[5] He was born in Tiraspol in the Moldavian SSR of the Soviet Union (now in Transnistria, Moldova) on 22 July 1957 and has lived in Moscow since 1968.

According to Snob magazine, by the early 2020s, Avvakumov had designed around 100 exhibitions as an architect, participated in approximately 500 as an artist, and curated about 50.

[6] In 1984, Avvakumov introduced the term "paper architecture" into Russian usage to describe the genre of conceptual design that emerged in the USSR during the 1980s.

[7][8][9] According to Snob magazine, which refers to Avvakumov as "one of the most renowned contemporary Russian architects,"[5] paper architecture is defined as "avant-garde creative projects not intended for realization."

Since 1984, Avvakumov has organized exhibitions of Paper Architecture, which have taken place in cities such as Moscow, Ljubljana, Paris, Milan, Frankfurt, Antwerp, Cologne, Brussels, Zurich, Cambridge, Austin, New Orleans, Amherst, Volgograd, Venice, and Berlin.

He has designed exhibitions for Lyubov Popova (1989), Konstantin Melnikov (1990), Olga Rozanova (1991), and Vladimir Tatlin (1993/1994).

In 1986, Avvakumov began a series of works titled Temporary Monuments, dedicated to the constructivism of the 1920s and its heroes.

In 2007, Avvakumov organized the exhibition BornHouse at the VKHUTEMAS Gallery in Moscow as part of the Second Biennale of Contemporary Art.

In 2014, he designed the exhibition Right of Correspondence, which featured notes and letters from political prisoners in Soviet camps, drawn from the archives of the society Memorial.