Anwesh Ray
Title: Massey Products and the Iwasawa Theory of Elliptic Curves
Abstract: Elliptic curves give rise to rich families of Galois representations whose associated Selmer groups encode arithmetic information, including data related to the Mordell-Weil rank. We investigate the algebraic structure of Selmer groups through the lens of Iwasawa theory, uncovering novel relationships with higher Massey products in Galois cohomology. These connections extend results of McCallum and Sharifi, who studied analogous phenomena for ideal class groups in cyclotomic towers.
Tam Nguyen
Title: Iwasawa theory over anticyclotomic extensions under the Heegner hypothesis
Abstract: This talk covers some important algebraic properties of dual Selmer groups of elliptic curves over the anticyclotomic \Z_p-extensions of an imaginary quadratic field K. When the Heegner point over K has infinite order, we are able to vastly improve the literature due to more explicit assumptions involving the Heegner index. In particular, numerical examples will be given. As an application, we study Iwasawa theory of congruent elliptic curves. The study of congruences also leads to new instances of the Iwasawa Main Conjecture. These results also apply to modular forms.