Dipartimento di Matematica

Prossimi Seminari

• Laser "su misura" per il trattamento di tumori
  Paola Saccomandi, Politecnico di Milano
  mercoledì 27 marzo 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21
• Some remarks on the forces exerted by a viscous fluid on a bluff body
  Gianmarco Sperone, Politecnico di Milano
  giovedì 28 marzo 2019 alle ore 15:15, Aula seminari 3° piano
  ABSTRACT
  ABSTRACT
  

  The theory of flight developed by Kutta, Lanchester and Zhukovsky is mainly based on the idea that a cambered surface produces lift through its ability to generate a vortex about itself. Since fluid flows around an obstacle generate vortices which are difficult to locate and to describe, in this talk we analyze the Stokes and Navier-Stokes equations for the two-dimensional motion of a viscous fluid in the exterior of a fixed obstacle. Firstly, we discuss nonstandard boundary conditions for the Stokes equations on a smooth obstacle, allowing for the generation of turbulence over the leeward wall of the body. Secondly, after studying the connection between the appearance of lift and the unique solvability of the Navier-Stokes equations, we show some numerical results that compare the aerodynamic response of different non-smooth obstacles, as the inlet velocity is increased until reaching the critical Reynolds number. The talk accounts for results contained in two articles prepared in collaboration with Filippo Gazzola and Andrei Fursikov (Moscow State University).
• Simplicial splines for representation of density functions
  Karel Hron e Jitka Machalova, Palacky University di Olomouc
  martedì 2 aprile 2019 alle ore 15:00 precise, Aula Seminari 'Saleri' VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano - Edificio 14
  ABSTRACT
  ABSTRACT
  

  In the context of functional data analysis, probability density functions as non-negative functions are characterized by specific properties of scale invariance and relative scale which enable to represent them with the unit integral constraint without loss of information. On the other hand, all these properties are a challenge when the densities need to be approximated with spline functions, including construction of the respective B-spline basis. The Bayes space methodology of density functions enables to express them as real functions in the standard L2 space using the clr transformation. The resulting functions possess the zero integral constraint. This is a key to propose a new B-spline basis, holding the same property, and consequently to build a new class of spline functions, called simplicial splines, which can approximate probability density functions in a consistent way. The contribution provides also construction of smoothing simplicial splines and possi!
  ble orthonormalization of the B-spline basis which might be useful in some applications. Finally, a concise analysis using simplicial splines is demonstrated with anthropometric data for the case of simplicial functional principal component analysis.
  
  Contact alessandra.menafoglio@polimi.it
  
• Stima del valore aggiunto di scuola: stato dell'arte del modello INVALSI e prospettive. Quali implicazioni di policy?
  Tommaso Agasisti, Politecnico di Milano
  mercoledì 3 aprile 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21
• On the modelling of particle and pedestrian motion with Fokker-Planck equations
  Alfio Borzì, University of Wuerzburg -Germania-
  giovedì 4 aprile 2019 alle ore 14:00, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
  ABSTRACT
  ABSTRACT
  

  Since the pioneering works of A. Einstein, M. von Smoluchowski, and P. Langevin, stochastic processes and the related Fokker-Planck equations have been used to model irregular motion in different situation. These equations are also considered to be adequate for modelling the motion of one pedestrian and of a crowd of people under certain circumstances. Therefore they can play a central role in the design of control strategies for different purposes as well as in the analysis and calibration of microscopic models of pedestrian interaction. The purpose of this talk is to review some mathematical results in this field, which includes different modelling issues concerning the optimal control of a single pedestrian subject to perturbation, the development of a new framework for pedestrians' avoidance dynamics based on the formulation of a Nash game, and a new approach to the analysis of superresolution 2D images of moving molecules on a cell membrane to obtain quantitative results on the organization of the membrane and on the interaction between the molecules.
  
  [1] M. Annunziato, A. Borzì, A Fokker-Planck control framework for stochastic systems, EMS Surveys In Mathematical Sciences, 5 (2018), 65-98.
  [2] M. Annunziato, A. Borzì, A Fokker-Planck control framework for multidimensional stochastic
  processes, Journal of Computational and Applied Mathematics, 237 (2013), 487-507.
  [3] S. Roy, A. Annunziato, A. Borzì, C. Klingenberg, A Fokker-Planck approach to control collective motion, Computational Optimization and Applications, 69 (2018), 423-459.
  [4] S. Roy, A. Annunziato, A. Borzì, A Fokker-Planck feedback control-constrained approach for modelling crowd motion, Journal of Computational and Theoretical Transport, 45 (2016), 442-458.
  [5] S. Roy, A. Borzì, A. Habbal, Pedestrian motion modelled by Fokker-Planck Nash games, Royal Society open science, 4, (2017) 170648-17.
  
