Andrei Jorza
University of Notre Dame, Notre Dame IN, USA

$p$-adic $L$-functions have been crucial in some of the most striking advances in number theory, most notably in recent advances towards proving the Birch and Swinnerton-Dyer conjecture for certain abelian surfaces by Loeffler and Zerbes. Recently, with Barrera, Dimitrov, Graham and Williams we have constructed such $p$-adic $L$-functions in $GL(2n)$-families around unramified representations. I will present further work, with Mladen Dimitrov, on parahoric families, with an eye toward proving trivial zero conjectures.