Number Theory Seminar
In the 1980s Gross made some conjectures about Brumer-Stark units. The first of these conjectures, known as the Gross-Stark conjecture, was recently resolved jointly with Samit Dasgupta and Kevin Ventullo. In this talk I will speak about Gross's tower of fields conjecture as well as its generalisation due to Rubin, Burns and Popescu. We will see how techniques developed for the Gross-Stark conjecture can be applied to tackle this conjecture. We will also see applications to Hilbert's 12th problem. This is all a joint work in progress with Samit Dasgupta.