiny.cc/fdsCM2021
Seminar
Fischer decomposition for massless field equations
Roman Lavicka, Charles University Prague
mercoledì 19 maggio 2021 alle ore 17:00
On line

ABSTRACT

ABSTRACT
Massless field equations are fundamental in particle physics. In Clifford analysis, a version of these equations in Euclidean space of dimension 4 have been studied. In this talk, we shall discuss a recent development on this topic. In particular, for fields with values in a general irreducible spin module, as an analogue of massless field equations we propose the so-called generalized Cauchy-Riemann equations introduced by E. Stein and G. Weiss. Then we describe Fischer decompositions of massless fields up to spin 3/2. This is a joint work with V. Soucek, W. Wang, F. Brackx and H. De Schepper.
Seminar
Meccanica statistica e fenomeni sociali
Giuseppe Toscani , Università di Pavia
mercoledì 26 maggio 2021 alle ore 12:15
online: tiny.cc/fdsCM2021

Seminari Passati

Cerca

Seminar
Modal analysis of some nonlinear beam equations
Matteo Fogato, Dipartimento di Matematica, Politecnico di Milano
mercoledì 14 aprile 2021 alle ore 15:15 precise
polimi-it.zoom.us/j/82401456185?pwd=MS90c0hET3dXV0xxcmN5RTlqUGhQQT09

ABSTRACT

ABSTRACT
We consider the equation $u_{tt}+\delta u_t +\|A^{\theta/2}u\|^2 A^\theta u=g$ where $A^2$ is a diagonal, self-adjoint and positive-definite operator, $\theta\in [0,1]$ and we study some finite-dimensional approximations of the problem. First, we analyze the dynamics in the case when the forcing term $g$ is a combination of a finite number of modes. Next, we estimate the error we commit by neglecting the modes larger than a given $N$. We then prove, for a particular class of forcing terms, a theoretical result allowing to study the distribution of the energy among the modes and, with this background, we refine the results.
Some generalizations and applications to the study of the stability of suspension bridges are given.
Seminar
Local discontinuous Galerkin methods for prestrained and bilayer plates
Ricardo H. Nochetto, University of Maryland
lunedì 12 aprile 2021 alle ore 17:00
us02web.zoom.us/j/87144322081

ABSTRACT

ABSTRACT
Prestrained plates are slender materials that develop internal
stresses at rest, deform out of plane even without external forces, and
exhibit nontrivial 3d shapes. Bilayer plates are slender structures made of
two materials that react differently to environmental (thermal,
electrical or chemical) actuation. In both cases the plates can exhibit large
bending deformations that are geometrically nonlinear. We present
reduced nonconvex models, develop variational formulations, and
design local discontinuous Galerkin methods (LDGs). Moreover, we prove
Gamma-convergence of the discrete energies and analyze discrete gradient
flows for the computation of minimizers that provide control of the
metric defect. We document the performance of the LDG methods with
several insightful simulations.
Seminar
Which magnetic fields support a zero mode?
Michael Loss , Georgia Institute of Technology, Atlanta, GA, US
lunedì 12 aprile 2021 alle ore 15:00
online

ABSTRACT

ABSTRACT
I present some results concerning the size of magnetic fields
that support zero modes for the three dimensional Dirac equation and
related problems for spinor equations. The critical quantity, is the 3/2
norm of the magnetic field B. The point is that the spinor structure
enters the analysis in a crucial way.
This is joint work with Rupert Frank at Caltech.
Seminar
The Epistemic Route to Reflection
Marianna Antonutti Marfori , MCMP, LMU Munich
giovedì 8 aprile 2021 alle ore 15:00
online: politecnicomilano.webex.com/politecnicomilano/j.php?MTID=md18a1c58416f6039dd546beedad7b9ad

ABSTRACT

ABSTRACT
Gödel’s incompleteness theorems show that any formal theory that contains a certain minimal amount of arithmetic is incomplete: there are statements in the language of the theory that the theory cannot either prove or disprove. Such statements include statements (called reflection principles) that formally express the soundness of the theory, i.e. that everything that is provable from the axioms is true. This seems to contrast with our pre-theoretical understanding of arithmetic in everyday life and in science, and with our readiness to accept that every statement that can be proved from our axioms is true. Many authors have therefore sought to justify the addition to our formal theories of such reflection principles by different means. This paper presents a new way of justifying the addition of reflection principles on the basis of epistemic considerations, by employing certain uncontroversial properties of the notion of informal or absolute provability for arithmetic. S!
tarting from the observation that the fundamental properties of this notion can be formally characterised by using the axioms of the modal logic S4 (along the lines already proposed by Gödel), I will show that the recognition that the axioms and rules of inference of Peano arithmetic (PA) correctly formalise informal arithmetical reasoning is sufficient to formally imply the local and uniform reflection schemes.
Seminar
Optimization of eigenvalues of partially hinged rectangular composite plates
Alessio Falocchi, Dipartimento di Scienze Matematiche, Politecnico di Torino
martedì 30 marzo 2021 alle ore 11:15 precise
polimi-it.zoom.us/j/85332796977?pwd=QlhtRDZSWXkxaDhUTjFQQlEyL0NOUT09

