Time：14:00-16:00, Wednesday, November 4 2026
Venue：E14-215
Speaker: Boban Velickovic, Université de Paris
Title：When do higher derived limits vanish?
Abstract: Derived functors of the inverse limit, lim^n, measure how far local data are from determining global data. They appear naturally in algebraic topology and homological algebra. In 1988, Mardešić and Prasolov showed that additivity of strong homology, even for simple subsets of Euclidean space, would force the vanishing of lim^n A for a single, very concrete inverse system A of abelian groups. More recently, Clausen and Scholze found that the same groups compute certain Ext groups in condensed mathematics.
Surprisingly, whether these groups vanish cannot be decided by the usual axioms of mathematics. I will explain how methods from set theory, such as forcing, Baire category and infinitary Ramsey theory, have now largely settled what is possible. I will also present recent joint work with C. Lambie-Hanson and A. Vignati. One result shows that "tame" coherent families are always trivial; the other is a combinatorial principle that ensures vanishing in all degrees. No background in logic will be assumed.
