Antonio Lerario: Sard properties for polynomial maps in infinite dimension

Abstract

Sard’s theorem asserts that the set of critical values of a smooth map from one Euclidean space to another one has measure zero. A version of this result for infinite-dimensional Banach manifolds was proven by Smale for maps with Fredholm differential. It is well-known, however, that when the domain is infinite dimensional and the range is finite dimensional, the result is not true – even under the assumption that the map is “polynomial” – and a general theory is still lacking. Addressing this issue, in this seminar I will provide sharp quantitative criteria for the validity of Sard’s theorem in this setting. Based on a joint work with L. Rizzi and D. Tiberio.