Akash Kumar, Random walks and Forbidden Minors

Random walks and spectral methods have had a strong influence on modern graph algorithms as evidenced by the extensive literature on the subject. In this talk, I will present how random walks helped make progress on algorithmic problems on planar graphs.
In particular, I show how random walk based (i.e., spectral) approaches led to progress on finding forbidden minors [K.-Seshadhri-Stolman, FOCS 2018] as well as on deciding planarity [K.-Seshadhri-Stolman, STOC 2019] in bounded degree graphs within the property testing framework. I will also cover how these approaches eventually led to progress on the so-called “efficient partition oracle” problem [K.-Seshadhri-Stolman, FOCS 2021].
The talk will assume minimal background by presenting a stand-alone story that should be of interest to students/researchers in computer science.