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

### Prossimi Seminari

• Pricing and hedging in rough Heston models
Omar El Euch, Spire Europe Limited
martedì 22 ottobre 2019 alle ore 14:15, Aula seminari del terzo piano
• Symmetry results for critical $p$-Laplace equations
Giulio Ciraolo, Università degli Studi di Milano
mercoledì 23 ottobre 2019 alle ore 15:15, Aula seminari 3° piano
• Clinical Personalization of Computational Models of Total Heart Function
Gernot Plank, Medical University of Graz, Austria
giovedì 24 ottobre 2019 alle ore 14:00, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
• One Hunderd Years of Universes
John Barrow, University of Cambridge
martedì 29 ottobre 2019 alle ore 11:30, Palazzo di Brera, Via Brera 28, Milano, Sala Maria Teresa
• On Mean Field Games
Pierre-Louis Lions, Collège de France
martedì 29 ottobre 2019 alle ore 14:40, Palazzo di Brera, Via Brera 28, Milano, Sala Maria Teresa
• On the Power of Geometric Illustration in Mathematics and Science
Roger Penrose, University of Oxford
martedì 29 ottobre 2019 alle ore 16:00, Palazzo di Brera, Via Brera 28, Milano, Sala Maria Teresa
• 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
• 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
• On the highly compressible limit for the Navier-Stokes-Korteweg model with density dependent viscosity
Matteo Caggio, University of L'Aquila
martedì 12 novembre 2019 alle ore 14:30, Aula seminari 3° piano
• 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
• 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
• 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
• Un viaggio nel mondo dei poliedri
Giuseppe Conti, Università di Firenze
mercoledì 27 novembre 2019 alle ore 15:00, Sala Consiglio - piano 7° - edificio 14
• Come utilizzare le prove invalsi nella pratica d’aula
Alice Lemmo, Università degli studi dell’Aquila
mercoledì 4 dicembre 2019 alle ore 15:00, Sala Consiglio - piano 7° - edificio 14
• Translating cardiac models into the clinic
Steven Niederer, Biomedical Engineering, King’s College London
giovedì 12 dicembre 2019 alle ore 14:00,  Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
• Nonlinear Peridynamic Models
Giuseppe Maria Coclite, Politecnico di Bari
mercoledì 22 gennaio 2020 alle ore 15:15, Aula seminari 3° piano

### Seminari Passati

• On the quasistatic limit for a debonding model in dimension one; a vanishing inertia and viscosity approach
Filippo Riva, SISSA
giovedì 6 giugno 2019 alle ore 15:15, Aula seminari 3° piano
ABSTRACT
In the theory of linearly elastic fracture mechanics one-dimensional debonding models, or peeling tests, provide a simplified but still meaningful version of crack growth models based on Griffith's
criterion. They are both described by the wave equation in a time-dependent domain coupled with suitable energy balances and irreversibility conditions.Unlike the general framework, peeling tests allow to deal with a
natural issue of great interest arising in fracture mechanics. It can be stated as follows: although all these models are dynamic by nature, the evolution process is often assumed to be quasistatic (namely the
body is at equilibrium at every time) since inertial effects can be neglected if the speed of external loading is very slow with respect to the one of internal oscillations. Despite this assumption seems to
be reasonable, its mathematical proof is really far from being achieved.In this talk we validate the quasistatic assumption in a particular damped debonding model, showing that dynamic evolutions converge to the quasistatic one as inertia and viscosity go to zero. We also highlight how the presence of viscosity is crucial to get this kind of convergence.
• Robin eigenvalues on domains with cusps
Hynek Kovarik, Università degli studi di Brescia
giovedì 6 giugno 2019 alle ore 14:00, Aula seminari 3° piano
ABSTRACT
We consider the Laplace operator with the Robin boundary condition with negative coefficient
on bounded domains with cusps. We show that if the cusps is not too strong, then the operator is bounded from below and calculate the leading term in the asymptotic expansion of its negative eigenvalues as the coefficient of the boundary condition tends to infinity. This is a joint work with Konstantin Pankrashkin.
• Behavioral models in the banking activity
Matteo Formenti , UniCredit
martedì 4 giugno 2019 alle ore 12:15, Aula seminari del terzo piano
ABSTRACT
The NMD behavioural models are a crucial driver of the maturity transformation activity and bank's profitability because their goal is to estimate the stable source of funding, the volume that can be used for medium long term lending, and the volume that represents a fixed rate cost. Being the nature of the behavioural models very heterogeneous, and the use within the bank so widespread, this presentation aims at introducing a Framework, composed by six Principles, that allows to set the proper modelling of the clients' behavior jointly with the banks' need. Furthermore, an application of the most advanced modeling that considers the financial wealth allocation at clients level will be shown.
• Semi-implicit finite-volume integrators for all-scale atmospheric dynamics
Piotr Smolarkiewicz, European Centre for Medium-Range Weather Forecasts, Reading, Berkshire, United Kingdom
giovedì 30 maggio 2019 alle ore 14:00, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT
This talk outlines a novel numerical approach for accurate and computationally efficient integrations of PDEs governing all-scale atmospheric dynamics. Such PDEs are not easy to handle, due to a huge disparity of spatial and temporal scales as well as a wide range of propagation speeds of natural phenomena captured by the equations. Moreover, atmospheric dynamics constitutes only a small perturbation about dominant balances that result from the Earth gravity, rotation, composition of its atmosphere and the energy input by the solar radiation. Maintaining this mean equilibrium, while accurately resolving the perturbations, conditions the design of atmospheric models and subjects their numerical procedures to stringent stability, accuracy and efficiency requirements.
The novel Finite-Volume Module of the Integrated Forecasting System (IFS) at ECMWF (hereafter IFS-FVM) solves perturbation forms of the fully compressible Euler/Navier-Stokes equations under gravity and rotation using non-oscillatory forward-in-time semi-implicit time stepping and finite-volume spatial discretisation. The IFS-FVM complements the established semi-implicit semi-Lagrangian pseudo-spectral IFS (IFS-ST) with the all-scale deep-atmosphere formulation cast in a generalised height-based vertical coordinate, fully conservative and monotone advection, flexible horizontal meshing and a predominantly local communication footprint. Yet, both dynamical cores can share the same quasi-uniform horizontal grid with co-located arrangement of variables, geospherical longitude-latitude coordinates and physics parametrisations, thus facilitating their synergetic relation.
The focus of the talk is on the mathematical/numerical formulation of the IFS-FVM with the emphasis on the design of semi-implicit integrators and the associated elliptic Helmholtz problem. Relevant benchmark results and comparisons with corresponding IFS-ST results attest that IFS-FVM offers highly competitive solution quality and computational performance.

