p-adic representations, modularity, and beyond

Original Announcement

The current progress on modularity of Galois representations originates with Wiles's work on Fermat's Last Theorem. New ideas from p-adic Hodge theory have enabled a number of authors to improve Wiles's results, but significant technical challenges stand in the way of obtaining stronger results. These difficulties now seem to be related to questions about p-adic Langlands correspondences; thanks to the work of many people, understanding of these correspondences has improved rapidly in recent years.

The main goals of the workshop are to clarify the connections between the aforementioned fields, and to identify some target results for both the short and long term. Some specific topics to be discussed include:

• new methods in p-adic Hodge theory, including links to p-adic differential equations;
• the Taylor-Wiles method and modular lifting theorems in higher weight;
• concrete steps towards a p-adic Langlands correspondence.

Material from the workshop

The workshop schedule.

A report on the workshop activities.

Notes from workshop lectures

Notes from:
Breuil's talk
Berger's talk.

Report on the working group on mod plocal Langlands.