# Logic Blog 2022

## TL;DR

The 2022 logic blog explores the interplay between group theory and logic, highlighting recent advances such as Gardam's refutation of a longstanding conjecture, and examining topological groups and their computational and duality properties.

## Contribution

It introduces new connections between logic and group theory, including a computational theory for tdlc groups and a duality involving locally Roelcke precompact groups.

## Key findings

- Refutation of the Higman/Kaplansky unit conjecture
- Development of a computational framework for tdlc groups
- Establishment of a duality between certain topological groups and meet groupoids

## Abstract

The 2022 logic blog has concentrated on the connections of group theory and logic. It discusses Gardam's 2021 refutation of the Higman/ Kaplansky unit conjecture, and its connections to logic and to computation. The rest is about topological groups of various kinds, in particular a computational theory of tdlc groups, and a duality between locally Roelcke precompact groups and certain countable structures called meet groupoids.