The Laplacian of a graph is a key object in the theory of graphs and can be viewed as the generator of a continuous time Markov chain on the graph.
Simplicial complexes, or hypergraphs, are combinatorial objects which generalizes graphs for which there also exist a notion of Laplacian. We investigate the notion of random walk on such objects with the goal to find a link between this generalized Laplacian and the generator of the Markov process.
Laurent Decreusefond is a Professor at Telecom Paris and have recently joined the LINCS lab.