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Anna Karenina begins with the well-positioned bureaucrat Oblonsky (Matthew Macfadyen) laid out in a barber's chair on a bare stage. 

It is fitting in this starkly theatrical setting that the barber (Elias Lazaridis, one of thirteen dancers in the film from Cherkaoui's Antwerp-based troupe, Eastman) behaves like a matador, snapping the barber's sheet like a cape and flourishing the razors like lances. Mundane routine as ritual blood sport: how dangerous a world ringed round by custom can be. 

 And how mechanical: we follow Oblonsky, fresh from his ablutions, to the long chamber over which he presides, where row upon row of buttoned-up clerks stamp and rearrange papers in a syncopated ballet blanc: stamp, stamp, flutter of paper; repeat; repeat; repeat. The thick stack on the left shrinks as the thin stack on the right grows. "Paperwork," Oblonsky later exclaims, "is the soul of Russia." As he passes each row, his minions rise like pistons in a well-oiled machine to the music's chug and wheeze. 

If the opening scenes establish the world we're in (richly adorned, deeply sublimated, and minutely calibrated) and how its story will be told (ebulliently, inventively, and, above all, theatrically), the ball -- in which Vronsky (Aaron Taylor-Johnson) and Anna (Keira Knightley) whirl themselves into a passion and cast Kitty (softly radiant Alicia Vikander) aside -- carries us into the story's romance. Most directors appreciate the scene's importance without making much of the dancing. (A notable exception is the 1935 Greta Garbo version, in which the dancers exchange not only partners but salty badinage.) Wright hands this pivotal moment over to the dance. 

 Cherkaoui set himself the task of inventing a variation on the waltz that would re-awaken it in all its allure. When he went "back into the books," he says, "I read a lot about how the waltz was considered indecent. Not proper. It came from Poland" -- a colonial outback by Russian lights -- "but it seeped into the aristocracy, and people would do it because they couldn't help themselves. 

 "I've always found this relationship between popular and aristocratic culture interesting. And here I was playing between these two: how we transform something to make it more proper but how at the end of the day it is still a man and a woman and their desire to fly away together. 

"Waltzes can be like a cosmos," he continues, "all these couples twirling around each other but also around the other couples. You would lean in to the arm of your partner in such a way that both partners have the feeling they have no weight." They could spin all the way to the moon. They could fly too close to the sun. That thrill and danger resounds in the waltzes of Brahms, Tchaikovsky, Mahler, Ravel -- and Marianelli, whose waltz for Anna and Vronsky grows progressively discordant the faster it turns.

 "Anna and Vronsky's passion is at the heart of the waltz," Cherkaoui notes. The other couples freeze until the duo -- "generating an energy like some kind of organic clockwork" -- sweeps them along in its wake. 

 The choreographer did not meddle with the patterns of the feet -- they lend the waltz its necessary force -- but he embellished the arms and upper body to bring out the waltz's strict comportment as well as its erotic appeal and to adapt it for the camera, which generally favors faces -- "how people look at each other" -- over feet. 

 To underscore the form's exacting rules of engagement, he accented the man's initial move: the raising of the back of the wrist to lead the woman on to the dance floor. Cherkaoui has the man's wrist suddenly jut up. It doesn't bode well for the lady otherwise. When Vronsky spots Anna after he has already agreed to give Kitty a turn, he lifts his wrist so desultorily that you feel the insult.

Bored Vronsky, entranced Kitty

 As for the waltz's legendary raciness, Cherkaoui began by thinking about the prescribed limits to touch at the 19th century ball: "You would hold the hand without the palms touching." Only fingers were clasped. "Touching the inside of the hand was considered very intimate, very sensual." In his version, only the lower arm's pale undersides graze. 

The hands are free to undulate and unfurl like time-lapse vines winding up trellises and flowering. "The looseness of the wrist only suggests touch. The hands flow through one another like weaving. I wanted the waltz to be magical, and you know how when you cast a spell it is with the weaving of hands?"

