I am attempting to find my footing as an student who is ending his undergraduate studies and getting ready to embark on his journey to grad school in pure maths. In this capacity, I have been doing a lot of reading and exploring of areas of mathematics which are new and in some way connected to things I have previously (albeit, perhaps naively) studied (i.e. alg geom, representation thy, and mathematical physics).

I have become very interested in the theory of nilpotent derivations as it relates to geometric embeddings and the theory of algebraic groups (e.g., the work of P. Russell at McGill and others). This is an area which seems to bear deep and interesting results in complex geometry, and I was wondering if work has been done to apply these results to problems in mathematical physics (viz., the study of Calabi-Yau manifolds) where such geometric embeddings are pertinent.

Where might I find a survey of such an application? And what is the best treatment of nilpotent derivations through the lens of affine algebraic geometry?

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    $\begingroup$ I don't understand the second paragraph (what results? is this pure speculation?), but the best way to find out more details of application of the work of X at Y that you are very interested in is to write an email to him! $\endgroup$ Jul 19, 2010 at 8:06


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