Professor David Loeffler, ERC Consolidator Grant
Shimura varieties and the BSD Conjecture
Professor David Loeffler from Warwick Mathematics Institute will undertake an ERC-funded project exploring and attempting to solve one of the most famous open problems in mathematics, the Birch and Swinnerton-Dyer Conjecture.
This is a question about the solutions to a certain kind of equation, defining a so-called "elliptic curve".
This is an open problem in the field of number theory and is widely recognised as one of the most challenging mathematical problems.
In the 1960s, mathematicians Bryan Birch and Peter Swinnerton-Dyer calculated the solutions of lots of equations of this type, using one of the earliest computers, and made a striking observation that the number of solutions seemed to be determined by a certain "magic number" called an L-value.
The conjecture has been at the centre of mathematical research for more than 50 years. As of 2021, only special cases of the conjecture have been proven, whilst the full conjecture remains unsolved.
An example of the Birch-Swinnerton-Dyer conjecture for an elliptic curve. See more.
Euler systems
Professor Loeffler's ERC project will focus on attacking this problem using sophisticated tools called Euler systems, which have been the focus of his research for over a decade. He has previously received several other research grants and prizes for his work on Euler systems, many of these jointly with his wife and research collaborator, Professor Sarah Zerbes of University College London.
Professor Loeffler commented: "The Birch-Swinnerton-Dyer conjecture is one of the crown jewels of number theory. I really feel it's a privilege to be able to work on this beautiful theory, and I'm hugely grateful for the ERC grant which will allow me to focus on it full-time.”