27 Marzo, 2019 12:15

Seminari di Cultura Matematica

Laser "su misura" per il trattamento di tumori

Paola Saccomandi, Politecnico di Milano

Politecnico di Milano Campus Bonardi Edificio14 aula B21

20 Marzo, 2019 12:15

Seminari di Cultura Matematica

L’avventura dell'infinitamente piccolo oltre il bosone di Higgs: LHC e i futuri super-acceleratori del CERN

Lucio Rossi, CERN

Politecnico di Milano Campus Bonardi Edificio14 aula B21

13 Marzo, 2019 12:15

Seminari di Cultura Matematica

Il futuro dell'uomo nello Spazio: Marte prossima frontiera

Luigi Bignami, Giornalista scientifico

Politecnico di Milano Campus Bonardi Edificio14 aula B21

13 Marzo, 2019 15:15 oclock

Sezione di Fisica Matematica

The SQRA Operator: Convergence Behaviour and Applications

Martin Heida, Weierstrass Institute Berlin

Aula Seminari III piano

abstract

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.

12 Marzo, 2019 16:30 oclock

Seminario Matematico e Fisico di Milano

Lanford’s Theorem and the Emergence of Irreversibility

Jos Uffink, University of Minnesota

Sala Consiglio, 7 piano, Ed. La Nave

abstract

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.

11 Marzo, 2019 16:30 oclock

Seminario Matematico e Fisico di Milano

Tame topology and algebraic geometry

Bruno Klingler, Humboldt Universitaet Berlino

Aula Seminari 6 piano, Ed. La Nave

abstract

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.

8 Marzo, 2019 11:00

Sezione di Analisi

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

Roberto Cominetti, Universidad Adolfo Ibáñez

Sala del Consiglio 7° piano

abstract

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.

7 Marzo, 2019 15:30

MOX Colloquia

Optimization with expensive and uncertain data - challenges and improvements

Coralia Cartis, Mathematical Institute, University of Oxford, UK

Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

abstract

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

Coralia Cartis (BSc Mathematics, Babesh-Bolyai University, Romania; PhD Mathematics, University of Cambridge) has joined the Mathematical Institute at Oxford University in 2013 as Associate Professor in numerical optimization. Previously, she worked as a research scientist in numerical analysis at Rutherford Appleton Laboratory, and assistant professor in the School of Mathematics, University of Edinburgh. Since 2016, she is also a Turing Fellow at the Alan Turing Institute (UK’s national institute for data science), London. Her research addresses the development and analysis of algorithms for solving difficult optimization problems - nonconvex, with and without derivatives, local and global. She has also worked on compressed sensing and parameter estimation for climate modelling.

7 Marzo, 2019 14:30 oclock

Sezione di Geometria, Algebra e loro applicazioni

Testing families of analytic discs

Luca Baracco, Università di Padova

Aula seminari del 3 piano

abstract

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.

Coralia Cartis (BSc Mathematics, Babesh-Bolyai University, Romania; PhD Mathematics, University of Cambridge) has joined the Mathematical Institute at Oxford University in 2013 as Associate Professor in numerical optimization. Previously, she worked as a research scientist in numerical analysis at Rutherford Appleton Laboratory, and assistant professor in the School of Mathematics, University of Edinburgh. Since 2016, she is also a Turing Fellow at the Alan Turing Institute (UK’s national institute for data science), London. Her research addresses the development and analysis of algorithms for solving difficult optimization problems - nonconvex, with and without derivatives, local and global. She has also worked on compressed sensing and parameter estimation for climate modelling.

5 Marzo, 2019 12:30 oclock

Sezione di Finanza Quantitativa

The Value of Informational Arbitrage

Claudio Fontana, Università degli Studi di Padova

Aula Seminari al Terzo Piano

abstract

abstract

In the context of a general semimartingale model, we aim at answering the following question: How much is an investor willing to pay for learning some inside information that allows to achieve arbitrage? If such a value exists, we call it the value of informational arbitrage. In particular, we are interested in the case where the inside information yields arbitrage opportunities but not unbounded profits with bounded risk. In the spirit of Amendinger et al. (2003), we provide a general answer to this question by means of an indifference valuation approach. To this effect, we establish some new results on models with additional information and study optimal investment-consumption problems in the presence of additional information and arbitrage, also allowing for the possibility of leverage. We characterize when the value of informational arbitrage is universal, in the sense that it does not depend on the preference structure. This talk is based on joint work with H.N. Chau and A. Cosso.

Coralia Cartis (BSc Mathematics, Babesh-Bolyai University, Romania; PhD Mathematics, University of Cambridge) has joined the Mathematical Institute at Oxford University in 2013 as Associate Professor in numerical optimization. Previously, she worked as a research scientist in numerical analysis at Rutherford Appleton Laboratory, and assistant professor in the School of Mathematics, University of Edinburgh. Since 2016, she is also a Turing Fellow at the Alan Turing Institute (UK’s national institute for data science), London. Her research addresses the development and analysis of algorithms for solving difficult optimization problems - nonconvex, with and without derivatives, local and global. She has also worked on compressed sensing and parameter estimation for climate modelling.