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# Abstract Shen-Ning Tung

Shen-Ning Tung will speak on

On the automorphy of 2-dimensional Galois representations of G_{\Qp}

Abstract: Using $p$-adic local Langlands correspondence for $GL2(\mathbb{Q}_p)$, we prove that the support of patched Hecke modules $M_{\infty}(\sigma)[1/p]$ constructed in \cite{MR3529394} meets every irreducible component of $R_{\infty}(\sigma)[1/p]$. This gives a new proof of the Breuil-M\'{e}zard conjecture for 2-dimensional representations of the absolute Galois group of $\\mathbb{Q}_p$ when $p \geq 3$, which is new in the case $p=3$ and $\bar{r} = begin{pmatrix} \bar{\epsilon} & * \\ 0 & \mathbbm{1} \end{pmatrix} \otimes \chi$.