# Blog de la Biblioteca de Matemàtiques i Informàtica

## SIMBa: Restricted and unrestricted weak type operators on Lorentz spaces

Dilluns, 16 de juny, se celebrarà una nova sessió del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Tommaso Bruno
Universitat: Università degli Studi di Milano-Bicocca /UB

Data: dilluns, 16 de juny de 2014
Hora: 17:45, cafè; 18:00, inici. 19:00: Assemblea. 19:30: Inici preparatius sopar de germanor.
Lloc: Aula IMUB (al terrat), Facultat de Matemàtiques de la Universitat de Barcelona.

Títol: Restricted and unrestricted weak type operators on Lorentz spaces.
Resum: Many important operators in harmonic analysis are not bounded when acting between certain function spaces, and only satisfy a boundedness inequality if restricted to characteristic functions of measurable sets. We shall study when this restricted property is equivalent to a stronger type of boundedness of the operator. Lorentz spaces arise as the natural context for these problems and a brief introduction will be worthwhile; we will also show that the measure space on which they are considered strongly influences the behaviour of the operator. In particular, we shall focus on restricted weak type (1,1) that turns out to be the critical and most interesting case. Many positive and few negative results have been proved but in some situations optimal conditions are still unknown. In the hope of receiving useful suggestions, some open questions will be presented at the end.

Anunci especial: Recordem que en acabar el seminari farem el sopar de final de curs.

Si voleu rebre informació dels propers seminaris us podeu subscriure a la llista de correu. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.

## SIMBa: Resonant dynamics of Trojan exoplanets

Dilluns, 26 de maig, se celebrarà una nova sessió del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Rocío-Isabel Paez
Universitat: Università degli Studi di Roma Tor Vergata (Dip. di Matematica)

Data: dilluns, 26 de maig de 2014
Hora: 17:45, cafè; 18:00, inici
Lloc: Aula IMUB (al terrat), Facultat de Matemàtiques de la Universitat de Barcelona.

Títol: Resonant dynamics of Trojan exoplanets.
Resum: In this talk, I will present some recent results regarding the resonant structure as well as the stability and long term diffusion  phenomena for hypothetical Trojan companions to giant exoplanets. In particular, I will discuss a theoretical formalism appropriate for the study of secondary resonances in the space of proper elements (actions), defined for tadpole motions. I will also introduce some numerical results obtained within the framework of the elliptic restricted three body problem using:

• FLI stability maps and
• integrations of ensembles of orbits within the web of secondary resonances.

Si voleu rebre informació dels propers seminaris us podeu subscriure a la llista de correu. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.

## SIMBa: Asteroids: Fear and lure of rocks of outer space

Dilluns, 12 de maig, se celebrarà una nova sessió del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Joan-Pau Sánchez
Universitat: Department de Matematica aplicada I, (Universitat Politèecnica de Catalunya).

Data: dilluns, 12 de maig de 2014
Hora: 17:45, cafè; 18:00, inici
Lloc: Aula IMUB (al terrat), Facultat de Matemàtiques de la Universitat de Barcelona.

Títol: Asteroids: Fear and lure of rocks of outer space.
Resum: As remnants of the formation of our solar system, asteroids and comets provide a precious opportunity to unveil the mysteries of the solar system formation, evolution and composition. More recently, however, the airburst over the Russian city of Chelyabinsk has reminded us that these small objects hit the Earth periodically. Asteroid impacts range from mass extinction events such as the Cretacious-Terciary impact that resulted on the extinction of the dinosaurs, to much more modest impacts such as the Chelyabinsk meteor. As of late, there has also been a lot of speculation about the riches held by these objects. Some argue, for example, that a an orbital neighbour such as 3554 Amun, a2.5 km wide metallic asteroid, contains resources valued in \$20 trillion dollars in Earth’s commodity markets. Among all the asteroid population, near Earth objects, such as 3554 Amun, are of particular interest because they can be easily reached from Earth, many being even easier to reach than the Moon.
This presentation will rst explore the fear of rocks of outer space by discussing impact risk and current technological capability to mitigate this risk by de ecting an asteroid from its Earth impacting trajectory. However this capability to nudge away asteroids from their original trajectories for planetary defence, bring as a consequence the realisation that
asteroids’ orbit may potentially be modi ed to serve other purposes, such as space science or resource exploitation. Hence, secondly, the presentation will explore the potential for asteroid retrieval missions enabled by invariant manifold dynamics. An asteroid retrieval mission envisages a spacecraft that rendezvous with an asteroid, lassos it and then hauls it back to Earth neighbourhood. This type of mission, albeit arguably ambitious, is now receiving serious consideration by NASA, and 105 million dollars have been dedicated solely to this mission concept in FY 2014.

Si voleu rebre informació dels propers seminaris us podeu subscriure a la llista de correu. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.

