Serre's thesis and its aftermath rolled in a golden age of algebraic topology which led to the impression that we can really understand (necessarily highly nonlinear) maps from one space to another. With the work of Thom on cobordism and Smale on immersions and the Poincare conjecture, a paradigm developed where geometric problems would be solved by reduction to algebraic topological ones. This talk is about the inadequacies of this highly successful paradigm (or more positively, the benefits of proceeding from the qualitative to the quantitative). I will talk about examples and many conjectures, and a very few theorems. This is related to joint work done with A.Nabutovsky, S.Ferry, A.Dranishnikov, G.Chambers, D.Dotterer, and F.Manin, among others - depending on which examples are discussed.
Thu, 19/11/2015 - 14:30 to 15:30
Manchester Building (Hall 2), Hebrew University Jerusalem