Seminario Dottorato: An introduction to stochastic ergodic control

Wednesday 15 January 2014, h. 15:15, room 1BC45
Marco Cirant (Padova - Dip. Mat.)
"An introduction to stochastic ergodic control"

Abstract
In this talk we give an introduction to stochastic ergodic control problems, where an agent aims at minimizing a long-time average cost by controlling his own state.
We will show, through a toy example, the main features of the problem and how it is possible to produce an optimal control by solving a suitable elliptic nonlinear partial differential equation.
In the final part of the talk we will explore briefly how the minimization problem for a single agent can be considered more in general for a continuum of identical agents. This research field is called Mean Field Games and has attracted the experts' attention in the last ten years.

Seminario Dottorato: An introduction to the Clemens-Schmid exact sequence

Wednesday 18 December 2013, h. 14:30, room 2BC30
Genaro Hernandez Mada (Padova - Dip. Mat.)
"An introduction to the Clemens-Schmid exact sequence"

Abstract
In this talk, we give a very elementary introduction to the Clemens-Schmid exact sequence. In a classical setting, this is a topological result about certain families of complex varieties or manifolds. Therefore, the purpose of the talk is to explain all the concepts involved.
If time allows, we will introduce the elements to understand in which cases we can obtain an arithmetic version of this result.

Rif. int. C. Marastoni, T. Vargiolu

Seminario Dottorato: Some applications of potential theory to Markov chains

Wednesday 4 December 2013, h. 14:30, room 2BC30
Alessandra Bianchi (Padova - Dip. Mat.)
"Some applications of potential theory to Markov chains"

Abstract
The link between potential theory and probability started in the last century with the work of Kakutani concerning the analysis of the Dirichlet problem. Since then, this connection has been explored by many authors and it has found applications in different contexts of probability.
In this talk I will review some of these classical results and focus on applications to Markov chains.

Rif. int. C. Marastoni, T. Vargiolu

Seminario Dottorato: What is a Hopf algebra?

Wednesday 20 November 2013, h. 14:30, room 2BC30
Nicolas Andruskiewitsch (Univ. Cordoba - Argentina)
"What is a Hopf algebra?"

Abstract
I will explain from scratch the notion of Hopf algebra, how and when it appeared, the basic examples and some applications.

Rif. int. C. Marastoni, T. Vargiolu

Seminario Dottorato: Option pricing in a defaultable model: a characteristic function approach

Wednesday 6 November 2013 h. 14:30, room 2BC30
Stefano Pagliarani (Dip. Mat. - Padova)
"Option pricing in a defaultable model: a characteristic function approach"

Abstract
We consider a defaultable stock (i.e. a financial risky asset) whose predefault dynamics follows a stochastic differential equation driven by a Levy process. Under suitable assumptions on the default time, the price of a contingent claim (i.e. a financial derivative) is obtained in terms of the characteristic function (i.e. the Fourier transform) of the terminal log price. We characterize it as the solution of a complex valued infinite dimensional system of first order ordinary differential equations, which can be seen as an ordinary differential equation in a suitably chosen Banach space. By using this, we provide an explicit eigenfunction expansion for the characteristic function and use it to price contingent claims by means of standard Fourier inversion techniques. Finally, we present numerical results to demonstrate accuracy and efficiency of the method.

Rif. int. C. Marastoni, T. Vargiolu

Seminario Dottorato: An overview on the complex Monge-Ampere equation

Wednesday 23 October 2013 h. 15:00, room 2BC30
Ly Kim Ha (Dip. Mat. - Padova)
"An overview on the complex Monge-Ampere equation"

Abstract
In this seminar we present a tutorial on the Dirichlet problems for the complex Monge-Ampere equation.
After a large initial part devoted to a general introduction to the subject, we shall briefly concentrate on the study of Holder continuity of the solutions, showing how it can be handled for classical complex domains and also for some domains where the classical regularity properties fail to be true.

Rif. int. C. Marastoni, T. Vargiolu

Seminario Dottorato: An introduction to Ramification Theory for Number Fields

Wednesday 19 June 2013 h. 15:00, room 2BC60
Sophie Marques (Padova, Dip. Mat. and Bordeaux)
"An introduction to Ramification Theory for Number Fields"

Abstract
The question of prime decomposition in a finite extension of fields motivates classical ramification theory for field extensions. We propose to give a very little introduction to this deep subject which can also be extended to arithmetic geometry.
After recalling some basic facts around finite field extensions, we will explain how to do arithmetic in number fields. This will permit us to define the ramification for number field and to give some criteria permitting to decide which primes are ramified or not. Finally, we will study the particular case of quadratic extensions in order to see how we can apply this theory.

Rif. int. C. Marastoni, T. Vargiolu

Seminario Dottorato: Elliptic curves, an introduction and beyond

Wednesday 29 May 2013 h. 15:00, room 2BC/30
Rene' SCHEIDER (Regensburg)
"Elliptic curves, an introduction and beyond"

Abstract
The talk provides a very elementary introduction to elliptic curves and their geometry, with the final aim of understanding the analytic geometry of the universal family with level N structure.
As a broad audience shall be addressed, only few and basic prerequisites are required.
In more detail, the plan is to cover the following topics:
We explain how elliptic curves over a general field are defined and introduce their group law as well as the Weil Pairing. We then outline how these algebraic data express analytically if we work over the field of complex numbers. After this we are prepared to construct the universal elliptic curve with level N structure as a complex manifold.

Rif. int. C. Marastoni, T. Vargiolu

Seminario Dottorato: A class of derivative-free nonmonotone algorithms for unconstrained optimization

Wednesday 22 May 2013 h. 15:00, room 2BC30
Francesco RINALDI (Padova, Dip. Mat.)
"A class of derivative-free nonmonotone algorithms for unconstrained optimization"

Abstract

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