*Wissenschaftliches Programm* *Liste der Vortragenden*

**Sektion Plenum**

Dienstag, 19.09.2000,
11.30 Uhr, Großer Mathematik-Hörsaal, Trefftz-Bau

#### Vladimir S. Buslaev, St. Petersburg State University

If the coefficients of a linear differential equation on R^{d} are slow functions of the variables,

the
equation can possess wide classes of formal semiclassical solutions that vary faster compared with the
coefficients. It is well known that these solutions admit very natural geometric interpretations
and their theory is a source of significant analytical, geometrical and even physical ideas and
constructions.
We shall show that all general classes of such solutions and the general constructions related to them can
be naturally generalized to the wider class of the equations:

the
symbols L(x, y, p) of which are periodic functions of x. The combination of such two dependencies
(periodic and slow) generates many new geometrical questions and changes essentially the spectral
properties of the corresponding operators.
These generalized semiclassical equations and operators have also many important physical and technical
applications. They were objects of intensive study during the last decades.