**Clique Aqui!**

Seminários do IMPA

Geometria Diferencial

Título |
$\Gamma$-Calculus and a Curvature-Dimension Condition for Graphs |

Expositor |
Zachary McGuirk
CUNY |

Data |
Quinta-feira, 18 de janeiro de 2018, 15:30 |

Local |
Sala 236. |

Resumo |

Using the $\Gamma$-Calculus of Bakry and Émery for Markov diffusion operators, one can construct a discrete version of an inequality due to Bochner for smooth functions on manifolds. By ascribing a (synthetic) notion of a lower curvature bound and an upper dimensional bound for a graph to the constant which appear in the discretized inequality one can formulate a curvature-dimension condition for graphs and study the properties of graphs which satisfy that condition. By constructing a cone over the vertices of a graph and restricting the curvature-dimension inequality to just the cone point, one can construct a Poincaré inequality for the graph with an explicit constant. We refer to this restriction to just the cone point as a conical curvature-dimension condition and in this talk results that naturally devolve from the Poincaré inequality mentioned earlier will be presented.