Spectral graph theory and random walk
Spectral graph theory is a subfield of graph theory that mainly concerns properties of a graph pertinent to eigenvalues and eigenvectors of its adjacency or Laplacian matrix. In 1990s, Chung and Yau revolutionized spectral graph theory by introducing spectral geometric methods. On the other hand, a random walk on a graph is a special case of a Markov chain.
We are interested in topics like curvature properties of graphs, electric networks and various applications of random walks.