20 Novembre, 2024 15:00

Seminari FDS

Archimede, l'arte della misura

Marco Andreatta, Università di Trento

Aula Laboratorio FDS - tiny.cc/zoomfds

abstract

abstract

Misurare lo spazio è cruciale per il nostro processo di conoscenza. Archimede è un pioniere della geometria, nella sua accezione più letterale di «misura della terra». Primo nel misurare enti curvi nello spazio e nel calcolare la superficie della sfera, fu geniale nel metodo, che affascinò tutti i grandi protagonisti della scienza moderna: da Galileo che ne riprenderà le dimostrazioni con una sensibilità nuova, a Gauss che ne estende i calcoli con conseguenze mirabolanti, fino a Einstein che con la sua equazione di campo scopre una delle formule più famose della storia del pensiero scientifico, un'espressione che può essere pensata come la versione contemporanea della formula di Archimede.

18 Novembre, 2024 11:00 in punto

Sezione di Geometria, Algebra e loro applicazioni

Partitions, motives and Hilbert schemes

Sergej Monavari, EPFL Lausanne

Aula seminari III piano

abstract

abstract

Counting the number of higher dimensional partitions is a hard classical problem. Computing the motive of the Hilbert schemes of points is even harder. I will discuss some structural formulas for the generating series of both problems, their stabilisation properties when the dimension grows very large and how to apply all of this to obtain (infinite) new examples of motives of singular Hilbert schemes. This is joint work with M. Graffeo, R. Moschetti and A. Ricolfi.

15 Novembre, 2024 10:00

Sezione di Analisi

On well-posedness of systems arising from fluid dynamics

Danica Basaric, Politecnico di Milano

Aula Seminari - III Piano

abstract

abstract

Well-posedness of systems describing the motion of compressible fluids in the class of strong and weak solutions represents one of the most challenging problems of the modern theory of PDEs. In the first part of the talk, we are going to define and construct a larger class of solutions, the measure-valued and dissipative ones, which unable us to handle the problem of existence for large times and large initial data; we will also discuss the possible advantages of considering this weaker notion of solution when solving some related problems arising from fluid dynamics. In the second part of the talk, we are going to show that, by performing a suitable selection, it is possible to select one "good" solution satisfying the semigroup property, even in the context when the system lacks uniqueness. After showing this procedure in an abstract setting, we will apply it to specific systems, such as the compressible Euler and Navier-Stokes ones.

13 Novembre, 2024 11:00

Sezione di Finanza Quantitativa

Continuous-time persuasion by filtering

Ofelia Bonesini, London School of Economics

Aula III piano

abstract

abstract

We frame dynamic persuasion in a partial observation stochastic control game with an
ergodic criterion. The receiver controls the dynamics of a multidimensional unobserved state process. Information is provided to the receiver through a device designed by the sender that generates the observation process.
The commitment of the sender is enforced and an exogenous information process outside the control of the sender is allowed. We develop this approach in the case where all dynamics are linear and the preferences of the receiver are linear-quadratic.
We prove a verification theorem for the existence and uniqueness of the solution of the HJB equation satisfied by the receiver’s value function. An extension to the case of persuasion of a mean field of interacting receivers is also provided. We illustrate this approach in two applications: the provision of information to electricity consumers with a smart meter designed by an electricity producer; the information provided by carbon footprint accounting rules to companies engaged in a best-in-class emissions reduction effort. In the first application, we link the benefits of information provision to the mispricing of electricity production. In the latter, we show that when firms declare a high level of best-in-class target, the information provided by stringent accounting rules offsets the Nash equilibrium effect that leads firms to increase pollution to make their target easier to achieve.
This is a joint work with Prof. René Aïd, Prof. Giorgia Callegaro and Prof. Luciano Campi.

Ofelia is the recipient of the 2023 Bruti Liberati prize for the best Phd thesis in mathematical finance

13 Novembre, 2024 11:30 in punto

Sezione di Fisica Matematica

Uniqueness of KMS States for Quantum and Classical Models within the Framework of Berezin Quantization

Lorenzo Pettinari, Università di Trento

Aula seminari MOX VI piano

abstract

abstract

Strict (C*-algebraic) deformation quantization is a rigorous approach to both the quantization process of classical theories and to the precise description of the classical limit problem for
quantum theories. In this talk, we will show how this framework can be adapted to the study of algebras associated with infinite lattices, which are used for the description of thermodynamic limits of physical theories. Subsequently, we will see that, within this setting, quantum KMS states can have a definite classical limit in terms of classical KMS states. Finally, we will focus on proving, in the specific case of a Berezin-Toeplitz quantization on the two sphere, a uniqueness condition for quantum KMS states, which only depends on the properties of the, quantized, classical theory. The proof of the latter result is partly inspired by the works of Bratteli and Robinson, but adapted for our setting with the use of the SU(2) group structure. (Joint work with N. Drago and C. van de Ven)

Ofelia is the recipient of the 2023 Bruti Liberati prize for the best Phd thesis in mathematical finance

7 Novembre, 2024 15:30 in punto

Sezione di Geometria, Algebra e loro applicazioni

Secondary fans of hypersimplices

Laura Casabella, Max Planck Institute Leipzig

Aula seminari III piano

abstract

abstract

The secondary fan of a polytope stratifies the regular subdivisions of the polytope and provides a combinatorial framework to understand them. We compute this fan for specific polytopes, namely the hypersimplices (2,7) and (3,6). In this case, there are connections to tropical geometry, matroid theory and finite metric spaces. We also find new families of rays of the secondary fan of general hypersimplices.
This is joint work with Michael Joswig and Lars Kastner.

