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Robertson’s Conjecture in topology.

Event Category:
Discrete Math Seminar
Eric Ramos
Bowdoin College

One of the most famous statements in graph theory is that of Kuratowski’s theorem, which states that a graph is non-planar if and only if it contains one of K3,3 or K5 as a topological minor. That is, if some subdivision of either K3,3 or K5 appears as a subgraph of your graph. In this case we say that the question of planarity is determined by a finite set of forbidden minors. A conjecture of Robertson, whose proof was recently announced by Chun-Hung Liu, characterizes the kinds of graph theoretic properties that can be determined by finitely many forbidden minors. In this talk I will present a categorical, or algebraic, version of Robertson’s conjecture. I will then illustrate how this conjecture, if proven true, would be able to prove many non-trivial statements in the topology of graph configuration spaces.

Friday, March 11, 2022 - 10:00am
LGRT 1638