Protect Our Universities Act of 2019 This bill restricts student participation in sensitive research projects and prohibits the use of certain technologies for such projects. The bill requires each student, prior to participating in a sensitive research project, to provide proof of citizenship to the institution of higher education where the project is being carried out. Specifically, it prohibits students who are citizens of China, Iran, or Russia from participating in such a project unless the student applies for and receives approval. It prohibits certain technologies developed by listed entities, including Huawei Technologies Company and ZTE Corporation, from being used to carry out sensitive research projects. It also requires the Department of Homeland Security to establish a national security technology task force, which must maintain a list of sensitive research projects and provide guidance to the institutions of higher education where such projects are being carried out.