CORDIS Project
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This project focuses on developing algorithms to determine mod l-Galois representations of classical modular forms and applies these methods to significant mathematical problems, including the Inverse Galois Problem and Lehmer's Conjecture. It aims to enhance understanding in arithmetic geometry and modular forms.
In groundbreaking work, the researcher has developed the first ever algorithm for explicitly determining the mod l-Galois representations of classical modular forms.
He has applied this to the Inverse Galois Problem and to Lehmer's Conjecture on the non-vanishing of the Ramanujan tau-function.
Arguably the greatest advance in arithmetic geometry within the last decade has been the proof by Khare and Wintenberger of Serre's Conjectures over the rationals. A version of Serre's Conjectures over tot…
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