Dipartimento di Matematica – Politecnico di Milano

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Prossimi Eventi

feb 25 mar 2020

MOX Seminar
Elena Bachini, Geometrically intrinsic modeling of shallow water flows, 25-02-2020, ore 16:00

MOX Seminar
Elena Bachini
Università degli Studi di Padova
Geometrically intrinsic modeling of shallow water flows
Martedì 25 febbraio 2020 alle ore 16:00
Aula Saleri, VI piano
Abstract

Shallow water models of geophysical flows must be adapted to geometric characteristics in the presence of a general bottom topography with non-negligible slopes and curvatures, such as a mountain landscape. In this work we derive an intrinsic shallow water model from the Navier-Stokes equations defined on a local reference frame anchored on the bottom surface. The resulting equations are characterized by non-autonomous flux functions and source terms embodying only the geometric information. We show that the proposed model is rotational invariant, admits a conserved energy, is well-balanced, and it is formally a second order approximation of the Navier-Stokes equations with respect to a geometry-based order parameter. We then derive a numerical discretization by means of a first order upwind Godunov Finite Volume scheme intrinsically defined on the bottom surface. We study convergence properties of the resulting scheme both theoretically and numerically. Next, we extend the approach to derive a second order Discontinuous Galerkin method and show its properties.
Simulations on several synthetic test cases are used to validate the theoretical results as well as more experimental properties of the solver. The results show the importance of taking into full consideration the bottom geometry even for relatively mild and slowly varying curvatures.

Contatto: luca.bonaventura@polimi.it
Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

feb 26 mer 2020

Seminar
Giulia Cavagnari, Lagrangian and eulerian formulations for multi-agent optimal control problems, 26-02-2020, ore 15:15

Seminar
Giulia Cavagnari
Politecnico di Milano
Lagrangian and eulerian formulations for multi-agent optimal control problems
Mercoledì 26 febbraio 2020 alle ore 15:15
Aula seminari 3° piano
Abstract

In this talk we present and compare two approaches to study deterministic optimal control problems for interacting multi-agent systems: Lagrangian and Eulerian.
Different research fields comes into play: optimal control and transport theory to set out the variational model and analyze the underlying principles, and a random variable approach to deal with the problem in its various Lagrangian formulations on a fixed probability space ? (space of parametrizations).
On one side, the state of the system is expressed by a random variable in L^2(?) and the nonlocal velocity field driving the dynamics depends on the realizations of a Borel measurable control map. The lack of existence of minimizers for a generic cost functional, even after relaxation, makes it fundamental to recover optimality through the study of the problem from an Eulerian viewpoint. Here the problem is set in the 2-Wasserstein space of probability measures. The relation with the previous approach lies on the identification of the time-dependent measure, solving a controlled continuity equation, as the law of the evolving random variable.
After stating the problem, we prove the equivalence between the Lagrangian and Eulerian value functions through an intermediate formulation based on the Superposition Principle by Ambrosio-Gigli-Savaré.
Finally we deal with stability and ?-convergence results for the corresponding problems involving a finite number of agents to the mean-field ones.
This is a joint work with Stefano Lisini (University of Pavia), Carlo Orrieri (University of Trento) and Giuseppe Savaré (University of Pavia).
Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

feb 28 ven 2020

MOX Seminar
Wolfgang Bangerth, Finite element methods at realistic complexities, 28-02-2020, ore 14:00

MOX Seminar
Wolfgang Bangerth
Department of Mathematics, Campus Delivery, Fort Collins, CO, USA NUMETH-HPC
Finite element methods at realistic complexities
Venerdì 28 febbraio 2020 alle ore 14:00
Aula Saleri VI piano
Abstract

Solving realistic, applied problems with the most modern numerical methods introduces many levels of complexity. In particular, one has to think about not just a single method, but a whole collection of algorithms: a single code may utilize fully adaptive, unstructured meshes; nonlinear, globalized solvers; algebraic multigrid and block preconditioners; and do all this on
1,000 processors or more with realistic material models.
Codes at this level of complexity can no longer be written from scratch. However, over the past two decades, many high quality libraries have been developed that make writing advanced computational software simpler. In this talk, I will briefly introduce the deal.II finite element library
(http://www.dealii.org) whose development I co-lead and show how it has enabled us to develop the ASPECT code (http://aspect.geodynamics.org) for simulation of convection in the earth mantle. I will discuss some of the results obtained with this code and comment on the lessons learned from developing this massively parallel code for the solution of a complex problem.

