|
ВИДЕОТЕКА |
Международная конференция Contemporary mathematics, приуроченная к 80-летию В. И. Арнольда
|
|||
|
Complex cellular structures G. Binyamini Weizmann Institute of Science |
|||
Аннотация: In tame geometry, a cell (or cylinder) is defined as follows. A one dimensional cell is an interval; a two-dimensional cell is the domain bounded between the graphs of two functions on a one-dimensional cell; and so on. Cellular decomposition (covering or subdividing a set into cells) and preparation theorems (decomposing the domain of a function into cells where the function has a simple form) are two of the key technical tools in semialgebraic, subanalytic and o-minimal geometry. Cells are normally seen as intrinsically real objects, defined in terms of the order relation on Complex cells are closely related to uniformization and resolution of singularities constructions in local complex analytic geometry. In particular we will see that using complex cells, these constructions can be carried out uniformly over families (which is impossible in the classical setting). If time permits I will also discuss how this relates to the Yomdin–Gromov theorem on Язык доклада: английский |