Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conformal de Rham Hodge theory and operators generalising the
  Q-curvature   We look at several problems in even dimensional conformal geometry based
around the de Rham complex. A leading and motivating problem is to find a
conformally invariant replacement for the usual de Rham harmonics. An obviously
related problem is to find, for each order of differential form bundle, a
``gauge'' operator which completes the exterior derivative to a system which is
both elliptically coercive and conformally invariant. Treating these issues
involves constructing a family of new operators which, on the one hand,
generalise Branson's celebrated Q-curvature and, on the other hand, compose
with the exterior derivative and its formal adjoint to give operators on
differential forms which generalise the critical conformal power of the
Laplacian of Graham-Jenne-Mason-Sparling. We prove here that, like the critical
conformal Laplacians, these conformally invariant operators are not strongly
invariant. The construction draws heavily on the ambient metric of
Fefferman-Graham and its relationship to the conformal tractor connection and
exploring this relationship will be a central theme of the lectures.

16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
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The categories of this paper are: eess
11
The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph