Alexander is interested in the relation between the built environment and the social, economic, political, and cultural factors that shape it and in turn are shaped by it. His research explores three main themes:
Modern and contemporary religious architecture. His dissertation, tentatively titled Building Catholic Modernity: Religion, Settlement, and Architecture in Cologne, 1919-1960 looks at 20th-century churches and settlements (Siedlungen) dveeloped in the West German city of Cologne as a way to shape Catholic life-worlds between tradition and modernity. He has also studied what happens when religious organizations act as real estate developers in the United States. His peer-reviewed article "Skyscraper Churches and Material Disestablishment at the Fifth Churches on Christ Scientist" proposes the term "material disestablishment" to describe the effacement of religious symbols that often occurs in church-led development projects in large U.S. cities.
Alexander's work also addresses historic preservation. His master's thesis analyzes the portrayal of museums in Die Denkmalpflege, the leading German historic preservation magazine, from its founding in 1899 until it changed its name in 1922. With Dr. Volker M. Welter and Iain Boyd White, Alexander co-edited Constructing and Reconstructing History in Twentieth-Century German Architecture (Abingdon, UK: Routledge, 2025), a volume of translations that includes his translation of Hermann Muthesius's essay "The 'Restoration' of Our Old Buildings."
Finally, Alexander thinks and writes about architecture and landscape in the Western United States. He is interested in how architects, clients, and landscape architects helped create an image of the American West. Architecture could open up to or exclude the landscape, construct bucolic images or shelter from a dystopian fantasy. This landscape, in turn, often included or stood in for large-scale water management, social anxieties, and the erasure and/or romanticization of Indigenous peoples.