His first book of poetry was published in 2005, followed by a book on the late novels of Icelandic Nobel laureate Halldor Laxness (2009) and the historical novel November 1976 (2011, published in German 2016). For his latest book of poetry, Vistarverur/Ecostentialism (2018), Ingvarsson won the prestigious Tomas Gudmundsson literary price. Ingvarsson defended his PhD thesis on the reception of American novelist William Faulkner in Iceland on 27th of August 2020. The thesis will be published by The Icelandic Historical Society in September 2021. His forthcoming book of poetry is called Menn sem elska menn/Men Who Love Men – Bio written by poet and friend Eiríkur Örn Norðdahl.