### Seminari

### Prossimi Seminari

- Deep Learning meets Parametric Partial Differential Equations

Gitta Kutyniok, Institute of Mathematics, Technische Universität Berlin (DE)

giovedì 16 luglio 2020 alle ore 14:00, Online seminar: https://mox.polimi.it/elenco-seminari/?id_evento=1977&t=763724

### Seminari Passati

- 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 55ABSTRACTIn 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 MILANOABSTRACTAdvances 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° pianoABSTRACTIt 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 pianoABSTRACTIt 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/pABSTRACTL'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. - Control problems in Wasserstein space

Antonio Marigonda, University of Verona

lunedì 14 ottobre 2019 alle ore 15:15, Aula seminari 6° pianoABSTRACTIn this talk we present recent results about the existence and uniqueness of the viscosity solution for a certain classes on Hamilton-Jacobi Equations in the Wasserstein space of probability measure, arising in problem of mean field control of multi-agent systems. We consider a multi-agent system subject to a centralized controller

aiming to minimize a cost function. The microscopic dynamics of each agent is given by a differential inclusion. We model the distribution of agents by a probability measure, and formulate the minimization problem

as a Mayer problem for a dynamics in the Wasserstein space represented by a controlled continuity equation describing the macroscopical evolution of the system. We prove that the value function V of the

problem solves a Hamilton-Jacobi equation in the Wasserstein space in a suitable viscosity sense, and prove a comparison principle for such an equation, thus characterizing V as the unique viscosity solution of the

Hamilton-Jacobi equation associated to the problem. - How Mathematics helps structuring climate discussions

Rupert Klein, FU Berlin & ECMWF Fellow

giovedì 3 ottobre 2019 alle ore 14:00, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANOABSTRACTMathematics in climate research is often thought to be mainly a provider of techniques for solving the continuum mechanical equations for the flows of the atmosphere and oceans, for the motion and evolution of Earth's ice masses, and the like. Three examples will elucidate that there is a much wider range of opportunities. Climate modellers often employ reduced forms of the continuum mechanical equations to efficiently address their research questions of interest. The first example discusses how mathematical analysis can provide systematic guidelines for the regime of applicability of such reduced model equations. Meteorologists define 'climate', in a narrow sense, as the statistical description in terms of the mean and variability of relevant quantities over a period of time (World Meteorological Society, http://www.wmo.int; see the website for a broader sense definition). Now, climate researchers are most interested in changes of the climate over time, and yet there is no unique, well-defined notion of time dependent statistics. In fact, there are restrictive conditions which data from time series need to satisfy for classical statistical methods to be applicable. The second example describes recent developments of analysis techniques for time series with non-trivial temporal trends. Modern climate research has joined forces with economy and the social sciences to generate a scientific basis for informed political decisions in the face of global climate change. One major type of problems hampering progress of the related interdisciplinary research consists of often subtle language barriers. The third example describes how mathematical formalization of the notion of 'vulnerability' has helped structuring related interdisciplinary research efforts.

Contact: luca.bonaventura@polimi.it

This seminar is organized within the H2020-FETHPC-2016-2017 Research project ESCAPE-2 (Energy-efficient SCalable Algorithms for weather and climate Prediction at Exascale), that has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 800897.