Shielding Public Spaces from Vehicular Terrorism Act (Sec. 2) This bill amends the Homeland Security Act of 2002 to include among the responsibilities 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. The bill also 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. (Sec. 3) The Federal Emergency Management Agency (FEMA) shall 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. The bill prohibits the use of such grants for the provision to any person of a firearm or training in the use of a firearm. (Sec. 4) DHS shall 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. Such report shall also compare any public benefit of such vehicles against any vulnerabilities and threats.