Title: Anticyclotomic Iwasawa theory of elliptic curves at Eisenstein primes

Abstract: Castella--Grossi--Lee--Skinner first established anticyclotomic Iwasawa theory for elliptic curves at good ordinary Eisenstein primes under some technical hypothesis, which can be applied to obtain certain $p$-converse theorems and rank $1$ BSD formula when combined with others' works. We explain how to remove their technical hypothesis and discuss generalizations of their results to elliptic curves at primes of multiplicative reduction and potentially ordinary reduction. If time permits, we will also discuss generalizations to higher weight newforms. This is partially joint work with Timo Keller.