INdAM Program on Serre Conjectures and the p-adic local Langlands program
The aim of the school is to explore recent developments in the arithmetic Langlands program, a vast series of conjectures which have had enormous impact in arithmetic algebraic geometry in the past 50 years. Its ultimate goal is to relate solutions of algebraic equations (and related Galois representations) to harmonic analysis and automorphic forms: among its most spectacular materializations is the proof of Fermat's Last Theorem and the Shimura-Taniyama-Weil conjecture (the celebrated statement that all elliptic curves over Q are modular).
This special school aims at giving a thorough overview of the current state of research in this field. We expect to encourage Ph.D students and young researchers to start new projects within the rich frame of the arithmetic Langlands program.
The school will consist in a series of specialized courses at graduate or early postgraduate level. Main target audience will consist of Ph.D students and young researchers. Each topics is expected to be of developed independently, while the overall plan will encompass most of the ideas and tools underlying research in the p-adic local Langlands program: Galois deformation spaces, automorphic forms, modular representation theory, classical Langlands conjectures...