On the p-adic Local Langlands Correspondence

Explore the current state of knowledge regarding the $p$-adic local Langlands correspondence in this hour-long lecture. Delve into the specific case of ${\mathrm GL}_2({\mathbb Q}_p)$, with particular emphasis on a geometric construction of part of this correspondence. Learn about the joint works of Pierre Colmez, Gabriel Dospinescu, and Wielawa Niziol, which contribute to this area of study. Gain insights into why the $p$-adic local Langlands correspondence remains a theoretical concept and understand the progress made in this challenging field of mathematics.