  Contact: marco.verani@polimi.it
  
  
• Problemi di frontiera libera nelle scienze applicate
  Sandro Salsa, Politecnico di Milano
  mercoledì 10 aprile 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21
• Errori sistematici e confondimento degli studi osservazionali basati sui dati dal mondo reale
  Giovanni Corrao, Università degli Studi di Milano-Bicocca
  mercoledì 8 maggio 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21
• Inverse Problems in Adaptive Optics
  Ronny Ramlau, RICAM, Austrian Academy of Sciences, Linz, Austria
  mercoledì 8 maggio 2019 alle ore 14:00, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
  ABSTRACT
  ABSTRACT
  

  The image quality of ground based astronomical telescopes suffers from turbulences in the atmosphere. Adaptive Optics (AO) systems use wavefront sensor measurements of incoming light from guide stars to determine an optimal shape of deformable mirrors (DM) such that the image of the scientific object is corrected after reflection on the DM(s). The operation of the AO systems of the new generation of large astronomical telescopes under construction requires new mathematical methods that achieve reconstruction in real time. In the talk we will in particular focus on methods for wavefront reconstruction from pyramid sensor data and an analysis of the atmospheric tomography operator.
  
  Contact christian.vergara@polimi.it
  
• Forma e complessità in Natura: perché il mondo è matematico?
  Pasquale Ciarletta, Politecnico di Milano
  mercoledì 15 maggio 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21
• 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
• 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
• 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
  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
  

Seminari Passati

• L’avventura dell'infinitamente piccolo oltre il bosone di Higgs: LHC e i futuri super-acceleratori del CERN
  Lucio Rossi, CERN
  mercoledì 20 marzo 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21
• Il futuro dell'uomo nello Spazio: Marte prossima frontiera
  Luigi Bignami, Giornalista scientifico
  mercoledì 13 marzo 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21
• The SQRA Operator: Convergence Behaviour and Applications
  Martin Heida, Weierstrass Institute Berlin
  mercoledì 13 marzo 2019 alle ore 15:15 precise, Aula Seminari III piano
  ABSTRACT
  

  The Squareroot Approximation Operator (SQRA) is a numerical FV-operator that has recently been derived by M. Weber and coworkers and has the form of a discrete spatial chemical master equation. We use methods from stochastic homogenization to prove convergence in the context of high dimensional numerical implementation. We furthermore show that the SQRA is equivalent with the Scharfetter-Gummel scheme and use this insight to prove convergence of order 1 of both schemes in low dimensional settings. This is particularly possible due to a deep connection between the SQRA and the gradient structure of the Fokker-Planck equation discussed by Jordan, Kinderlehrer and Otto. We finally discuss physical implications of our insights and possible future applications to hydrodynamic limits arising in the modelling of organic semiconductors.
  ABSTRACT
• Lanford’s Theorem and the Emergence of Irreversibility
  Jos Uffink, University of Minnesota
  martedì 12 marzo 2019 alle ore 16:30 precise, Sala Consiglio, 7 piano, Ed. La Nave
  ABSTRACT
  

  It is a longstanding problem to show how the irreversible behaviour of macroscopic systems can be reconciled with the time-reversal invariance of these same systems when considered from a microscopic point of view. A theorem by Lanford shows that, under certain conditions, the famous Boltzmann equation, describing the irreversible behaviour of a dilute gas, can be obtained from the time-reversal invariant Hamiltonian equations of motion for the hard spheres model. This raises the question whether and how Lanford’s theorem succeeds in deriving this remarkable emergence of irreversibility. Many authors (Cercignani, Illner & Pulvirenti, 1994; Lebowitz 1983, Spohn 1991) have expressed very different views on this question. In this talk, I will argue that the theorem actually does not imply irreversibility at all.
  ABSTRACT
• Tame topology and algebraic geometry
  Bruno Klingler, Humboldt Universitaet Berlino
  lunedì 11 marzo 2019 alle ore 16:30 precise, Aula Seminari 6 piano, Ed. La Nave
  ABSTRACT
  

