September 30, 2023

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

The scattering 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 97).

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 Tokyo-1990 (plenary))

    You can browse RBM's home page in MIT.