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Seminários do IMPA

Geometria Diferencial

$\Gamma$-Calculus and a Curvature-Dimension Condition for Graphs
Zachary McGuirk

Quinta-feira, 18 de janeiro de 2018, 15:30
Sala 236.

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.