On the Locally Analytic p-adic Langlands Program

The locally analytic p-adic Langlands program is an extension of the classical Langlands program into the p-adic setting, focusing on understanding the relationship between p-adic Galois representations and representations of p-adic reductive groups that are locally analytic. This framework has seen significant progress in recent years, especially for GL(2,Qp), and connects deeply with p-adic Hodge theory, representation theory, and rigid geometry. The talk will survey foundational results and highlight current research directions and open problems.