After three seasons of “Doctor Who,” David Tennant has a nerdtastic following in the US — two rounds on “Broadchurch” also rallied fans of country-cottage procedurals. No wonder the British star’s New York stage debut is playing to sold-out houses. Incredibly, he makes “Richard II,” not one of Shakespeare’s solid-gold hits, into a compelling ride.

A longtime Shakespearean back home, Tennant is charismatic in the title role, even with a laughable stringy wig. You can’t take your eyes away as his petulant, preening child-king faces conspirators and a forbidden love.

The show is presented by the Royal Shakespeare Company in repertory with Parts 1 and 2 of “Henry IV” as well as “Henry V.” If you curse any hint of modernity in a Bard production, these ultra-traditional offerings will be catnip — we’re talking period chain mail and live trumpeters. (At BAM through May 1.)

Anne Washburn is an offbeat young playwright who’s so far given us one masterpiece: “Mr. Burns,” in which “The Simpsons” have become the new canon of the post-apocalypse. But her latest, “Antlia Pneumatica” (named for an obscure constellation), is slight at best. Washburn’s called it her version of “The Big Chill,” but the only similarity is the group of old friends reuniting for a funeral — the show drifts aimlessly, and a late-minute twist feels tacked on. Even Annie Parisse, so vibrant as a record-company exec in “Vinyl,” can’t breathe life into her barely-there character. (At Playwrights Horizons through April 24.)