XXXVIII Workshop on Geometric Methods in Physics | 30.06-6.07.2019 |

VIII School on Geometry and Physics | 24-28.06.2019 |

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## Farzad Fathizadeh## Heat kernel expansion of the Dirac-Laplacian of multifractal Robertson-Walker metricsI will talk about a recent work in which we find an explicit formula for each Seeley-deWitt coefficient in the full heat kernel expansion of the Dirac-Laplacian of a Robertson-Walker metric with a general cosmic expansion factor. We use the Feynman-Kac formula and combinatorics of Brownian bridge integrals heavily. The extension of the result to the inhomogeneous case, where the spatial part of the model has a fractal structure, will also be presented. This is joint work with Yeorgia Kafkoulis and Matilde Marcolli. |

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University of Bialystok |

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