Activities This Week

We will present a refinement, developed in collaboration with Bjorklund, of Furstenberg’s ergodic-theoretic approach tailored to addressing the problem of identifying ‘twisted infinite patterns’ in positive-density subsets of the integer lattice. These patterns correspond to an infinite structure within the ‘sum-products’ formed by such sets. The talk is based on joint work with Bjorklund, Bulinski, and Skinner.

I will demonstrate how careful analysis of group relations yields unexpected constructions, addressing several central questions in group theory. These include a question by Elliott, Jonusas, Mesyan, Mitchell, Morayne, and Peresse regarding Zariski topologies on groups and semigroups, a series of questions by Amir, Blachar, Gerasimova, and Kozma concerning algebraic group laws, and a longstanding question by Wiegold on invariably generated groups.