Matisse stands for modernism's up side and there's plenty in this capsule show to feel good about. As you'd expect from Matisse's nudes, languid flesh reclines in the shade of green fronds or spills from a silky bathrobe, and the sea never seems far away. At the Helly Nahmad gallery, W1, until the 23 July
Photograph: PR
Alÿs's poetic, politically pointed actions range from solo missions to epics. In one of his best-known works, 500 shovel-wielding students laboured for hours to move a Peruvian sand dune four inches. This major show chronicles 20 years of extraordinary output, documenting 30 such projects, alongside animation, painting and objects and the premiere of his latest video, Tornado, where he runs headlong into whirlwinds. At Tate Modern, Tuesday 15 June to 5 September
Photograph: PR
The American polymath visionary John Cage remains one of the most influential composers and thinkers of our time, some 18 years after his death. In this show, subtitled Sculpture & Sound, eight artists, including sound-sculpture radicals such as Paul Ramirez Jonas, use Cage's novel take on musical notation. At BALTIC, until 19 September
Photograph: PR
Mantzios's fragmented, wall-based assemblages certainly intrigue. Flea-market picture frames are hung in geometric riddles, with individual glass panels scratched to form cryptic symbols. A mesmerising conundrum. At Bloc, until 20 June
Photograph: PR
To coincide with Penzance's Golowan festival, Lees is setting up a sewing circle and basket-weavers workshop in the Exchange gallery to create a fully functioning hot-air balloon. In the spirit of 18th-century adventurers, at the end of this two-week project the artist intends to fly the balloon and anyone brave enough can join him. Starts Saturday until 26 June
Photograph: PR
A fascinating pairing on a theme of abstract sculpture. The coiled and spiralling organic elaborations of the half-Scottish and half-Swiss Hermann Obrist (1862-1927) are arguably the first modern art abstract sculptures. Polish photo artist Alina Szapocznikow's exhibition, titled Out Of My Mouth features monochrome images of biomorphic forms that turn out to be lumps of orally-modelled chewing gum. At the Henry Moore Institute, until 29 August
Photograph: Heinrich Helfenstein
The American artist's first UK public gallery show, spanning 20 years of protean output, has love heart paintings, spider webs spun from silver chains, and drawings of cloudbursts finely wrought with ink and spittle. Hodges's method is as time-consuming as his results are fragile. At Camden Arts Centre, until 5 September
Photograph: Marta Buso
A show of specially commissioned video pieces by the Cypriot-born artist, to coincide with her installation at Tate Modern. Epaminonda adapts collage painting to video editing. Mixing filmed footage with found old flicks, mostly from the 1950s and 60s, she builds up free associational reveries. Circus elephants and palm tree jungles combine surreally. At the Site gallery, until 21 August
Photograph: PR
