ICA, London, until 20 December 2015
In 2000, curator Mark Francis invited 50 artists to present 50 separate successive solo exhibitions over 50 weeks of the year. Fig-1, the title of Francis’s project, saw contributions by artists including Richard Hamilton, Jeremy Deller, Runa Islam and Anish Kapoor RA, with each artist only invited to take part a few weeks in advance, in order to keep the project organic and informal.

Curator Fatos Üstek launched Fig-2 last week, a sequel that updates the format for 2015. While Fig-1 commandeered a small room in a Soho club, Fig-2 takes over a small studio at the ICA. Each Monday a new show or project is presented. This week saw an installation by Laura Eldhert that hung tapestries from the ceiling; on Monday 12 January, Charles Avery – whose practice revolves around the continual visualisation of an imagined island society – takes over the space.

Whitechapel Gallery, London, 15 January – 6 April 2015
The RA’s show of South American abstract art, ‘Radical Geometry’, examined how geometric abstraction travelled diagonally across the Atlantic from Europe, taking compelling new forms inspired by local political and social circumstances.

The Whitechapel expands this investigation across more countries and continents this week, with ‘Adventures of the Black Square’. The show starts at the beginning of geometric abstraction, in Russia with Malevich, before journeying, via the Dutchmen Mondrian and Van Doesburg, to the American minimalism of Dan Flavin and Carl Andre, to the work of today’s artists, including painter Sarah Morris and New York-based performance artist Andrea Fraser.

Flowers, London, 16 January – 21 February 2015
In view of the Whitechapel show, it is timely that Flowers gallery focuses on British abstraction from the 1970s. Works by seven artists – Colin Cina, Bernard Cohen, Noel Forster, Derek Hirst, Michael Kidner RA, Jack Smith and Richard Smith – developed the form in divergent directions, from the hard-edged paintings of Hirst to Kidner’s optically expanding pattern pieces.

Timothy Taylor Gallery, London,14 January–21 February 2015
To continue any adventure into abstraction, art lovers can visit Timothy Taylor Gallery, in Mayfair, to see the first solo presentation of Serge Poliakoff’s work in London for over 50 years. The Russian-born painter fled the revolution to work in Paris, and became a significant figure in Taschism, a catch-all term for pre- and post-war French abstraction, which departed from Cubism and Constructivism for more rough-and-tumble, spontaneous, expressionistic styles (for this reason it is often seen as the European equivalent of the Abstract Expressionism of De Kooning and co in New York). The exhibition focuses on Poliakoff’s more restrained series of ‘Silent Paintings’ from the 1950s.

Richard Green, London, 14 – 31 January 2015
And from the purely abstract to the sublimely figurative, in the form of paintings by Ken Howard RA, who presents his impressionistic cityscapes of London, Paris and New York at Richard Green gallery from Wednesday. For those who follow Howard’s work, the Academician’s paintings of the American city will be a particular highlight: they are his first of the Big Apple, and capture walkers in Central Park, Manhattan skyscrapers, the streets of Brooklyn and, most keenly of all, the changing conditions of light in the city that never sleeps.

Sam Phillips (@SamP_London) is Editor of RA Magazine.