Head of Dept: Prof. Giulio Magli
Vice-Head of Dept: Prof. Gabriele Grillo
Department Manager: Dr.ssa Franca Di Censo

### Seminars

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### Upcoming seminars

• 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
• Zero-dimensional symmetry, or locally profinite groups
George Willis, University of Newcastle, Australia
giovedì 21 novembre 2019 alle ore 16:00, Aula U5-3014 (Edificio 5, terzo piano) del Dipartimento di Matematica e Applicazioni dell'Università di Milano-Bicocca, in Via Cozzi 55
• 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
• Propagation of singularities for solutions to Hamilton-Jacobi equations
Piermarco Cannarsa, Università di Roma Tor Vergata
lunedì 2 dicembre 2019 alle ore 15:30, Sala Consiglio del 7 piano, Dipartimento di Matematica, Via Ponzio 31-33, Milano
• 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
• Explainability, intepretability and sensitivity analysis
Emanuele Borgonovo, Department of Decision Sciences, BIDSA, Bocconi University, Milano
venerdì 6 dicembre 2019 alle ore 14:30, Aula Saleri - VI piano
• The mysteries of L-values
Sarah Zerbes, University College London
martedì 10 dicembre 2019 alle ore 14:00, Sala di Rappresentanza, Dipartimento di Matematica, Via C. Saldini 50
• 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

### Past Seminars

• 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
• 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.
• 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.
• 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.
• Stochastic atomic congestion games:  Price-of-Anarchy and convergence for large games
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.
• 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