Pavle Blagojević - Bedlewo: Shadows of Cohen's Vanishing Theorem

Explore the significance and applications of Cohen's Vanishing theorem in a 40-minute lecture delivered by Pavle Blagojević at the Applied Algebraic Topology Network conference in Bedlewo. Delve into the theorem's origins in Springer Lecture Notes 533 and its impact on computing cohomology algebras of unordered configuration spaces. Discover how this seemingly technical result has found applications in diverse fields such as convex and combinatorial geometry, measure partition problems, and the study of periodic trajectories in Finsler billiards. Learn about the theorem's role in solving the Nandakumar and Ramana-Rao problem, its connection to Araki-Kudo-Dyer-Lashof homology operations, and its influence on the existence of Ks,s-free graphs and complex skew embeddings. Follow the lecture's structure as it progresses through the introduction, theorem statement, equality considerations, Sullivan Romano problem, map definitions, and the theorem's "shadow" effects on various mathematical concepts.

Introduction
Cohens theorem
Equality
Theorem
Sullivan Romano problem
Defining a map
The shadow of the vanishing theorem
Splitting necklaces
Iterated Partitions
Example
Spectral sequence
Proof