Contact: luca.bonaventura@polimi.it
• Comunicare il progetto. Storytelling e tecniche di rappresentazione
Francesca Piredda, Politecnico di Milano
mercoledì 29 maggio 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21
• Game-theoretical models of debt and bankruptcy
Alberto Bressan, Penn State University
martedì 28 maggio 2019 alle ore 17:00, Aula seminari del terzo piano
ABSTRACT
The talk will be concerned with problems of optimal debt management. In a basic model, the interest rate as well as the bankruptcy risk are given a priori. In this case the borrower faces a standard problem of optimal control.
In alternative, debt management can be modeled as a noncooperative game between a borrower and a pool of lenders, in infinite time horizon with exponential discount. The yearly income of the borrower is governed by a stochastic process. When the debt-to-income ratio surpasses a given threshold, bankruptcy occurs.
The interest rate charged by the risk-neutral lenders is precisely determined in order to compensate for this possible loss of part of their investment.
Existence and properties of optimal feedback strategies for the borrower will be discussed, in a stochastic framework as well as in the limit deterministic setting.
• Multiple solutions for the 2-dimensional Euler equations
Alberto Bressan,  Pennsylvania State University
lunedì 27 maggio 2019 alle ore 16:00 precise, Aula U5-3014 (Edificio 5 terzo piano), Dip. Matematica e Applicazioni, Via Cozzi 55, Milano
ABSTRACT
In one space dimension, it is well known that hyperbolic conservation
laws have unique entropy-admissible solutions, depending continuously on
the initial data. Moreover, these solutions can be obtained as limits of
vanishing viscosity approximations.

For many years it was expected that similar results would hold in
several space dimensions. However, fundamental work by De Lellis,
Szekelyhidi, and other authors, has shown that multidimensional
hyperbolic Cauchy problems usually have infinitely many weak solutions.
Moreover, all known entropy criteria fail to select a single admissible one.

In the first part of this talk I shall outline this approach based on a
Baire category argument, yielding the existence of infinitely many weak
solutions.

I then wish to discuss an alternative research program,
aimed at constructing multiple solutions to some specific Cauchy
problems. Starting with some numerical simulations, here the eventual
goal is to achieve rigorous, computer-aided proofs of the existence of
two distinct self-similar solutions with the same initial data.
While solutions obtained via Baire category have turbulent nature, these
self-similar solutions are smooth, with the exception of one or two
points of singularity. They are thus much easier to visualize and
understand.
• Matematica, società, economia e sviluppo
Giulia di Nunno, University di Oslo
mercoledì 22 maggio 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21