Ofelia is the recipient of the 2023 Bruti Liberati prize for the best Phd thesis in mathematical finance

6 Novembre, 2024 14:30

MOX Seminar

Estimation of passive and active biomechanical parameters in cardiac models using physics-informed neural networks

Federica Caforio, University of Graz, Medical University of Graz, BioTechMed-Graz, Austria

Aula Saleri

abstract

abstract

Biophysical models of cardiac function are gaining traction due to their ability to predict patient outcomes and optimise treatment strategies. Accurately calibrating the parameters of these models is essential for a detailed understanding of myocardial function, but it remains challenging in clinical practice. This seminar investigates a novel approach [1] that combines physics-informed neural networks [2] with advanced three-dimensional nonlinear cardiac biomechanical models to reconstruct displacement fields and estimate patient-specific biophysical properties, such as passive stiffness and active contractility. A key feature of the proposed learning algorithm is that it solely relies on displacement and strain data routinely obtained in clinical settings. Benchmark tests demonstrate the method’s accuracy, robustness, and its potential to efficiently estimate patient-specific biophysical parameters in nonlinear, time-dependent biomechanical models. This approach opens up new possibilities for detecting and characterising tissue inhomogeneities, such as fibrotic regions, and could drastically improve the diagnosis and treatment planning of cardiac conditions.

[1] Caforio, F., Regazzoni, F, Pagani, S., Karabelas, E., Augustin, C., Haase, G., Plank, G. and Quarteroni, A. (2023). Physics-informed neural network estimation of material properties in soft tissue nonlinear biomechanical models. Computational Mechanics, pp.1-27.

[2] Raissi, M., Perdikaris, P., and Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378:686-707.

Contatti:
stefano.pagani@polimi.it
francesco.regazzoni@polimi.it

Ofelia is the recipient of the 2023 Bruti Liberati prize for the best Phd thesis in mathematical finance

5 Novembre, 2024 14:00

MOX Seminar

A non-iterative domain decomposition time integrator for the linear wave equation

Tim Buchholz, KIT - Karlsruhe Institute of Technology, Germany

Aula Saleri

abstract

abstract

In this talk we will motivate, construct and analyze a non-iterative domain decomposition time integrator for the linear wave equation. The central concept involves combining an implicit solution step on spatial subdomains with a cost-effective, yet precise, local, explicit prediction step. In that sense the method is similar to methods from Blum, Lisky and Rannacher or Dawson and Dupont, which have been designed mainly for parabolic problems. While the locality of the prediction combined with the decomposition into subdomains allows for parallelization across space, the scheme progresses sequentially through time. However, unlike similar methods, this time stepping is only performed once, without any iterations involved. We show that the scheme achieves second-order convergence in time and conclude the presentation with some words on its parallel implementation and numerical experiments.

The talk is based on joint work with Marlis Hochbruck. Funded by the Deutsche Forschungs-gemeinschaft (DFG, German Research Foundation) — Project-ID 258734477 — CRC 1173.

Contatti:
gabriele.ciaramella@polimi.it
ilario.mazzieri@polimi.it

Ofelia is the recipient of the 2023 Bruti Liberati prize for the best Phd thesis in mathematical finance

30 Ottobre, 2024 14:00 in punto

Sezione di Fisica Matematica

Semi-classical measures, two scale semi-classical measures and applications

Clotilde Fermanian Kammerer, Université d'Angers

Sala Consiglio, VII piano

abstract

abstract

In this lecture, we will present semi-classical measures and show how they describe the obstructions to strong convergence of bounded families of square integrable functions.
We will also describe applications for families of solutions to PDEs, in particular to wave equations.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

Ofelia is the recipient of the 2023 Bruti Liberati prize for the best Phd thesis in mathematical finance

30 Ottobre, 2024 15:00

Sezione di Analisi

A general integral identity with applications to a reverse Serrin problem

Riccardo Molinarolo, Università degli Studi del Piemonte Orientale "A. Avogadro"

Aula Seminari - III Piano

abstract

abstract

The talk aims to present a new general differential identity and an associated integral identity, which entails a pair of solutions of the Poisson equation with constant source term. This generalizes a formula that R. Magnanini and G. Poggesi previously proved and used to obtain quantitative estimates of spherical symmetry for the Serrin overdetermined boundary value problem.
As a first application of this new general differential identity, we prove a quantitative symmetry result for the ``reverse Serrin problem'', which we will introduce. In passing, we obtain a rigidity result for solutions of the aforementioned Poisson equation subject to a constant Neumann condition. This is a joint work with R. Magnanini and G. Poggesi.

Ofelia is the recipient of the 2023 Bruti Liberati prize for the best Phd thesis in mathematical finance