Ferrara
Variational methods for imaging
One of the most difficult challenges in scientific computing is the development of algorithms and software for large scale ill-posed inverse problems, such as imaging denoising and deblurring. Such problems are extremely sensitive to perturbations (e.g. noise) in the data. To compute a physically reliable approximation from given noisy data, it is necessary to incorporate appropriate regularization into the mathematical model. Numerical methods to solve the regularized problem require effective numerical optimization strategies and efficient large scale matrix computations. In these lectures we describe first and second-order methods, dual or primal-dual approaches, and Bregman-type schemes and how to efficiently implement the ideas with iterative methods on realistic large scale imaging problems.
Docenti: Valeria Ruggiero - Luca Zanni
Periodo: 18-20 Gennaio 2016 (15 ore)
Sede: Ferrara
Numerical methods for kinetic equations
Lecture I: Preliminaries on kinetic equations
Lecture III: Discrete velocity and spectral methods
Lecture VI: Fluid-kinetic coupling and hybrid methods
[1] G. Dimarco, L. Pareschi. Numerical methods for kinetic equations, Acta Numerica, 23 (2014), pp. 369–520.
Docente: Lorenzo Pareschi
Periodo: da stabilire con il docente 6/8 ore
Birational geometry
Abstract: An introduction to MMP, rational connection, rationality and unirationality and their interplay in the realm of algebraic varieties.
Docente: Massimiliano Mella
Periodo: gennaio febbraio, 10 ore
Infinite Dimensional Analysis
docente A. Lunardi, M. Miranda
abstract This is an introductory course about analysis in abstract Wiener spaces, namely separable Banach or Hilbert spaces endowed with a nondegenerate Gaussian measure. Sobolev spaces and spaces of continuous functions will be considered. The basic differential operators (gradient and divergence) will be studied, as well as the Ornstein-Uhlenbeck operator and the Ornstein-Uhlenbeck semigroup, that are the Gaussian analogues of the Laplacian and the heat semigroup. The most important functional inequalities in this context, such as Poincare' and logarithmic Sobolev inequalities, will be proved. Hermite polynomials and the Wiener chaos will be described.
periodo: prima fase ottobre 2015- febbraio 2016 seconda fase marzo 2016- maggio 2016 workshop finale giugno 2016.
Traveling waves in reaction-diffusion equations and in hyperbolic systems of conservation laws (a.a 14/15)
First part: Traveling waves in reaction-diffusion equations. Population dispersal models. Reaction-diffusion equations. Mono-stable and bi-stable reaction terms. Degenerate diffusivities. Convective behaviors. Traveling wave solutions. Admissible speeds. Comparison-type techniques for degenerate boundary value problems. Asymptotic speed of propagation. (Luisa Malaguti, 15 hours)
Second part: Traveling waves in hyperbolic systems of conservation laws. Weak solutions of systems of conservation laws. Entropy solutions. The Riemann problem. An application to Euler equations. Traveling waves as viscous profiles of shock waves. Sketch of the proof of the construction of a solution by the vanishing viscosity method. (Andrea Corli, 15 hours)
Docenti: Andrea Corli (Ferrara), Luisa Malaguti (Modena)
Periodo: tra marzo e giugno, 30 ore (15 + 15)
Calculus of Variations and Geometric Measure Theory; application to the theory of BV functions. (a.a 14/15)
M. Miranda
Abstract
Periodo
Gennaio-Marzo 2015