My neighbor identified them for me as 'Kudzu Bugs' and Walter Reeves' Georgia Gardener site confirmed them as the globular stinkbug (aka kudzu bug), Megacopta cribraria.
I wasn't going to worry about them eating wisteria -- I have plenty to share, hacking at it almost weekly to keep it contained -- until I learned that
- they are worse than ladybugs about wanting to winter in your house walls and
- they also attack figs.
After we sprayed the wisteria, I checked the fig bushes. I found only one. We'll have to keep a sharp watch.
It was a good time to spray; we're in between visits from butterflies and wisteria has finished blooming so there are no beneficial insects visiting it.
These are nasty bugs with a foul stink bug odor. Most of the sources I read said they do not bite. They do bite. I had a bite on my jaw just below my ear. It itched for two days.
I made no pictures. There are excellent photos on the Georgia Gardener site.
I hope we're done with them.