Shielding Public Spaces from Vehicular Terrorism Act This bill authorizes grants, and research and development, to combat emerging terrorist threats, including vehicular attacks. Specifically, the bill includes among the responsibilities of the Office of the Under Secretary for Science and Technology of the Department of Homeland Security (DHS) research and development to combat emerging terrorist threats, including vehicular attacks; includes demonstrated expertise in combating emerging terrorist threats, including vehicular attacks, among the criteria for the designation of colleges or universities as centers for homeland security; directs the Federal Emergency Management Agency (FEMA) to permit the recipient of a grant under the Urban Area Security Initiative or under the State Homeland Security Grant Program to use grant funds to address security vulnerabilities of public spaces, including through the installation of bollards and other target hardening activities; and requires DHS to submit to the congressional homeland security committees a report on potential terrorism vulnerabilities relating to emerging automotive technologies that support driverless vehicles and the threat such vehicles may pose to people in public spaces.