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

• Control problems in Wasserstein space
Antonio Marigonda, University of Verona
lunedì 14 ottobre 2019 alle ore 15:15, Aula seminari 6° piano
ABSTRACT
In 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 MILANO
ABSTRACT
Mathematics 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.
• Mountain pass structure, non-degeneracy conditions and variational gluing
Paul H. Rabinowitz, University of Wisconsin, Madison
venerdì 20 settembre 2019 alle ore 14:00, Sala di Rappresentanza, Via C. Saldini 50
ABSTRACT
The effect of non-degeneracy conditions on the applicability of variational gluing arguments for some variational problems possessing mountain pass structure will be discussed.

• Decay and Sobolev regularity properties for solutions at infinity of (nonlinear) PDEs
Stefano Pigola, Università dell’Insubria
venerdì 20 settembre 2019 alle ore 11:15, Aula seminari 3° piano
ABSTRACT
I will present some recent results on the global behaviour of nonnegative and bounded subsolutions of $\Delta_p u = f(u)$ over an exterior domain of a complete Riemannian manifold. I shall discuss geometric conditions under which such a subsolution decays to zero at infinity. The main tools are represented by (a nonlinear version of) the Feller property and some global comparison results. These, in turn, are related to a new characterization of the ($p$-)stochastic completeness of the manifold in terms of the Sobolev space $W^{1,p}$.
• Algebraic Option Pricing
Peter Carr, New York University
venerdì 13 settembre 2019 alle ore 12:15, Sala Consiglio settimo piano
ABSTRACT
Optionality arises whenever an investor can choose between owning either of two
assets. We treat the value of optionality as a modified sum. We then explore
options on options as sums of sums. This viewpoint allows us to derive a simple
closed form formula for a Bermudan option.
• Stability of some coupled partial differential equations in both bounded and unbounded domains
Abdelaziz Soufyane, University of Sharjah
giovedì 12 settembre 2019 alle ore 15:15, Aula seminari 3° piano
ABSTRACT
This talk deals with some recent results on the stability of a coupled partial differential equations. We will present the energy decay rates for many systems (arising in many applications) in the bounded domain, different approaches will be used to establish the energy decay. Also, we will discuss the rate decay for some models in the unbounded domain using the Fourier transformation, the multipliers techniques in Fourier image. We conclude our talk by giving some remarks and open problems.

This seminar is organized within the PRIN 2017 Research project «Direct and inverse problems for partial differential equations: theoretical aspects and applications» Grant Registration number 201758MTR2, funded by MIUR - Project coordinator Prof. Filippo Gazzola
• Curve di Osgood
Aljosa Volcic, Università della Calabria
giovedì 12 settembre 2019 alle ore 11:00 precise, Dipartimento di Matematica - 7° piano, Politecnico di Milano
ABSTRACT
La conferenza sarà dedicata a due argomenti vicini al classico argomento del teorema di Cantor sulla corrispondenza biunivoca (che non può essere continua) tra $[0,1]$ e $[0,1]^2$ ed alla curva di Peano.

Principalmente si parlerà di curve create nel 1903 da William F. Osgood il quale costruì, per ogni $\beta \in ]0,1[$ una curva iniettiva la cui immagine ha area $\beta$.
Si farà una breve storia di altre costruzioni analoghe, dedicandosi in particolare all'ultima di esse, dovuta a Karl Stromberg e Shiojenn Tseng.
In conclusione verrà presentata la dimostrazione dell'esistenza di una curva iniettiva definita su $]0,1[$ la cui immagine ha misura di Lebesgue bidimensionale uguale a $1$.
• Complexity in biomedicine
Caterina La Porta, Università degli Studi di Milano
giovedì 18 luglio 2019 alle ore 10:00, Dipartimento di Matematica - 7° piano, Politecnico di Milano
ABSTRACT
In this talk, I will discuss our recent advances in understanding phenotypic plasticity of cancer cells using a combination of experiments, analysis of big data and computational models of complex regulatory networks. Next, I will discuss our results on protein aggregation in neurodegenerative pathologies, such as Alzheimer's and Huntington's disease.

In particular, I will report on the importance of protein clearance from the endoplasmic reticulum to drive protein aggregation and on our recent results on huntingtin heterogenous aggregation in which mutated forms of the protein are able to form oligomers with non-mutated forms.

Contacts: paolo.finotelli@polimi.it
paolo.dulio@polimi.it