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

### Seminari Passati

• 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)
• Symmetry results for critical $p$-Laplace equations
Giulio Ciraolo, Università degli Studi di Milano
mercoledì 23 ottobre 2019 alle ore 15:15, Aula seminari 3° piano
ABSTRACT
It is known that positive solutions to $\Delta_p u + u^{p^*-1}=0$ in $\mathbb{R}^n$, with $n \geq 3$ and \$1
We provide a new approach to this problem which allows us to give a complete classification of the solutions in an anisotropic setting as well as to a suitable generalization of the problem in convex cones.

This is a joint work with A. Figalli and A. Roncoroni.
• Pricing and hedging in rough Heston models
Omar El Euch, Spire Europe Limited
martedì 22 ottobre 2019 alle ore 14:15, Aula seminari del terzo piano
ABSTRACT
It has been recently shown that rough volatility models, where the volatility is driven
by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and implied volatilities. However, due to the non-Markovian nature of the fractional Brownian motion, they raise new issues when it comes to derivatives pricing and hedging. Using an original link between nearly unstable Hawkes processes and fractional volatility models, we compute the characteristic function of the log-price in rough Heston models and obtain explicit hedging strategies. The replicating portfolios contain the underlying asset and the forward variance curve, and lead to perfect hedging (at least theoretically). From a probabilistic point of view, our study enables us to disentangle the infinite-dimensional Markovian structure associated to rough volatility models.
• L'interazione fra neuroscienze e matematica: analisi della connettività cerebrale utilizzando i grafi
Paolo Finotelli,  Politecnico di Milano
mercoledì 16 ottobre 2019 alle ore 15:30, Sala Consiglio - piano 7° - edificio 14 - via Ponzio 31/p
ABSTRACT
L'intento di questo seminario è mostrare come l'interazione fra le neuroscienze e la matematica sia in continua crescita e sia destinata a costituire la base della medicina moderna. In particolare, verranno introdotti i fondamenti della connettività cerebrale e della teoria delle reti complesse, di cui la teoria dei grafi costituisce l’impalcatura matematica. Come caso particolare verrà presentato un recente modello per la determinazione della connettività cerebrale basato sulla teoria dei grafi.