  In "Esquisse d'un programme" Grothendieck argues that general topology, which was developed for the needs of analysis, should be replaced by a "tame topology" if one wants to study the topological properties of natural geometric forms.
  Such a tame topology has been developed by model theorists under the name "o-minimal structures". The goal of this lecture will be to explain in simple topological terms the notion of o-minimal structure and its applications in algebraic geometry, in particular for studying periods of algebraic varieties.
  ABSTRACT
• Stochastic atomic congestion games:  Price-of-Anarchy and convergence for large games
  Roberto Cominetti, Universidad Adolfo Ibáñez
  venerdì 8 marzo 2019 alle ore 11:00, Sala del Consiglio 7° piano
  ABSTRACT
  

  We consider atomic congestion games with stochastic demand in which each player participates in the game with probability p, and incurs no cost with probability 1-p. For congestion games with affine costs, we  provide a tight upper bound for the Price-of-Anarchy as a function of p, which is monotonically increasing  and converges to the well-known bound of 5/2 when p converges 1. On the other extreme, for p? 1/4 the bound is constant and equal to 4/3 independently of the game structure and the number of players. For general costs we also analyze the asymptotic convergence of such games when the number of players n grows  to infinity but the probability tends to zero as $p_n=\lambda/n$, in which case we establish the convergence towards a Poisson limit game. In a different approach where the weight of the players tend to zero, we find that the limit yields a Wardrop equilibrium for a corresponding nonatomic game.
  ABSTRACT
• Optimization with expensive and uncertain data - challenges and improvements
  Coralia Cartis, Mathematical Institute, University of Oxford, UK
  giovedì 7 marzo 2019 alle ore 15:30, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
  ABSTRACT
  

  : Real-life applications often require the optimization of nonlinear functions with several unknowns or parameters - where the function is the result of highly expensive and complex model simulations involving noisy data (such as climate or financial models, chemical experiments), or the output of a black-box or legacy code, that prevent the numerical analyst from looking inside to find out or calculate problem information such as derivatives. Thus classical optimization algorithms, that use derivatives (steepest descent, Newton's methods) often fail or are entirely inapplicable in this context. Efficient derivative-free optimization algorithms have been developed in the last 15 years in response to these imperative practical requirements. As even approximate derivatives may be unavailable, these methods must explore the landscape differently and more creatively. In state of the art techniques, clouds of points are generated judiciously and sporadically updated to capture local geometries as inexpensively as possible; local function models around these points are built using techniques from approximation theory and carefully optimised over a local neighbourhood (a trust region) to give a better solution estimate.
  In this talk, I will describe our implementations and improvements to state-of-the-art methods. In the context of the ubiquitous data fitting/least-squares applications, we have developed a simplified approach that is as efficient as state of the art in terms of budget use, while achieving better scalability. Furthermore, we substantially improved the robustness of derivative-free methods in the presence of noisy evaluations. Theoretical guarantees of these methods will also be provided. Finally, despite derivative-free optimisation methods being able to only provably find local optima, we illustrate that, due to their construction and applicability, these methods can offer a practical alternative to global optimisation solvers, with improved scalability. This work is joint with Lindon Roberts (Oxford), Katya Scheinberg (Lehigh), Jan Fiala (NAG Ltd) and Benjamin Marteau (NAG Ltd).
  
  Contact: alfio.quarteroni@polimi.it
  
  ABSTRACT
• Testing families of analytic discs
  Luca Baracco, Università di Padova
  giovedì 7 marzo 2019 alle ore 14:30 precise, Aula seminari del 3 piano
  ABSTRACT
  

  
  It is a well-known fact in the theory of several complex variables that a function
  is holomorphic if and only if it is holomorphic in each variable separately. This
  result goes back to Hartogs. It is natural to consider a boundary version of Hartogs’ theorem. The general problem is to take a boundary function and ask if holomorphic extensions on some families of complex curves are enough to guarantee an extension which is holomorphic in all variables simultaneously.
  We will talk about the known results on the subject and show some new results obtained in collaboration with M. Fassina and S. Pinton for the spiecial case of the unit ball in C^n.
  ABSTRACT

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