Thursday 10 April 2014 h. 15:30, room 2BC30
Grady B. Wright (Department of Mathematics  Boise State University  USA)
"Solving PDEs on surfaces with radial basis functions: from global to local methods"
Abstract
Radial basis function (RBF) methods are becoming increasingly popular for numerically solving partial differential equations (PDEs) because they are geometrically flexible, algorithmically accessible, and can be highly accurate. There have been many successful applications of these techniques to various types of PDEs defined on planar regions in two and higher dimensions, and to PDEs defined on the surface of a sphere. Originally, these methods were based on global approximations and their computational cost was quite high. Recent efforts have focused on reducing the computational cost by using "local" techniques, such as RBF generated finite differences (RBFFD).
In this talk, we first describe our recent work on developing a new, highorder, global RBF method for numerically solving PDEs on relatively general surfaces, with a specific focus on reactiondiffusion equations. The method is quite flexible, only requiring a set of "scattered" nodes on the surface and the corresponding normal vectors to the surface at these nodes. We next present a new scalable local method based on the RBFFD approach with this same flexibility. This is the first application of the RBFFD method to general surfaces. We conclude with applications of these methods to some biologically relevant problems.
This talk represents joint work with Ed Fuselier (High Point University), Aaron Fogelson, Mike Kirby, and Varun Shankar (all at the University of Utah).
Wednesday 26 March 2014 h. 14:30, room 2BC30
Davide Buoso (Padova, Dip. Mat.)
"Shape optimization and polyharmonic operators"
Abstract
We will start by introducing the general shape optimization problem, giving motivations for its importance in applications.
Then we will turn to the problem of shape optimization for eigenvalues of elliptic operators (in particular, poyharmonic operators), which has regained popularity since 1993 with the paper by Buttazzo and Dal Maso. We will recall the most important classical results, giving the main ideas behind the proofs, together with the last ones.
Finally, we will move our attention to the problem of criticality with respect to shape deformations for eigenvalues of polyharmonic operators. After explaining the techniques involved, we will provide a characterization of criticality and show that balls are always critical.
Wednesday 12 March 2014 h. 14:30, room 2BC30
Chau Ngoc Huy (Padova, Dip. Mat.)
"Market models with optimal arbitrage"
Abstract
In this talk, we will introduce basic notions on financial mathematics, classical no arbitrage theory and some results on markets with arbitrage. We present a systematic method to construct market models where the optimal arbitrage strategy exists and is known explicitly.
Wednesday 26 February 2014 h. 14:30, room 2BC30
Nguyen Van Luong (Padova, Dip. Mat.)
"Minimum time function for linear control systems"
Abstract
In this talk, we will first introduce basic notions on linear control systems and minimum time function for linear control systems. We will end with some recent results on regularity of minimum time function for linear control systems.
Wednesday 12 February 2014 h. 14:30, room 2BC30
Athena Picarelli (ENSTA ParisTech and INRIA SaclayIle de France)
"Reachability problems via level set approach"
Abstract
Given a controlled dynamical system, the characterization of the backward reachable set, i.e. the set of initial states from which it is possible to reach a given target set, can be very interesting in many applications. However realistic models may involve some constraints on state and/or control variables (for taking into account physical or economical constraints, obstacles, etc.) and this can make the characterization of this set much more complicated.
After an introduction to the notion of backward reachability in the deterministic as well in the stochastic framework, aim of the talk is to present a technique, based on a level set approach, for characterizing and numerically computing the reachable set also if state constraints are taken into account.
Wednesday 29 January 2014, h. 14:30, room 2BC30
Federico Bambozzi (Padova  Dip. Mat.)
"An introduction to geometry over the field with one element"
Abstract
In this talk we first give a brief overview of the motivations behind the research on geometry over the field with one element. We then show one possible way to define affine schemes over the field with one element in analogy with the classical theories of algebraic varieties over the complex numbers and of schemes by Grothendieck. We end the talk by giving some examples of schemes over F_1.
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 longtime 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.
Wednesday 18 December 2013, h. 14:30, room 2BC30
Genaro Hernandez Mada (Padova  Dip. Mat.)
"An introduction to the ClemensSchmid exact sequence"
Abstract
In this talk, we give a very elementary introduction to the ClemensSchmid 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
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
 By servizio at 11/18/2013  18:07
