The Department of Mathematics & Manoa Math Ohana Invite you to Luana in the Afternoon Refreshments provided. All students and faculty welcome.
luana. Hawaiian. v. To be at leisure, enjoy pleasant surroundings and associates, enjoy oneself, relax, be content.
The Department of Mathematics & Manoa Math Ohana Invite you to Luana in the Afternoon Refreshments provided. All students and faculty welcome.
luana. Hawaiian. v. To be at leisure, enjoy pleasant surroundings and associates, enjoy oneself, relax, be content.
Title: Adelic Theory of Protori
by Wayne Lewis (University of Hawaiʻi) as part of Topological Groups
Lecture held in Elysium.
Abstract: TBA
Title: Classification of Finite-Dimensional Periodic LCA Groups
by Wayne Lewis (University of Hawaiʻi) as part of Topological Groups
Lecture held in Elysium.
Abstract
Generalized resolutions of protori have non-Archimedean component a periodic LCA group with finite non-Archimedean dimension. The previous session introduced the notion of non-Archimedean dimension of LCA groups. Applying published results by Dikranjan, Herfort, Hofmann, Lewis, Loth, Mader, Morris, Prodanov, Ross, and Stoyanov, we introduce new minimalist notation and accompanying definitions to clarify the structure of these groups and their Pontryagin duals, enabling a parametrization of the spectrum of resolutions of finite-dimensional protori (the Grothendieck group is a moduli space).
Title: Pontryagin Duals of Type Subgroups of Finite Rank Torsion-Free Abelian Groups
by Adolf Mader (University of Hawaiʻi) as part of Topological Groups
Lecture held in Elysium.
Abstract
Pontryagin duals of type subgroups of finite rank torsion-free abelian groups are presented. The interplay between the intrinsic study of compact abelian groups, respectively torsion-free abelian groups, is discussed (how can researchers better leverage the published results in each setting so there is a dual impact?). A result definitively qualifying, in the torsion-free category, the uniqueness of decompositions involving maximal rank completely decomposable summands is given; the formulation of the result in the setting of protori is shown to optimally generalize a well-known result regarding the splitting of maximal tori from finite-dimensional protori.