Thu, 21 May 2026
12:00
12:00
Lecture Room 4, Mathematical Institute
Tue, 19 May 2026
14:00
14:00
Online
Diameter of Random Spanning Trees in Random Environment
Rongfeng Sun
(National University of Singapore)
Abstract
We introduce a new spanning tree model which we call Random Spanning Trees in Random Environment (RSTRE), which was introduced independently by A. Kúsz. As the inverse temperature beta varies in the underlying Gibbs measure, it interpolates between the uniform spanning tree and the minimum spanning tree. On the complete graph with n vertices, we show that with high probability, the diameter of the random spanning tree is of order n1/2 when β=o(n/log n), and is of order n1/3 when β > n4/3 log n. We conjecture that the diameter exponent linearly interpolates between these two regimes as the power exponent of beta varies. Based on joint work with L. Makowiec and M. Salvi.
Further Information
Part of the Oxford Discrete Maths and Probability Seminar, held via Zoom. Please see the seminar website for details.
Tue, 05 May 2026
14:00
14:00
L5
On the Erdős-Rogers function
Julian Sahasrabudhe
(University of Cambridge)
Abstract
In this talk I will discuss some recent progress on a natural relative of the classical Ramsey problem, introduced by Erdős and Rogers. What is the largest K_s-free subset that can be found in every K_{s+1}-free graph on n vertices?
This is based on joint work with Rob Morris and Jacques Verstraete.
TPP is currently looking for bright students to join our close-knit technical team, this diverse role will allow you to kick start your career in the tech industry.
MARS: Mathematics for AI in Real-world Systems, based in the School of Mathematical Sciences at Lancaster University, is offering fully-funded, four-year PhD studentships for UK fees status students starting in October 2026.