4 papers · 1 filter
Resurgence and Complex Geodesics for the Heisenberg Heat Kernel
Xinxing Tang
We study complex geodesic actions and heat-kernel resurgence on isotropic Heisenberg groups. For real endpoints with , the nonzero finite singularities reached by analyt…
Picard-Lefschetz theory and alien calculus: a case study
Si Li, Yong Li, Xinxing Tang
We compare Picard--Lefschetz theory and resurgence in three basic one-dimensional exponential integrals: the Airy model, the Bessel model, and the Gamma model. On the Picard--Lefsc…
Heat Kernel and Resurgence
Si Li, Yong Li, Xinxing Tang
We study the resurgent structure of short--time heat kernel asymptotics from the viewpoint of Picard--Lefschetz theory. For a real analytic Riemannian manifold, we show the heat ke…
Path homology of circulant digraphs
Xinxing Tang, Shing-Tung Yau
We study GLMY path homology of circulant digraphs through step-word complexes and infinite cyclic lifts. We first prove chain retractions for interval connection sets. For a fixed…