Recent progress in the local Langlands programme
Thursday, 25 May 2017 - 3:00 pm to 3:30 pm
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    SPEAKER: Peter Latham (King's College London) ABSTRACT: The main objective of modern algebraic number theory is to understand the absolute Galois group of the rational numbers, which has an incredibly rich structure. As with many problems in number theory, this breaks into a family of local problems, namely the study of a certain decomposition subgroup for each prime number p" id="MathJax-Element-1-Frame" role="presentation" style="position: relative;" tabindex="0">p

. The local Langlands programme is an attempt to understand each of these local problems, by comparing the representation theory of these decomposition groups to that of p" id="MathJax-Element-2-Frame" role="presentation" style="position: relative;" tabindex="0">p

-adic Lie groups. I’ll give an introduction to the motivation behind and history of this programme, and explain some spectacular recent progress in using it to obtain explicit new results on the structure of Galois groups.