分野別セミナー

*代数学・代数幾何学 合同セミナー
A semialgebraic set is a subset of real space defined by
polynomial equations and inequalities. A semialgebraic set is a union of
finitely many maximally connected components. In this talk, we consider
the problem of deciding whether two given points in a semialgebraic set
are connected, that is, whether the two points lie in a same connected
component. In particular, we consider the semialgebraic set defined by f
not equal 0 where f is a given bivariate polynomial. The motivation
comes from the observation that many important/non-trivial problems in
science and engineering can be often reduced to that of connectivity.
Due to it importance, there has been intense research effort on the
problem. We will describe a method based on gradient fields and provide
a sketch of the proof of correctness based Morse complex. The method
seems to be more efficient than the previous methods in practice.