prof. Stepanov's seminar at SISSA

[Emanuele Tuillier Illingworth]

SEMINAR ANNOUNCEMENT

prof. Eugene Stepanov

Title: Measurable vector fields, rectifiable curves and flows of measures

Abstract. A smooth vector field (say, over a mainfold) may be defined
either as a linear operator on the algebra of smooth functions satisfying
Leibniz rule, or, equivalently, as a smooth field of directions of curves
(i.e. "vectors") at every point. The first notion easily generalizes to
what is known as measurable vector fields introduced by N. Weaver. These
vector fileds can in fact be identified with one-dimensional metric
currents of Ambrosio and Kirchheim. We show that an identification similar
to the smooth case is valid for a large class of measurable vector fileds
(but not all of them) and study the analogues of integral curves and ODE's
produced by such vector fields as well as the flows of measures generated
by them.


Thursday 23 January at 2 pm in lecture room 133