Cornejo received an MA and PhD in Fine Arts from Tokyo National University of Fine Arts and Music. He has received grants, awards and residencies from the Vermont Studio Center, Sculpture Space, Center for Book Art, Lower Manhattan Cultural Council, The British Council, The Arts Council of England, The Henry Moore Institute, The Tokyo National University Museum of Art and the Ministry of Education of Japan. Solo exhibitions have been held at Gallery Lightcontemporary in London, Gallery ARTCO and Peruvian-North American Cultural Institute Gallery in Lima and galleries Bellini, Gyokuei and Kobo Chika in Japan, He has participated in group exhibitions at New Art Birmingham; Situation Leeds, UK, The London Connection at Gallery Lisi Hammerlie, Austria, V Biennial Barro de America, Venezuela and V Biennial S-Files Museo del Barrio, NY. In recent years he has been working on the concept of Anti-architecture, he is currently working on the project to create The Puno Museum of Contemporary Art, a community based contemporary art museum in the mountains of Peru.