This blog is an attempt to give the reader(s) a glimpse into The Langlands Program which is an intricate web of results and conjectures linking seemingly disparate areas of mathematics and physics. The content of the posts might show a general bias towards number theory and algebraic geometry not so much because the Program has its origins in these areas but because I tend to be more clueless in other neighbourhoods. The occasional foray into historical and philosophical aspects should promptly be construed as me buying time so I can find something useful to say.There is no linear masterplan to lead the faithful into the heart of the Program. It is more in the spirit of “taking a left and venturing as the crow flies.” Earth-shattering knowledge of mathematics and physics is not a pre-requisite. Dodgy recollection of high school stuff is desirable.
June 14, 2008
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Explaining the Langlands Program starting from high school mathematics! Thats a rather ambitious goal. I think you might struggle to explain fundamental but elementary (in terms of the larger picture) concepts like automorphic forms, adeles and Galois representations. I hope you keep trying though. Good luck!
Comment by Tobias — June 17, 2008 @ 4:21 pm
Its not going to be easy. I think I can explain groups, rings, fields and Galois theory without getting too technical. Probability and algebraic topology have intuitive origins I hope to be able to appeal to. On the physics side I can probably do the same with basic relativity stuff, spacetime geometry and some string theory…after that, I admit I have to step things up and blog at a more technical level. I hope it’ll be a natural progression. I’m blogging for selfish reasons more than anything. It’ll be a good way to keep track of my understanding of maths and my progression as a mathematician. It will be an added bonus if, along the way, I can present some ideas to some curious people.
Comment by zetahype — June 17, 2008 @ 5:28 pm