## SIMBa: A Note on Mixed Norm Spaces

Aui, 7 d’abril, se celebrarà una nova sessió del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Universitat: Department de Matematica Aplicada i Anàlisi, (Universitat de Barcelona)

Data: dilluns, 28 d’abril de 2014
Hora: 17:45, cafè; 18:00, inici
Lloc: Aula IMUB (al terrat), Facultat de Matemàtiques de la Universitat de Barcelona.

Títol: A Note on Mixed Norm Spaces
Resum:  Estimates on mixed norm spaces already appeared in the works of Gagliardo and Nirenberg, to prove an endpoint case of the classical Sobolev embeddings. However, a more systematic approach to these spaces was fi rst shown explicitly by Fournier.
Our main goal in this talk is to further improve the mixed norm estimates due to Fournier to more general rearrangement invariant (r.i.) spaces. In particular we find the optimal domains and the optimal ranges for these embeddings between mixed norm spaces and r.i. spaces.

Si voleu rebre informació dels propers seminaris us podeu subscriure a la llista de correu. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.

## SIMBa: Stochastic Differential Equations

Dilluns, 7 d’abril, se celebrarà una nova sessió del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: David Ruiz
Universitat: Universitat d’Oslo (Department of Mathematics)

Data: dilluns, 7 d’abril de 2014
Hora: 17:45, cafè; 18:00, inici
Lloc: Aula IMUB (al terrat), Facultat de Matemàtiques de la Universitat de Barcelona.

Títol: Stochastic Differential Equations.
Resum: In this talk we want to explain what a stochastic differential equation (SDE) is. As an idea, we will recall what a (deterministic) ordinary differential equation (ODE) is and then we will add some “noise” to it. Such equations are widely used to study and model phenomena in nature such as for instance: the “random” movement of a particle in a fluid due to collisions with the molecules of the fluid, variable uncertainty, macroeconomic dynamics, etc. The solution of an SDE is therefore a stochastic process, i.e. think of it as a function whose image is not a real number, but a random variable. It is a big area of research to study the solutions of SDE’s and the densities of such solutions. It is very difficult to say something about the densities.

An SDE looks typically like

$dx(t) = f(t,x(t))dt + "noise", t_0\leq t \leq a, x(t_0)=x_0\in \mathbb{R}$

where the initial condition $x(t_0)=x_0$ is typically taken as a deterministic point $x_0 \in \mathbb{R}$ that we have observed or might also be taken as $x(t_0) = Z$ where $Z$ is a random variable (e.g. normal distributed).

Finally, we will mention some properties of SDE’s, like… For example, you know that the solution when $f$ is Lipschitz exists and it is unique for ODE’s (Picard’s theorem). In the case of SDE’s even if $f$ is very “ugly” a unique solution also exists! Meaning that, the “noise” somehow regularizes $x(t)$.

Si voleu rebre informació dels propers seminaris us podeu subscriure a la llista de correu. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.

## SIMBa: About the decomposition of pricing formulas under stochastic volatility models

Dilluns, 31 de març, se celebrarà una nova sessió del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Raúl Merino
Universitat: Universitat de Barcelona (Departament de Probabilitat, Lògica i Estadística)

Data: dilluns, 17 de març de 2014
Hora: 17:45, cafè; 18:00, inici
Lloc: Aula IMUB (al terrat), Facultat de Matemàtiques de la Universitat de Barcelona.

Títol: About the decomposition of pricing formulas under stochastic volatility models.
Resum: We compute a decomposition of a call option price using three different methods: classical Itô calculus, functional Itô calculus and Malliavin calculus. We notice that solving the problem using the techniques based on classical Itô calculus is equivalent to use the functional Itô calculus. In addition, we give expressions for the implied volatility in the three cases.

Si voleu rebre informació dels propers seminaris us podeu subscriure a la llista de correu. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.

## SIMBa: On non-reducible quasi-periodic skew-products

Dilluns, 17 de març, se celebrarà una nova sessió del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Marc Jorba Cuscó
Universitat: Universitat de Barcelona (Departament de Matemàtica Aplicada i Anàlisi)

Data: dilluns, 17 de març de 2014
Hora: 17:45, cafè; 18:00, inici
Lloc: Aula IMUB (al terrat), Facultat de Matemàtiques de la Universitat de Barcelona.

Títol: On non-reducible quasi-periodic skew-products.
Resum: Recall that Floquet’s Theorem states that a linear differential equation with periodic coefficients can be reduced, by means of a periodic change of variables, to a system with constant coefficients. The issue of reducibility can be extended to the discrete setting. We will talk about reducibility on dimension two of quasi-periodic linear skew-products and introduce examples where there are topological obstructions to this reducibility. Furthermore, one may ask if reducibility is just an algebraic impediment or if it has a visible impact in dynamics. We will also explore this question and see, for a particular example, that, indeed, non-reducibility can bring out strange behaviors that do not appear in reducible cases.

Si voleu rebre informació dels propers seminaris us podeu subscriure a la llista de correu. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.