Peter Winkler, Dartmouth
Random walk on a graph is a beautiful and (viewed from today) classical subject with elegant theorems, multiple applications in the theory of computing, and a close connection to the theory of electrical networks. The subject seems to be livelier now than ever, with a surprising number of new results.
We will discuss recent progress in some new directions. In particular, how long can it take to visit every edge of a graph, or to visit every vertex a representative number of times? Can random walks be coupled so that they don't collide? Can moving targets be harder to hit than fixed targets? How long does it take to capture a random walker?
Mentioned will be work by or with Omer Angel, Yaakov Babichenko, Jian Ding, Agelos Georgakopoulos, Ander Holroyd, Natasha Komarov, James Lee, James Martin, Yuval Peres, Ron Peretz, Perla Sousi, and David Wilson.