Dipartimento di Matematica

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
  ABSTRACT
  ABSTRACT
  

  It is known that positive solutions to $\Delta_p u + u^{p^*-1}=0$ in $\mathbb{R}^n$, with $n \geq 3$ and $1
  We provide a new approach to this problem which allows us to give a complete classification of the solutions in an anisotropic setting as well as to a suitable generalization of the problem in convex cones.
  
  This is a joint work with A. Figalli and A. Roncoroni.
• 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
  ABSTRACT
  ABSTRACT
  

  Advances in numerical techniques and the ever increasing computational power have rendered the execution of forward models of total heart function feasible. Using such models based on clinical images and parameterized to reflect a given patient's physiology, are a highly promising approach to comprehensively and quantitatively characterize cardiovascular function in a given patient. Such models are anticipated to play a pivotal role in future precision medicine as a method to stratify diseases, optimize therapeutic procedures, predict outcomes and thus better inform clinical decision making.
  However, to translate modeling into a clinically applicable modality a number of key challenges have to be addressed. In particular, expensive computational models must be made efficient enough to be compatible with clinical time frames. This can be addressed either with hierarchical models of varying complexity which are cheaper to evaluate, by using computational efficient techniques such as spatio-temporal adaptivity, or by exploiting the power of new HPC hardware through massive parallelization or the use of accelerators. Further, the etiology of most cardiac pathologies comprises Multiphysics aspects, requiring the coupling of various physics, which may be characterized by very different space and time scales, rendering their coupling a challenging endeavor. Finally and most importantly, to be of clinical utility generic models must be specialized based on clinical data, which requires complex parameterization and data assimilation procedures to match model behavior with clinical observations.
  In this presentation, I will give an overview of our multi-physics forward modelling framework and our recent work on m personalising models using clinical data.
  
  contact: 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)
  
• 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
  ABSTRACT
  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.
• 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
  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
  
  
• 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
  ABSTRACT
  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.
• 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
  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.
  
• 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
  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)
  
  
• 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
  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
• 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
  ABSTRACT
  ABSTRACT
  

  In questo seminario intendo esporre un argomento molto importante della geometria dello spazio, anche se, talvolta, questo viene trascurato, o presentato superficialmente, nei programmi della scuola superiore: i poliedri. Dopo avere introdotto la loro definizione e le loro principali proprietà, sarà mostrata la loro presenza nella natura, nella vita quotidiana e nell’arte, partendo dall’antica Grecia fino ad arrivare ai nostri giorni. Anzitutto saranno trattati i poliedri regolari; successivamente sarà introdotta l’importante famiglia, soprattutto nelle applicazioni, dei poliedri archimedei. Infine, saranno presentati gli interessanti poliedri di Goldberg
• 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
  ABSTRACT
  ABSTRACT
  

  L’obiettivo del seminario è riflettere su come, a partire dai dati restituiti dal Servizio Nazionale di Valutazione, si possano intraprendere azioni di consolidamento e miglioramento all’interno dalla propria classe, e non concentrarsi su cosa fare per preparare le prove INVALSI. Questo viene realizzato esplicitando il legame delle domande con le Indicazioni Nazionali e con le prassi didattiche, e utilizzando gli opportuni costrutti della didattica. Particolare rilievo verrà dato al fatto che gli obiettivi di apprendimento alla base delle pratiche d'aula sono fissati dalle Indicazioni Nazionali e non dalle prove che invece forniscono informazioni su come questi obiettivi sono raggiunti
• 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
  ABSTRACT
  ABSTRACT
  

  The ability to measure the heart, its shape, its structure and its function across multiple spatial and temporal scales continues to grow. Interpreting this data remains challenging. Computational biophysical models of the heart allow us to quantitatively link and interpret these large disparate data sets within the context of known cardiac physiology and invariable physical constraints. Within these models, we can infer unobservable states, propose and test new hypothesis and predict how systems will respond to challenges increasing our ability to interrogate and understand biological systems. We are increasingly applying this approach to modelling human hearts to investigate clinical applications. In this presentation, I will give an overview on our modelling work simulating anthracycline-induced heart failure, how we are using models of individual patients to study cardiac resynchronisation therapy and how we are using simulations to characterise the anatomy and pathophysiology of atrial fibrillation patients. Finally, I will present some of our preliminary results on simulating the four-chamber heart to begin simulating the interactions between atrial and ventricular function.
  
