Recently a great deal of progress has been made in the field of
asymptotic formulas that arise in the theory of the operators Dirac
and Laplace. These include not only the classical heat trace
asymptotics and heat content asymptotics, but the more exotic
objects working in the context of manifolds with boundary and
imposing suitable boundary conditions. Asymptotic Formulae in
Spectral Geometry focuses on the interplay between geometry
(invariance theory), partial differential equations, mathematical
physics and the combinatorial underpinnings. The formulas studied
are important not only for their intrinsic interest, but because
they can be applied to index theory, the zeta function
regularization, and more.
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