Direttore Vicario: Prof. Gabriele Grillo
Responsabile Gestionale: Dr.ssa Franca Di Censo

Seminari

 Selezionare una sezione Tutte Algebra e Informatica Teorica Analisi Analisi Numerica Calcolo delle variazioni Dipartimento FDS Finanza Quantitativa Fisica Matematica Geometria Lezioni Leonardesche Matematica Discreta MOX Probabilità Quantistica Probabilità e Statistica Matematica Seminario Matematico e Fisico Seminari di Cultura Matematica Tomografia e Applicazioni Parola da cercare

Prossimi Seminari

• A mathematical-physics approach to machine learning
Pierluigi Contucci, Dipartimento di Matematica Università di Bologna
giovedì 30 gennaio 2020 alle ore 14:00, Aula Saleri VI piano

Seminari Passati

• Sharp concentration estimates near criticality for sign-changing solutions of Dirichlet and Neumann problems
martedì 12 novembre 2019 alle ore 15:30, Aula seminari 3° piano
ABSTRACT
Consider the slightly subcritical problem $-\Delta u_\varepsilon = |u_\varepsilon|^{\frac{4}{n-2}-\varepsilon}u_\varepsilon$ either on $\mathbb{R}^n$ ($n\geq 3$) or in a ball $B$ satisfying Dirichlet or Neumann boundary conditions. For radial solutions, we provide sharp rates and constants describing the asymptotic behavior (as $\varepsilon\to 0$) of all local minima and maxima of $u_\varepsilon$ as well as its derivative at roots. As corollaries, we complement a known asymptotic approximation of the Dirichlet nodal solution in terms of a tower of bubbles and present a similar formula for the Neumann problem.
Moreover, we analyse the nonradial case with Neumann boundary conditions, namely the existence of least energy solutions and their dependence on the exponent $p$ up to the Sobolev critical exponent.
These are joint works with Alberto Saldaña and Massimo Grossi.
• 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
: 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

• 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
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.
• 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
• Regularity structures: from physics to probability, from analysis to algebra, from combinatorics to geometry
Lorenzo Zambotti, Sorbonne Université, Parigi
lunedì 28 ottobre 2019 alle ore 16:00, U3-07 dell'edificio U3 (piano terra, Piazza della Scienza), Università di Milano-Bicocca, in Via Cozzi 55
ABSTRACT
In this talk I wish to present some of the ideas at the heart of the theory of regularity structures (RS), introduced by Martin Hairer in 2014. RS are perhaps best described as a theory of Taylor expansions in a fractal (random) setting. I plan to show how this theory is based on a fascinating interplay between several different disciplines, as announced by my title.
• 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
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)