Please register for this talk here: https://zoom.us/meeting/register/tJwlduurrzMqE9PidEG3TfLJ2qHG9dEp5cua .

In this talk I will present integral refinements of the Gross-Stark conjecture, due to Gross, known as the tower of fields conjecture. I will then describe my on-going work proving this conjecture. The tower of fields conjecture implies a conjecture of Dasgupta that gives an explicit p-adic analytic formula for the Brumer-Stark units. I will sketch this along with an application to Hilbert’s 12th problem. This is all a joint work with Samit Dasgupta.

Preparatory talk video: https://youtu.be/oJIfdh1ibH4 .

Preparatory talk slides: https://www.fields.utoronto.ca/talk-media/1/26/64/slides.pdf .