Nell'ambito del programma "Longterm Visiting Professor", finanziato dalla Regione Sardegna, ll Prof. Michael Ruzhansky (Department of Mathematics, Imperial College London), terrà nella prima parte della sua permanenza a Cagliari:

 

 

Fourier Integral Operators and Applications

Lunedi, 22 settembre, 16.00-17.00, 17.15 -18.15

Martedi, 23 settembre, 17.00-18.00

aula D, presso il Dipartimento di Matematica e Informatica, via Ospedale 72.

 

The first part of the minicourse will focus on the basic definitions and properties of Pseudodifferential Operators and Fourier Integral Operators on open domains and on compact manifolds. We also exhibit motivating examples in geometrical optics, propagation of singularities of waves, the wave equations appearing in branches of Applied Sciences. The techniques for integration by parts in dealing with oscillatory integrals and the Stationary Phase Method will be introduced. The notion of (microlocal) singularities for distributions.

The second part is on a more advanced level. We plan to describe a new approach to global evolution problems. This allows us to globally reduce general classes of evolution equations to normal forms by means of Fourier Integral Operators. A comprehensive analysis will be presented of smoothing estimates for homogeneous and inhomogeneous, dispersive and also non-dispersive equations with constant coefficients. Applications are given to the detailed description of smoothing properties of the Schroedinger, relativistic Schroedinger, wave, Klein-Gordon, and other equations. Critical cases of some estimates and their relation to the trace estimates are discussed.

The minicourse is for the Ph.D. students in Mathematics but the lectures (at least the first part) will attract also Ph.D., postdocs and researchers in branches of Physics and Applied Sciences where mathematical methods of Fourier Analysis and Partial Differential Equations are used.

 

 

Mercoledi, 12.00 - 13.00,

aula Magna di Matematica

 

 

 

Prof. Todor V. Gramtchev (Gramchev)

Dipartimento di Matematica e Informatica Universita' di Cagliari via Ospedale 72, 09124 Cagliari

Tel: +39 070 6758534 Fax: +39 070 6758504 e-mail: todor@unica.it