Seminario EDP UAM-ICMAT
Heat propagation on abelian covers of principal bundles
Ponente: Sebastián Muñoz-Thon (LMO, Université Paris-Saclay)Fecha: viernes 30 de octubre de 2026 - 13:45Lugar: Aula Gris 1, ICMAT
Resumen:
In this talk, we will study the long-time asymptotics of heat kernels on Abelian covers of compact manifolds and on Abelian covers of compact principal bundles. For Abelian covers, we will establish three complementary asymptotic expansions: a distributional expansion describing correlations of the heat semigroup, a local pointwise expansion of the heat kernel on compact subsets, and a global expansion valid on the natural diffusive scale, revealing the Gaussian profile governing heat propagation. We then extend these results to horizontal heat kernels on principal bundles under natural holonomy and curvature assumptions. In this setting, we show that the leading asymptotics are entirely determined by the geometry of the underlying Abelian cover, while the nontrivial fiber modes decay exponentially fast due to a uniform spectral gap. The proof combines Floquet theory on Abelian covers with the Borel--Weil decomposition on principal bundles.
