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                * Princeton Discrete Math Seminar *
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Speaker: Scott Baldridge

Thursday 10th April, 3:00 in Fine Hall 224.

Title: State-reducibility and a new gauge-theoretic approach to the four color
theorem

The Birkhoff diamond has played a central role in attempts to prove
the Four Color Theorem since it was first identified over a century ago as the
minimal nontrivial reducible configuration. In this talk, I will present a new
proof of its reducibility using filtered $3$- and $4$-color homology, which
arise from a (2+1)-dimensional topological quantum field theory inspired by
Khovanov and Lee homologies. This approach avoids Kempe-switch techniques by
introducing the notion of state-reducibility, which analyzes face colorings on
ribbon graphs associated to the original graph. As an application of a broader
TQFT framework developed in earlier work, this result provides an independent
verification of a key configuration and suggests a potential pathway toward a
non-computer-assisted proof of the Four Color Theorem. This is joint work with
Ben McCarty.

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