Distinguished Lecturer Richard B.Melrose
Scattering theory, travelling waves and geodesics.
(For a general audience) One basic question of scattering theory is
"What can one tell from far away". I will discuss the properties of
plane waves, their perturbations and the scattering matrix. In more
specific cases of reflection and refraction of waves the high energy
limit leads to the important notion of sojourn time. Various results
on the recovery of information from the scattering matrix will be
described and conversely the existence of invisible data
matrix, trace formulae and asymptotics.
(For a general mathematical audience) A more mathematical description
of the scattering matrix in several settings will be given, with emphasis
on the wave equation and high energy limit.
Invertibility, index formulae and global invariants.
(For the experts in geometric analysis) The application of scattering
theory to the Laplacian for certain classes of complete metrics on
manifolds with corners will be described. This leads to appropriate
algebras of pseudodifferential operators and questions concerning
traces, commutators and ideals. Corresponding notions of wavefront
set lead to precise descriptions of the spectrum.
These lectures will be delivered Oct 27, 29, 31 during the Workshop
Microlocal Methods in Geometric Analysis (fall
Scientific statement of RBM:
- Mathematical Interests: Eclectic but tending to the geometric-analytic
- Other Interests: Eclectic but tending to the geopolitical-mycological
Comment of Victor Ivrii: The last statement is extremely
important. Everybody knows everything about geopolitics (or believes
so) and professor's error in geopolitical analysis are of no importance
at all (look at any department of political science full of "original
thinkers"). Errors in mathematical arguments can cost you reputation
but not the life. The same is true for an abstract, theoretical
or mathematical mycology. But the error in the domain of gastronomical
mycology (RBM is interested in this branch of the mycological
science) could be really deadly. And RBM is still alive and even
managed to get the Bocher's prize (1984) and to deliver two talks
on International Congresses of Mathematicians (Helsinki-1978 and
You can browse RBM's home page in MIT.