Colloquium Talk: Tuyen T. Truong (UiO): "Can we pullback a measure ?”
If X is a compact metric space, then a measure on X is a linear, bounded and positive operator on the space of continuous functions on X. If f:X->Y is a continuous map between compact metric spaces, then by tautology we can pushforward any measure on X. Can we pullback a measure? No answer had been found in the literature.
In this talk I will explain why we cannot pullback a measure to a measure in general, even in the case where f is an isomorphism over a dense open subset of Y. On the other hand, I will show that if f is a finite covering over a dense open subset of Y, then we can pullback any measure on Y to a more general class of so-called positive strong submeasures. This is then applied to dynamics of meromorphic maps of compact Kahler manifolds. This general class of strong submeasures can also be used in the problem of intersection of hypersurfaces.
NB! Coffee/Tea/Biscuits from 14.00.