Final Report Summary - HMF (Hilbert modular forms and Diophantine applications)
In particular, the project resulted in robust algorithms for computing Hilbert modular forms which were implemented and included in the computer algebra package MAGMA. The researcher also played a crucial role in resolving the long-standing Gross conjecture, an important open problem in the subject that was posed by Prof. Benedict Gross at Harvard.
Furthermore, one very active area of research in mathematics is the subject of automorphic forms and the Langlands programme. This is a vast web of conjectures that connect number theory, algebraic geometry, analysis and representation theory. The researcher's work was instrumental in providing key evidence, along with a precise formulation for conjectures, in the area of mod p Langlands and Serre's conjectures over totally real fields. The researcher's website was http://www.warwick.ac.uk/staff/L.Dembele/.