{
  "abstract": "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 kernel admits a 1-- Gevrey small--time expansion whose Borel transform detects complex--geometric data beyond the real geodesic sector. We formulate an infinite--dimensional Picard--Lefschetz problem of Morse--Floer type for the holomorphic energy functional on the complexified path space, and propose a heat--kernel analogue of the Picard--Lefschetz/Alien correspondence. In this framework, pointed alien operators acting on the asymptotic expansion associated with the real geodesic are predicted to produce the formal heat--kernel sectors associated with other holomorphic geodesics, with coefficients given by signed counts of connecting trajectories of the Morse flow. We perform a confirming test of this proposal on the hyperbolic plane $\\mathbb{H}_{\\R}^2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.21909",
  "author_total": 3,
  "authors": [
    {
      "name": "Si Li"
    },
    {
      "name": "Yong Li"
    },
    {
      "name": "Xinxing Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fdbf6me24nbw0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.21909",
  "fulltext_url": null,
  "id": "fdbf6me24nbw0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.21909",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7165687298",
  "pdf_url": "https://arxiv.org/pdf/2606.21909",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fdbf6me24nbw0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2606.21909",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.21909"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Heat Kernel and Resurgence",
  "title_text": "Heat Kernel and Resurgence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/fdbf6me24nbw0",
  "venue": "arXiv",
  "versions": []
}