Endoscopy

Why did Langlands call them Endoscopic Groups?

I don’t have a good answer to this question, but I will do a bit of digging. This is one question I will ask Prof. Shelstad¬†tomorrow.

Since the average length of papers relating to the Langlands program is over 50 pages, asking is the most efficient way to this kind of knowledge. However, these papers seem to be mostly self-contained.

This paper has a very good general overview of the definitions of endoscopy and lead all the way up to a concise statement of the Fundamental Lemma.

But to see beyond the basics and to look at things like Ngo’s 2009 proof, we’d probably need months of work and multiple graduates courses to even begin reading, not to mention fluency in mathematical French.

Those of you coming to the symposium are in for a nice treat. We are going to be surveying a lot of material in such a short period of time. The line-up has been put together very nicely and I expect to at least get a sense of the questions that are being asked.

It might help to refer to look things up on Wikipedia before coming to these lectures such as Endoscopic Group, Representation, Automorphic Representation, Unitary Representation, Reductive Group, Fibration/Fibre Bundle, Hitchin Fibration

I’m really looking forward to hearing how the speakers describe these objects tomorrow, especially Professor Shelstad who cleaned up many of Langlands’ conjectures. In particular, the Langlands-Shelstad Fundamental Lemma, which Ngo solved.

I will be taking notes and making posts on things that I feel are worthy to share, but this may mean a lot of work. I also need to get LaTeX on this blog!

-RJC

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Founder and Main Organizer for the Fields Undergraduate Network Will be using this blog on a regular basis
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