  Contact: 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)
• Nonlinear Peridynamic Models
  Giuseppe Maria Coclite, Politecnico di Bari
  mercoledì 22 gennaio 2020 alle ore 15:15, Aula seminari 3° piano
  ABSTRACT
  ABSTRACT
  

  Some materials may naturally form discontinuities such as cracks as a result of scale effects and long range interactions. Peridynamic models such behavior introducing a new nonlocal framework for the basic equations of continuum mechanics. In this lecture we consider a nonlinear peridynamic model and discuss its well-posedness in suitable fractional Sobolev spaces.
  Those results were obtained in collaboration with S. Dipierro (Perth), F. Maddalena (Bari) and E. Valdinoci (Perth).

Seminari Passati

• L'interazione fra neuroscienze e matematica: analisi della connettività cerebrale utilizzando i grafi
  Paolo Finotelli,  Politecnico di Milano
  mercoledì 16 ottobre 2019 alle ore 15:30, Sala Consiglio - piano 7° - edificio 14 - via Ponzio 31/p
  ABSTRACT
  

  L'intento di questo seminario è mostrare come l'interazione fra le neuroscienze e la matematica sia in continua crescita e sia destinata a costituire la base della medicina moderna. In particolare, verranno introdotti i fondamenti della connettività cerebrale e della teoria delle reti complesse, di cui la teoria dei grafi costituisce l’impalcatura matematica. Come caso particolare verrà presentato un recente modello per la determinazione della connettività cerebrale basato sulla teoria dei grafi.
  ABSTRACT
• Control problems in Wasserstein space
  Antonio Marigonda, University of Verona
  lunedì 14 ottobre 2019 alle ore 15:15, Aula seminari 6° piano
  ABSTRACT
  

  In this talk we present recent results about the existence and uniqueness of the viscosity solution for a certain classes on Hamilton-Jacobi Equations in the Wasserstein space of probability measure, arising in problem of mean field control of multi-agent systems. We consider a multi-agent system subject to a centralized controller
  aiming to minimize a cost function. The microscopic dynamics of each agent is given by a differential inclusion. We model the distribution of agents by a probability measure, and formulate the minimization problem
  as a Mayer problem for a dynamics in the Wasserstein space represented by a controlled continuity equation describing the macroscopical evolution of the system. We prove that the value function V of the
  problem solves a Hamilton-Jacobi equation in the Wasserstein space in a suitable viscosity sense, and prove a comparison principle for such an equation, thus characterizing V as the unique viscosity solution of the
  Hamilton-Jacobi equation associated to the problem.
  ABSTRACT
• How Mathematics helps structuring climate discussions
  Rupert Klein, FU Berlin & ECMWF Fellow
  giovedì 3 ottobre 2019 alle ore 14:00, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
  ABSTRACT
  

  Mathematics in climate research is often thought to be mainly a provider of techniques for solving the continuum mechanical equations for the flows of the atmosphere and oceans, for the motion and evolution of Earth's ice masses, and the like. Three examples will elucidate that there is a much wider range of opportunities. Climate modellers often employ reduced forms of the continuum mechanical equations to efficiently address their research questions of interest. The first example discusses how mathematical analysis can provide systematic guidelines for the regime of applicability of such reduced model equations. Meteorologists define 'climate', in a narrow sense, as the statistical description in terms of the mean and variability of relevant quantities over a period of time (World Meteorological Society, http://www.wmo.int; see the website for a broader sense definition). Now, climate researchers are most interested in changes of the climate over time, and yet there is no unique, well-defined notion of time dependent statistics. In fact, there are restrictive conditions which data from time series need to satisfy for classical statistical methods to be applicable. The second example describes recent developments of analysis techniques for time series with non-trivial temporal trends. Modern climate research has joined forces with economy and the social sciences to generate a scientific basis for informed political decisions in the face of global climate change. One major type of problems hampering progress of the related interdisciplinary research consists of often subtle language barriers. The third example describes how mathematical formalization of the notion of 'vulnerability' has helped structuring related interdisciplinary research efforts.
  
