Do they take a singular or plural verb? It depends on the sense, but use singular where possible.
Research groups, companies, universities, countries, governments and all other organizations, teams or collective bodies take a singular when functioning as an entity. But use a plural noun when the sense relates to the members of these collectives acting independently of each other. Above all, avoid drifting from singular to plural in references to, say, a research group. Choose whichever is more appropriate and stick to it. If that leaves you with an awkward sentence rewrite it: using “the researchers” instead of “the team” can sometimes get you out of a mess.
The abstract entities mathematics, physics, statistics, acoustics, economics, politics, etc always take a singular noun. But when they are preceded by the definite article (or could be) statistics (meaning a set of figures), economics (meaning financial detail), politics (meaning a set of activities or political beliefs) take a plural noun.