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Begun in 2022 due to the cancellation of the ICM in Russia, the Department mini-ICM returns to celebrate our invited speakers at the International Congress to be held in Philadelphia in July.
This year’s event will be on Monday May 11th (week 3) in L2, in the Mathematical Institute. The talks should be widely accessible, so do come along to hear about the work of our colleagues.
2.35 pm Patrick Farrell: Computing multiple solutions of systems of nonlinear equations with deflation. Chair: Mike Giles
One-Day Meeting in Combinatorics
The speakers are Penny Haxell (Waterloo), Guus Regts (University of Amsterdam), Annika Heckel (Uppsala), Standa Živný (Oxford), and Romain Tessera (Institut de Mathématiques de Jussieu-Paris Rive Gauche). Please see the event website for further details including titles, abstracts, and timings. Anyone interested is welcome to attend, and no registration is required.
12:00
14:00
Diameter of Random Spanning Trees in Random Environment
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.
Part of the Oxford Discrete Maths and Probability Seminar, held via Zoom. Please see the seminar website for details.