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One of the motivations of studying the Langlands Conjectures is the question

What are the finite extensions of the rational numbers?

The local Langlands Conjectures give a dictionary between the Galois Theory of local fields and the representation theory of locally compact reductive groups.

The following videos are of the first lecture by Dick Gross in a series of lectures given at Columbia University in Fall 2011 about the Langlands Conjectures where he explains this in more detail.

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I thought the following video would be a good start to this blog. It is of the announcement of John Tate receiving the 2010 Abel Prize at the Norwegian Academy of Science and Letters on March 24, 2010

John Tate wins the Abel Prize 2010

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