It is amazing what internet searches can find. https://www.wisconsin.edu/ohrwd/benefits/general-employee-info/payroll/

Under Taxes

Employees Exempt from Taxes:

• Advanced Opportunity Fellows, Fellows, Grad Interns/Trainees, Post-Doc Fellows, and Scholars/Trainees are exempt from Social Security and Medicare taxes. These employees are not exempt from federal and state income tax but the University will not withhold federal or state income tax from their earnings. Employees may be responsible for paying taxes on income when they file their tax return if they work in one of these positions. See IRS Publications 505 and IRS Publication 970 for more information.
• Universities of Wisconsin student employees are exempt from Social Security and Medicare taxes if enrolled and attending classes as a graduate or undergraduate student at the University of Wisconsin on at least a half-time basis. Half-time status is defined by each institution and is determined at the end of the add/drop period each semester. See UW System Administrative Policy 206 (formerly G18A), Student FICA Exemptions for specific rules.