Gorgeous, sumptuous, thrilling: here comes Abstract Expressionism riding into town, the first major overview in London since its own contemporary heyday in the 1950s. A clunky, unappealing label for such fabulously appealing stuff, it's best just to relax and enjoy this total immersion, for colour and gesture can never have been combined to such memorable effect. Nurtured by the melting pot of New York, this was the first homegrown group of American artists, its activities destined to put New York on the international culture map, wresting the crown of art capital from Paris.

The opening image of this new David Hockney exhibition – a sketchily painted portrait of a seated man, slumping heavily forward, his head buried in his hands – could be a portrait of Brexit despair.

The dazzling, controversial, fascinating exhibition In the Age of Giorgione at the Royal Academy inadvertently provides a striking example of an unavoidable and perhaps insoluble problem common to almost all exhibitions of painting – especially those with a high proportion of loans – in public museums and galleries.

Much is made of the mystery surrounding Giorgione, a painter of pivotal influence, about whom, paradoxically, we know almost nothing beyond the manner of his death. He died in a Venetian plague colony in 1510 aged about 33, and was as elusive in the 16th century as he is today, his paintings highly sought after but hard to come by, and by the time of his death already invested with mythic status.

Painting the Modern Garden explores the interstices between nature and ourselves as revealed in the cultivation of gardens, that most delightful and frustrating of occupations, and an almost obsessive subject for many artists. About 150 paintings from the 1860s to the 1920s, gathered together from private and public collections in North America and Europe are on view, amplified by letters, plans, documents, photographs and illustrated books on horticulture.

Unswervingly confident, relaxed and assured, the élite of the 18^th century are currently arrayed on the walls of the Royal Academy, gazing down at us with the utmost assurance of their unassailable place in the world, bright eyed and dressed to match. The swirls of public reputation are unpredictable: here is a revelation, the art of one of the most successful and highly prized portraitists of his day, Jean-Etienne Liotard (1702-1789), now almost completely unknown except to specialists.

Ai Weiwei’s first major survey in the UK is a better looking exhibition than I had anticipated, but what it gains in looks it sadly lacks in substance – backstory and information not being quite the same.

Whimsical, twee, sentimental. For those who love Joseph Cornell’s boxes, it’s hard to imagine that there are those who just don’t. “What? You mean you don’t like Cornell’s boxes because you think they’re whimsical? Twee? Sentimental?”

Made an Honorary Royal Academician just a few months before he died, in 1993, it’s taken till now for a posthumous Royal Academy survey to finally bring one of the absolute greats of American postwar painting to a UK audience. Of course, for those with long memories, there was the Whitechapel Gallery exhibition of 1991, but though it provided the impetus for the belated honour, it seemed to do little to bring the paintings of Richard Diebenkorn into the public realm.

What does it mean to be a great artist? Is it enough for your work to be admired, studied, emulated and quoted by contemporaries and subsequent generations, or is the value of art judged by a more complex set of criteria? By considering the extent of Rubens’ influence on artists from Rembrandt to Klimt, the Royal Academy is having a go at skinning a very old and troublesome cat: the elevation of Rubens from gifted confectioner to worthy Old Master.