  Contact: luca.bonaventura@polimi.it
  
  ABSTRACT
• Mountain pass structure, non-degeneracy conditions and variational gluing
  Paul H. Rabinowitz, University of Wisconsin, Madison
  venerdì 20 settembre 2019 alle ore 14:00, Sala di Rappresentanza, Via C. Saldini 50
  ABSTRACT
  

  The effect of non-degeneracy conditions on the applicability of variational gluing arguments for some variational problems possessing mountain pass structure will be discussed.
  
  
  ABSTRACT
• Decay and Sobolev regularity properties for solutions at infinity of (nonlinear) PDEs
  Stefano Pigola, Università dell’Insubria
  venerdì 20 settembre 2019 alle ore 11:15, Aula seminari 3° piano
  ABSTRACT
  

  I will present some recent results on the global behaviour of nonnegative and bounded subsolutions of $\Delta_p u = f(u)$ over an exterior domain of a complete Riemannian manifold. I shall discuss geometric conditions under which such a subsolution decays to zero at infinity. The main tools are represented by (a nonlinear version of) the Feller property and some global comparison results. These, in turn, are related to a new characterization of the ($p$-)stochastic completeness of the manifold in terms of the Sobolev space $W^{1,p}$.
  ABSTRACT
• Algebraic Option Pricing
  Peter Carr, New York University
  venerdì 13 settembre 2019 alle ore 12:15, Sala Consiglio settimo piano
  ABSTRACT
  

  Optionality arises whenever an investor can choose between owning either of two
  assets. We treat the value of optionality as a modified sum. We then explore
  options on options as sums of sums. This viewpoint allows us to derive a simple
  closed form formula for a Bermudan option.
  
  ABSTRACT
• Stability of some coupled partial differential equations in both bounded and unbounded domains
  Abdelaziz Soufyane, University of Sharjah
  giovedì 12 settembre 2019 alle ore 15:15, Aula seminari 3° piano
  ABSTRACT
  

  This talk deals with some recent results on the stability of a coupled partial differential equations. We will present the energy decay rates for many systems (arising in many applications) in the bounded domain, different approaches will be used to establish the energy decay. Also, we will discuss the rate decay for some models in the unbounded domain using the Fourier transformation, the multipliers techniques in Fourier image. We conclude our talk by giving some remarks and open problems.
  
  This seminar is organized within the PRIN 2017 Research project «Direct and inverse problems for partial differential equations: theoretical aspects and applications» Grant Registration number 201758MTR2, funded by MIUR - Project coordinator Prof. Filippo Gazzola
  ABSTRACT
• Curve di Osgood
  Aljosa Volcic, Università della Calabria
  giovedì 12 settembre 2019 alle ore 11:00 precise, Dipartimento di Matematica - 7° piano, Politecnico di Milano
  ABSTRACT
  

  La conferenza sarà dedicata a due argomenti vicini al classico argomento del teorema di Cantor sulla corrispondenza biunivoca (che non può essere continua) tra $[0,1]$ e $[0,1]^2$ ed alla curva di Peano.
  
  Principalmente si parlerà di curve create nel 1903 da William F. Osgood il quale costruì, per ogni $\beta \in ]0,1[$ una curva iniettiva la cui immagine ha area $\beta$.
  Si farà una breve storia di altre costruzioni analoghe, dedicandosi in particolare all'ultima di esse, dovuta a Karl Stromberg e Shiojenn Tseng.
  In conclusione verrà presentata la dimostrazione dell'esistenza di una curva iniettiva definita su $]0,1[$ la cui immagine ha misura di Lebesgue bidimensionale uguale a $1$.
  ABSTRACT

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