Colloquium abstracts

Jishnu Ray
TIFR, Mumbai
February 17, 2022

On topics in Iwasawa theory and p-adic Langlands program.:  Recent developments in the p-adic Langlands program allow us to revisit classical conjectures in Iwasawa Theory which help in understanding the arithmetic of Galois representations arising from elliptic curves, modular forms and automorphic forms. This talk will cover various aspects of my research domain and will be expository in nature. We will present results in Iwasawa Theory and p-adic Hodge Theory and combine them to frame the signed Iwasawa main conjectures for non-ordinary automorphic representations. Alongside, we will also discuss Greenbergā??s p-rationality conjecture and use it to construct Galois representations with big open images in reductive groups. Furthermore, we will discuss results in p-adic functional analysis and show the existence of rigid analytic vectors in the crystalline representations arising from the p-adic Langlands program. These works are a culmination of several projects with various collaborators.