CORDIS Project
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This project aims to solve significant problems in number theory, including proving conjectures related to Galois representations and automorphic forms. It seeks to establish connections between different mathematical theories and improve existing results in these areas.
I propose to solve three problems.
The first is to prove Serre’s conjecture for real quadratic fields. I will do this by using automorphic induction to transfer the problem to U(4) over the rational numbers, where I will use automorphy lifting theorems and results on the weight part of Serre's conjecture that I established in my earlier work to reduce the problem to improving results in small weight and level. I will prove these base cases via integral p-adic Hodge theory and discriminant bounds…
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