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

• 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
• The LLV decomposition for hyper-Kaehler cohomology
Radu Laza, Stony Brook
venerdì 12 luglio 2019 alle ore 14:30, Sala di Rappresentanza, Via C. Saldini 50
ABSTRACT
Looijenga—Lunts and Verbitsky (LLV) have shown that the cohomology of
a compact hyper-Kaehler manifold admits the action of a big Lie
algebra g, generalizing the usual sl(2) Hard Lefschetz action. We
compute the LLV decomposition of the cohomology for the known classes
of hyper-Kaehler manifolds (i.e. K3^n, Kim_n, OG6, and OG10). As an
application, we easily recover the Hodge numbers of the exceptional
example OG10. In a different direction, we establish the so-called
Nagai’s conjecture (on the nilpotency index for higher degree
monodromy operators) for the known cases. More interestingly, based
on the known examples, we conjecture a new restriction on the
cohomology of compact hyper-Kaehler manifolds, which in particular
implies the vanishing of the odd cohomology as soon as the second
Betti number is large enough relative to the dimension.
This is joint work with M. Green, Y. Kim, and C. Robles.
• Preconditioning of multiphysics problems with applications to the biomechanics of the brain
Kent - Andre Mardal, University of Oslo and Simula Research Laboratory
giovedì 11 luglio 2019 alle ore 14:00, Aula consiglio VII piano, Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT
In this talk we will discuss preconditioning algorithms for monolithic schemes of coupled problems involving the coupling of porous and viscous flow as well as fluid-structure interaction and dimension reduction problems.
We explore how fractional Laplacian solvers may be utilized to obtain parameter robust schemes. The schemes are discussed in the context of biomechanical modelling of the waste clearance processes in the brain that is believed to fail in various forms of dementia such as Alzheimer's and Parkinson's diseases.

Contact: paolo.zunino@polimi.it