Department of Mathematics

Hilbert’s 12-th Problem concerns the construction of class fields using special values of analytic functions, especially modular forms. The Stark Conjectures (work of my advisor Harold M. Stark) conjecturally construct various class fields, particularly real quadratic fields, using special values of L-functions at s = 0. We review Hilbert’s 12th problem and the Stark conjectures and describe an unexpected connection of the Stark Conjectures to the (conjectured) existence of maximal systems of complex equiangular lines in Cn, known as SIC- POVM’s in quantum information theory. The latter is work of my student Gene Kopp (PhD 2017).