Concorso pubblico per l'ammissione al Corso di Dottorato in Scienze Matematiche (XXX ciclo) (Curriculi: Matematica, Matematica Computazionale) - A.A. 2014/2015

Concorso Pubblico per l’ammissione al
Corso di Dottorato in SCIENZE MATEMATICHE (XXX ciclo)
(Curriculi: Matematica, Matematica Computazionale) – A.A. 2014/2015

Pubblicazione esito “valutazione titoli”
Si ricorda che la presente graduatoria ha carattere provvisorio. La graduatoria definitiva verrà pubblicata, come da bando di concorso (art. 8) entro il 16 settembre 2014 mediante:

Jacobi matrices, orthogonal polynomials and Gauss quadrature An introduction and some results for the non-hermitian case

Seminario Dottorato - Stefano POZZA (Numerical Analysis)
Mercoledì 18 Giugno 2014 h14:30-16:00 - 2BC30

"Jacobi matrices, orthogonal polynomials and Gauss quadrature - An introduction and some results for the non-hermitian case"

This seminar is divided in two parts.

In the first one we will give an introduction to the matter. We will present the concept of orthogonal polynomials and we will focus on the properties of the Jacobi matrix linked to them. Then we will see their application for the approximation of integrals (Gauss quadrature).

In the second part we will see how the first part can be extended to the non-hermitian case. In particular we will present formal orthogonal polynomials and we will see the spectral properties of a generally complex Jacobi matrix. This will lead us to some results about the extension of the Gauss quadrature in the complex plane.

Introduction to representation growth

Wednesday 4 June 2014 h. 14:30, room 2BC30
Michele Zordan (Bielefeld)
"Introduction to representation growth"

Abstract
This seminar is intended as an accessible introduction to representation zeta functions. Given a group, representation zeta functions are Dirichlet generating functions encoding the numbers of its irreducible representations sorted by dimension.
This analytic tool allows the use of analytic methods to compute the rate of growth of the numbers of irreducible representations as their dimension grows.
Much akin to the Riemann's zeta function, these representation zeta functions are often Euler's product of local factors. The computation of these factors, therefore, holds the key to understanding the representation growth of the group.
In this talk I shall introduce the subject with appropriate examples and discuss the methods that given a group allow us to compute the local factors.

A visual introduction to tilting

Wednesday 21 May 2014 h. 14:30, room 2BC30
Jorge Vitoria (University of Verona)
"A visual introduction to tilting"

Abstract
The representation theory of a quiver (i.e., an oriented graph) can sometimes be understood by... another quiver! Such pictures of complex concepts (such as categories of modules or derived categories) are a source of intuition for many phenomena, among which lie the tools for classification and comparison of representations: tilting theory. The aim of this talk is to give an heuristic view (example driven) of some ideas in this area of Algebra.

Extrapolation techniques and applications to row-action methods

Wednesday 7 May 2014 h. 14:30, room 2BC30
Anna Karapiperi (Padova, Dip. Mat.)
"Extrapolation techniques and applications to row-action methods"

Abstract
The talk will be divided in three parts.
First we will introduce extrapolation methods and notions related to them, such us kernel and convergence acceleration. These definitions will be well understood by the examples of Aitken's Delta-squared process, Shanks' transformation and various generalizations.
Afterwards, we will pass to row-action methods that have several interesting properties (i.e. no changes to the original matrix and no operations on the matrix as a whole). We will focus on Kaczmarz and Cimmino method.
At the end we will see how extrapolation methods can be used for accelerating the convergence of the aforementioned row-action methods.

An introduction to representation theory of groups

Wednesday 30 April 2014 h. 14:30, room 2BC30
Martino Garonzi (Padova, Dip. Mat.)
"An introduction to representation theory of groups"

Abstract
Label the faces of a cube with the numbers from 1 to 6 in some order, then perform the following operation: replace the number labeling each given face with the arithmetic mean of the numbers labeling the adjacent faces. What numbers will appear on the faces of the cube after this operation is iterated many times? This is a sample problem whose solution is a model of the application of the theory of representations of groups to diverse problems of mathematics, mechanics, and physics that possess symmetry of one kind or another.
In this introductory talk I will present the tools from representation theory needed to solve this problem. I will also point out the connection with harmonic analysis by expressing Fourier analysis as an instance of representation theory of the circle group (the multiplicative group of complex numbers with absolute value 1) and by stating a version of Heisenberg's uncertainty principle for finite cyclic groups.

Geometric modeling and splines: state of the art and outlook

Wednesday 9 April 2014 h. 14:30, room 2BC30
Michele Antonelli (Padova, Dip. Mat.)
"Geometric modeling and splines: state of the art and outlook"

Abstract
We will give an introductory presentation of the research field of geometric modeling and its applications, with specific attention to the use of splines for the representation of curves and surfaces.
In particular, we will start by introducing basic notions of geometric modeling leading up to the definition of splines, which are piecewise functions with prescribed smoothness at the locations where the pieces join. Splines will be exploited for the representation of parametric curves and surfaces, and we will present their application in the context of computer-aided geometric design for shape description by means of approximation and interpolation methods. Finally, we will discuss some open problems in this topic and we will sketch some recent approaches for addressing them.

Solving PDEs on surfaces with radial basis functions: from global to local methods

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 (RBF-FD).
In this talk, we first describe our recent work on developing a new, high-order, global RBF method for numerically solving PDEs on relatively general surfaces, with a specific focus on reaction-diffusion 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 RBF-FD approach with this same flexibility. This is the first application of the RBF-FD 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).

Seminario Dottorato: Shape optimization and polyharmonic operators

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.

Seminario Dottorato: Market models with optimal arbitrage

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.

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