## Introduction to kernel-based methods

Wednesday 18 March 2015 h. 14:30, room 2BC30
"Introduction to kernel-based methods"

Abstract
In this talk we give an introduction to kernel-based methods and to their application in different fields of applied mathematics.
We consider some examples that motivate the use of kernel-based techniques. Each example can be included in the same framework, but allows to show and discuss different features that arise naturally in the particular application. The examples deal with multivariate scattered data approximation, optimal recovery in Hilbert spaces, numerical solution of PDE, machine learning, and statistics.
After building up the fundamental tools of kernel-based methods, we will introduce the problem of the determination of optimal subspaces for kernel-based multivariate approximation. We will give some insight into the problem and discuss possible applications.

## Automorphism-invariant modules

Wednesday 25 February 2015 h. 15:30, room 2BC30
Khanh Tung Nguyen (Padova, Dip. Mat.)
"Automorphism-invariant modules"

Abstract
In this talk, after recalling some basic concepts, we mention the class of injective modules, the class of quasi-injective modules and their generalization, the class of automorphism-invariant modules.
Next, we give some results related to the endomorphism rings of automophism-invariant modules and their injective envelopes.
Finally, we show a connection between automorphism-invariant modules and bolean rings.

## Metastability of the Ising model on random graphs at zero temperature

Wednesday 11 February 2015 h. 14:30, room 2BC30
Sander Dommers (Bologna, Dip. Mat.)
"Metastability of the Ising model on random graphs at zero temperature"

Abstract
In this talk I will introduce a random graph model known as the configuration model. After this, I will discuss the Ising model, which is a model from statistical physics where a spin is assigned to each vertex in a graph and these spins tend to align, i.e., take the same value as their neighbors. It is especially interesting to study the Ising model on random graphs. I will discuss some properties of this model. In particular, I will talk about the dynamics and metastability in this model when the interaction strength goes to infinity. This corresponds to the zero temperature limit in physical terms.

## Shape sensitivity analysis for vibrating plate models

Wednesday 28 January 2015, h. 14:30, room 2BC30
"Shape sensitivity analysis for vibrating plate models"

Abstract
In this talk, we consider two different models for the vibration of a clamped plate: the Kirchhoff-Love model, which leads to the well known biharmonc operator, and the Reissner-Mindlin model, which instead gives a system of differential equations. We point out similarities and differences, showing the connections between these two problems. Then we show some results concerning the stability of the spectrum with respect to domain perturbations.
After recalling the known results in shape optimization for the biharmomic operator, we state some analyticity results for the dependence of the eigenvalues upon domain perturbations and Hadamard-type formulas for shape derivatives. Using these formulas, we prove that balls are critical domains for the symmetric functions of the eigenvalues under volume constraint.

## An introduction to density estimates for diffusions

Wednesday 26 November 2014 h. 14:30, room 2BC30
"An introduction to density estimates for diffusions"

Abstract
We recall some notions in Malliavin calculus and some general criteria for the absolute continuity and regularity of the density of a diffusion. We present some estimates for degenerate diffusions under a weak Hormander condition, obtained by starting from the Malliavin and Thalmaier representation formula for the density. As an example, we focus in particular on the stochastic differential equation used to price Asian Options.

## Singular perturbations of stochastic control problems with unbounded fast variables

Wednesday 19 November 2014 h. 14:30, room 2BC30
"Singular perturbations of stochastic control problems with unbounded fast variables"

Abstract.
In this talk, we first give a short introduction to singular perturbations problems and to the Hamilton-Jacobi approach to the singular limit $\epsilon \to 0$. And we will end by considering a specific singular perturbation problem of a class of optimal stochastic control problems with unbounded fast variables and discussing some recents results.

## The stochastic mesh method to price swing contracts

Our first seminar of 2014/15 will be held as a special event inside the Opening Day of the Doctoral School (15:00 - 1A150)

Wednesday 5 November 2014, h.15:45, room 1A150
"The stochastic mesh method to price swing contracts"

Abstract
This talk is based on the results achieved during a six-month internship in the Risk Department of a leading energy company. Our goal is twofold: on the one hand we give a brief survey on the problem of pricing swing contracts by the stochastic mesh method, on the other hand we describe our experience in the use of advanced mathematics in a private company.
Firstly, we consider the case of American options and study the original formulation of the stochastic mesh method, introduced by Broadie and Glasserman in 1997. Secondly, we try to improve the method by optimally calibrating the parameters, by a literature review and by the use of variance reduction techniques. Finally, we use the revised method to price swing options in energy markets.

## 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.