This seminar runs every Monday during the semester at 2PM in Hill 705. The current organizers are Jeff Kahn, Bhargav Narayanan, Swee Hong Chan, and Natalya Ter-Saakov.
If you wish to join our listserv, please email Natalya Ter-Saakov at nt399@math.rutgers.edu.
Click here for the abstract archive for this semester, and here for older abstracts.
Next Talk:
Date: March 2, 2026 at 2:00pm
Speaker: Yuval Wigderson (ETHZurich)
Title: Triangle-free graphs and the odd Hadwiger conjecture
Abstract: Hadwiger's conjecture, first formulated in 1943, is a vast generalization of the four-color theorem, and remains one of the central open problems in graph theory. An even stronger statement, known as the odd Hadwiger conjecture, was proposed in 1993 by Gerards and Seymour. For many decades, progress on one problem was quickly followed by progress on the other, and recent developments indicate that Hadwiger's conjecture and its odd variant are very closely linked.
However, as it turns out, the odd Hadwiger conjecture is false. The key ingredient to the counterexamples is a new random model of triangle-free graphs, which arose in the recent breakthrough work of Hefty et al. on off-diagonal Ramsey numbers. In this talk, I will describe this construction, and sketch how it can be used to disprove the odd Hadwiger conjecture.
Based on joint work with Marcus Kühn, Lisa Sauermann, and Raphael Steiner.
March 2 --- Yuval Wigderson (ETHZurich)
March 9 --- Ian Jauslin (Rutgers)
March 23 --- Sam Spiro (Georgia State)