Balanchine once said: "Probably dance would stop if we didn't have Stravinsky." The composer gave him solid foundations on which to build dances, an education in composition, and confidence. In 1972, a year after Stravinsky's death, the New York City Ballet organised a now-legendary festival of a whopping 31 ballets to his scores, including 21 premieres. For the next two weeks, the company presents the cream of that crop: 13 Balanchines, beginning with Apollo, Orpheus and Agon, the only three whose music Stravinsky made to order. Of this "Greek trilogy", Apollo and Orpheus were conceived as a pair, yoked musically and philosophically and also perfect opposites. 

The music for the 1928 Apollo is all grand, sunny certitude. Stravinsky's tell-tale pulse may rollick as the young Olympian struggles to rein in his muses, but the music is too sweet to suggest trouble ahead. As for the choreography, the three muses' spiky legs evoke the sun's rays and their circling arms its body. Even as the steps shift between constructivist flatness and sculptural roundness, Apollo's eventual stature as the pillar of well-proportioned art is assured. 

 Still, he has some growing to do - where would the drama be otherwise? On opening night, Robert Fairchild presented the god evolving beat by beat. He favoured muscular impetus over static line, a brave and unusual choice that gave the performance the edge it lacked last year at his debut in the role. 

  Orpheus is as saturnine as Apollo is bright, but it has echoes of the earlier work.

No matter the style, dance involves a paradox: the body's vital solidity against the dancing's ephemerality. Jason Akira Somma's keenly promising Phosphene Variations deploys vaporous films and hallucinatory screen versions of live dancers to home in on this anomaly. 

Enclosed in a palm reader's black curtains - though here they are only cordoning off a section of the interdisciplinary SoHo gallery Location One - a holographic Baryshnikov warps and wobbles on a stream of vapour. With every bend in the projector's misty light, his white shirt and beige slacks striate into bars of brown and grey. When you dip your hand into the airstream, he devolves into a muddy swirl, out of which another luminary emerges, such as Ailey alum Carmen DeLavallade or Somma's mentor (under Rolex's arts mentoring scheme) Jirí Kylián. 

 We do not need to recognise the artist, however, for these 3D figures to prompt a shiver of dread. Baryshnikov's belovedness and his greying may intensify intimations of mortality, but the film's ghostly silence and the cloud by which we see it would arouse such sentiments for anyone. The holograph comes so close to simulating life that you feel the gap. 

The ensuing show in Location One's theatre (each week a rotating cast of local performers improvises with their trippy live screen version) might have strayed from this sombre theme - have been a loose end - if not for Frances Wessells. She is 93. The founder of Virginia Commonwealth University's adventurous dance department, Wessells began seated. On four variously sized video screens, Somma multiplied and stacked her silhouette, outlined in fluorescent hues, until it filled a whole virtual theatre, as if all her selves were watching a movie of her years slide by. 

Eventually Somma - lanky, muscular and 32 - handed his camera to a colleague and joined Wessells. Imagine a panther cavorting with a dandelion.

Eclipse is perfect for inaugurating BAM's handsome, $50m, 250-seat Fishman Space for experimental work, around the corner from the opera house. Taking full advantage of the flexible seating, Bokaer has the audience frame the dancers both at ground and balcony level. McCall's tilted grid of 36 hanging light bulbs also calls attention to dimension and perspective. The piece's drama is largely spatial: the romance of volume and plane. At the hour's cosmic start, all the Mars-red bulbs blazing at once seemed to emanate from a distant point.

Everyone but the choreographer. Photo by Stephanie Berger 

The dancers brought the astral plane down to earth, beginning with Bokaer, who palmed one globe, then another, and kneeled to enfold a nimbus of light in a muscular embrace - an odd and poignant gesture. The other four (the excellent Tal Adler-Arieli, CC Chang, Sara Procopio and Adam Weinert) left the bulbs alone to translate space into time. If objects appear closer together the farther away they are from us, movement - time embodied - seems to slow as it recedes. So the dancers on the perimeter progressed through chunky patterns at zombie speed and orbited tightly around themselves while a gravity-driven loner reversed his path repeatedly as he slipped and slid, lunged, turned and flailed. Eventually someone else assumed his role and he gravitated to the margins.