Contatto: luca.dede@polimi.it
Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

mar 04 mer 2020

Seminar
Stefano Biagi, Some global results for homogeneous hormander sums of squares, 04-03-2020, ore 15:15

Seminar
Stefano Biagi
Politecnico di Milano
Some global results for homogeneous hormander sums of squares
Mercoledì 4 marzo 2020 alle ore 15:15
Aula seminari 3° piano
Abstract

In this talk we present several global results concerning homogeneous Hormander sums of squares L.
These operators intervene in various contexts of interest, such as CR geometry, Lie group Theory, sub-Riemannian manifolds, Mathematical Finance, etc.
After a brief introduction on general sub-elliptic operators (of which our L’s are a particular case), we properly introduce the class of the homogeneous Hormander sums of squares and we discuss some global `qualitative' aspects regarding these operators: global lifting on Carnot groups; existence/global estimates for the associated fundamental solution and heat kernel; maximum principles on unbounded domains.

The results presented in this talk are contained in several papers in collaboration with A. Bonfiglioli, M. Bramanti and E. Lanconelli.
Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

mar 11 mer 2020

Seminar
Maurizio Melis, Comunicare la scienza: manuale di sopravvivenza, 11-03-2020, ore 12:15
- Seminar
- Maurizio Melis
- Giornalista scientifico
- Comunicare la scienza: manuale di sopravvivenza
- Mercoledì 11 marzo 2020 alle ore 12:15
- aula B21
- Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

mar 12 gio 2020

MOX Colloquia
Herbert De Gersem, Modelling and simulation of magnetoquasistatic and electroquasistatic fields, 12-03-2020, ore 14:00

MOX Colloquia
Herbert De Gersem
Institute for Accelerator Science and Electromagnetic Fields (TEMF), TU Darmstadt, Germany
Modelling and simulation of magnetoquasistatic and electroquasistatic fields
Giovedì 12 marzo 2020 alle ore 14:00
Dip. di Matematica, Politecnico di Milano ed. 14 "La Nave", via Ponzio 31/P- Aula Consiglio, VII piano
Abstract

Magnetoquasistatic field problems arise in, e.g., transformers, electric machines and superconducting magnets. Electroquasistatic field problems arise in high-voltage engineering and on printed circuit boards. Both are expressed by a nonlinear parabolic partial differential equation, which is typically discretised by finite elements on an unstructured tetrahedral mesh and time-stepped by implicit methods. The talk addresses contemporary challenges such as, e.g., the increasing level of detail, multiphysical phenomena, multirate behaviour and nontrivial materials. Recent developments in numerical methods dedicated to the quasistatic setting will be discussed, e.g., hybrid spatial discretisation schemes, field-circuit coupling, multirate time stepping and sparse surrogate modelling. The methods will be illustrated by examples from electrical engineering and accelerator science.

Contatto: carlo.defalco@polimi.it
Herbert De Gersem is born in 1971 and obtained the MSc and PhD degrees in electrical engineering at the KU Leuven (Belgium) in 1994 and 2001, respectively. From 2001 to 2006, he worked as a postdoc at TU Darmstadt (Germany). Since 2006, he is an associated professor at the KU Leuven. Since 2014, he is a full professor at the TU Darmstadt (www.temf.de). He authored and co-authored more than 130 publications in international journals. His major research topics are electromagnetic field simulation with volumetric discretisation methods (finite element method, finite integration technique, discontinuous Galerkin method) and the application thereof to electrical energy transducers (machines, actuators, transformers) and accelerator components (conventional and superconductive magnets and resonating cavities).

Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

mar 13 ven 2020

Convegno
Piday2020
13/03/2020
- CONVEGNO
- Piday2020
- organizzatori
  Laboratorio
- Venerdì 13 marzo 2020 - Venerdì 13 marzo 2020
  aula Rogers - via Ampère, 2
Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568
mar 18 mer 2020

Seminar
Stefano Capolongo, Design and health, 18-03-2020, ore 12:15
- Seminar
- Stefano Capolongo
- Politecnico di Milano
- Design and health
- Mercoledì 18 marzo 2020 alle ore 12:15
- aula B21
- Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

mar 25 mer 2020

Seminar
Paolo Biscari, Geometria iperbolica: da escher alle deformazioni plastiche, 25-03-2020, ore 12:15

Seminar
Paolo Biscari
Politecnico di Milano
Geometria iperbolica: da escher alle deformazioni plastiche
Mercoledì 25 marzo 2020 alle ore 12:15
aula B21
Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

mar 25 mer 2020

Seminar
Benedetta Noris, Radial positive solutions for a class of neumann problems without growth conditions, 25-03-2020, ore 15:15

Seminar
Benedetta Noris
Politecnico di Milano
Radial positive solutions for a class of neumann problems without growth conditions
Mercoledì 25 marzo 2020 alle ore 15:15
Aula seminari 3° piano
Abstract

We consider a class of semilinear and quasilinear partial differential equations on bounded radial domains, subject to homogeneous Neumann boundary conditions. The nonlinear term is possibly supercritical in the sense of Sobolev embeddings.
We investigate the existence of positive non-constant radial solutions: we prove existence and multiplicity, and examine the oscillatory behavior.
In case the nonlinearity is subcritical in the sense of Sobolev embeddings, we also prove a priori bounds of solutions.
The talk is based on papers in collaboration with several authors.
Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

apr 22 mer 2020

Seminar
Fabio Peri, ''l'amor che move il sole e l'altre stelle''. il cielo nella divina commedia, 22-04-2020, ore 12:15

Seminar
Fabio Peri
Civico Planetario U. Hoepli di Milano
''l'amor che move il sole e l'altre stelle''. il cielo nella divina commedia
Mercoledì 22 aprile 2020 alle ore 12:15
aula B21
Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

apr 29 mer 2020

Seminar
Giovanni Corrao, Dati ed evidenze del mondo reale. un'occhiata al metodo, 29-04-2020, ore 12:15

Seminar
Giovanni Corrao
Università degli Studi di Milano-Bicocca
Dati ed evidenze del mondo reale. un'occhiata al metodo
Mercoledì 29 aprile 2020 alle ore 12:15
aula B21
Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

mag 06 mer 2020

Seminar
Marco Bramanti, La delta di dirac: storia di un mostro, 06-05-2020, ore 12:15
- Seminar
- Marco Bramanti
- Politecnico di Milano
- La delta di dirac: storia di un mostro
- Mercoledì 6 maggio 2020 alle ore 12:15
- aula B21
- Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

mag 13 mer 2020

Seminar
Camilla Colombo, Progetto compass: control for orbit manoeuvring through perturbations for application to space systems, 13-05-2020, ore 12:15

Seminar
Camilla Colombo
Politecnico di Milano
Progetto compass: control for orbit manoeuvring through perturbations for application to space systems
Mercoledì 13 maggio 2020 alle ore 12:15
aula B21
Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

mag 20 mer 2020

Seminar
Lorenzo Brufani, Gestire la comunicazione di situazioni di crisi, 20-05-2020, ore 12:15
- Seminar
- Lorenzo Brufani
- Competence CEO
- Gestire la comunicazione di situazioni di crisi
- Mercoledì 20 maggio 2020 alle ore 12:15
- aula B21
- Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568
mag 27 mer 2020

Seminar
Giuseppe Toscani, Meccanica statistica e fenomeni sociali, 27-05-2020, ore 12:15
- Seminar
- Giuseppe Toscani
- Università di Pavia
- Meccanica statistica e fenomeni sociali
- Mercoledì 27 maggio 2020 alle ore 12:15
- aula B21
- Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

giu 11 gio 2020

giu 12 ven 2020

Convegno
Big data and machine learning in finance
11/06/2020 - 12/06/2020

CONVEGNO
Big data and machine learning in finance
organizzatori
Emilio Barucci (Politecnico di Milano, chair), Filippo Della Casa (UNIPOL), Paolo Giudici (Università di Pavia), Daniele Marazzina (Politecnico di Milano), Andrea Prampolini (Banca IMI), Marcello Restelli (Politecnico di Milano).
Giovedì 11 giugno 2020 - Venerdì 12 giugno 2020
Sala Consiglio - piano 7° - edificio 14

Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568