Spanning Trees and Continued Fractions
15 Apr 2026
11.30 AM - 12.30 PM
MAS EC ROOM 1 (SPMS-MAS-03-06)
Current Students
Abstract
Consider the set of positive integers representing the number of spanning trees in simple graphs with n vertices. How quickly can this set grow as a function of n? In this talk, we discuss a proof of the exponential growth of this set, which resolves an open problem of Sedlacek from 1966. The proof uses a connection with continued fractions and advances towards Zaremba’s conjecture in number theory. This is joint work with Alex Kontorovich and Igor Pak.
Biography
Chan Swee Hong earned his undergraduate degree from the Division of Mathematical Sciences at Nanyang Technological University (NTU) in 2012, followed by a Ph.D. in Mathematics from Cornell University. After completing his doctoral studies, he served as a Hedrick Assistant Professor at UCLA before joining Rutgers University
as an Assistant Professor. His research interests lie at the intersection of combinatorics, computer science, probability, and number theory, with a focus on utilizing technologies from one subject to solve problems in another. He also maintains a fond (or perhaps obligatory) interest in the endurance-testing hobby of climbing the many stairs across the NTU campus since his undergraduate days.