Wednesday 25 March 2026 at 4:45 pm, as part of the Insalate di Matematica seminar cycle, Julian Feuerpfeil (University of Milano-Bicocca) will give the following talk
Title: Why Class Groups Matter: From Fermat’s Last Theorem to Modern Arithmetic
Abstract: One of the most famous equations in mathematical history is: Xⁿ+Yⁿ=Zⁿ Does it have nontrivial integer solutions for n>2? In 1637, Pierre de Fermat famously claimed-without proof-that it does not. About 200 years later Kummer approached this problem by introducing class groups, which are finite abelian groups attached to number fields measuring their arithmetic complexity. In this talk, we begin with this classical story and then turn to more modern developments, focusing on Iwasawa theory, where one studies how class groups behave in infinite towers of number fields. If time permits, we will also discuss recent results on a Hilbert 90-type property for generalized class groups and its connection to an open conjecture in Iwasawa theory. There is a marvelous Fermat joke, but this abstract is too small to contain it - join the talk to find out more.
Keywords: Class groups, Fermat's last theorem, Iwasawa theory, Hilbert 90
Information to attend
The seminar will be held in Room U9-13 (U9 Building | Viale dell’Innovazione 10, Milano) and will also be available online by this link (password: insalate, 46725283 from phones).
For more information, visit the website