Chris Birkbeck

Slopes of modular forms

Work of Buzzard and Kilford (among others) on slopes (the p-adic valuation of the Up eigenvalues) modular forms gave us great insights into the geometry of the associated eigenvarieties and are the basis of many conjectures. This is an active area of research and in many cases these conjectures are now known. In my talk I will discuss some of the recent progress in the area and how far one can extend these results to the setting of Hilbert modular forms, where very little is known.