ABSTRACT

ABSTRACT
We study the spectrum of non-homogeneous partially hinged rectangular plates having structural engineering applications. A possible way to prevent instability phenomena is to optimize the frequencies of certain oscillating modes with respect to the density function of the plate. In striking contrast to what happens under Dirichlet boundary conditions, we prove a result of positivity preserving property for the biharmonic operator of the related problem through fine estimates of the Fourier expansion of the corresponding Green function. This is useful in order to get qualitative properties, e.g. symmetry and monotonicity, of the eigenfunction corresponding to the density minimizing the first eigenvalue.
This is a joint work with Elvise Berchio (Politecnico di Torino).
Seminar
Progetto COMPASS: Control for Orbit Manoeuvring Through Perturbations for Application to Space Systems
Camilla Colombo , Politecnico di Milano
mercoledì 24 marzo 2021 alle ore 12:15
online: tiny.cc/fdsCM2021
Seminar
Explicit bounds for the generation of a lift force exerted by steady-state Navier-Stokes flows over a fixed obstacle
Gianmarco Sperone, Dept. of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University in Prague
mercoledì 24 marzo 2021 alle ore 15:15 precise
Url: polimi-it.zoom.us/j/87365124649?pwd=SjZOcDgrQU9qUGZCM3FZRmxCTUhlUT09

ABSTRACT

ABSTRACT
We analyze the steady motion of a viscous incompressible fluid in a two- and three-dimensional channel containing an obstacle through the Navier-Stokes equations under different types of boundary conditions. In the 2D case we take constant non-homogeneous Dirichlet boundary data in a (virtual) square containing the obstacle, and emphasize the connection between the appearance of lift and the unique solvability of Navier-Stokes equations. In the 3D case we consider mixed boundary conditions: the inflow is given by a fairly general datum and the flow is assumed to satisfy a constant traction boundary condition on the outlet. In the absence of external forcing, explicit bounds on the inflow velocity guaranteeing existence and uniqueness of such steady motion are provided after estimating some Sobolev embedding constants and constructing a suitable solenoidal extension of the inlet velocity. In the 3D case, this solenoidal extension is built through the Bogovskii operator and explicit bounds on its Dirichlet norm (in terms of the geometric parameters of the obstacle) are found by solving a variational problem involving the infinity-Laplacian. The talk accounts for results obtained in collaboration with Filippo Gazzola and Ilaria Fragalà (both at Politecnico di Milano)
Seminar
COVID Narrative Risk: A Computational Linguistic Approach to the Econometric Identification of Narrative Risk During the COVID-19 Pandemic
Valerio Potì, University College Dublin
lunedì 22 marzo 2021 alle ore 17:30 precise
polimi-it.zoom.us/j/88530102123

ABSTRACT

ABSTRACT
In this paper, we study the role in financial markets of narratives related to the ongoing COVID-19 pandemic. The pandemic represents a natural setting for the development of narratives that may effects or be affected by financial markets. We thus treat the pandemic as a natural experiment on the relation between prevailing narratives and financial markets. We adopt the SIR model and natural language processing on financial newspaper news and Twitter tweets that deal at the same time with financial market topics and COVID-19 to study the dynamics and determinants of coronavirus narrative epidemics. Our aim is to establish whether there an “infodemic” develops, and whether the prevailing narrative, whether resemnbling an infodemic or otherwise, drives or is driven by financial markets developments, controlling for developments regarding the COVID-19 pandemic. We find associations between narratives about the epidemic, stock market dynamics (both regarding returns and volatility) and government responses to COVID-19. We also find that the narrative spread does resemble an infodemic, since it is well described by the SIR epidemic model. Our estimates of the shape of the narrative infodemic curves in different countries depend on whether the COVID-19 outbreak occurred early and on its severity. Negative tones and tones communicating uncertainty are prevalent in the growing stage of the infodemic. We find preliminary evidence of a causality relation between the negative and uncertainty tones of coronavirus tweets and both market return and volatility change.

Ricerca - Laboratori - Formazione

Prossimi Seminari

Seminari Passati

Cerca

Seminari Matematici
Politecnico di Milano

Seminari Matematici
Milano e dintorni

Prossimi Seminari

Seminari Passati

Cerca

Seminari MatematiciPolitecnico di Milano

Seminari MatematiciMilano e dintorni

Seminari Matematici
Politecnico di Milano

Seminari Matematici
Milano e dintorni