Compact Holonomy G2 Manifolds Need Not Be Formal

Explore a mathematics colloquium talk that challenges established conjectures about the formality of compact manifolds with special and exceptional holonomy. Delve into groundbreaking research that disproves the long-standing conjecture that all compact manifolds with special and exceptional holonomy should be formal, specifically focusing on compact holonomy G_2 manifolds. Learn about the historical context, including the significant work of Deligne, Griffiths, Morgan, and Sullivan who proved that compact Kaehler manifolds are formal, and understand how this new counterexample reshapes our understanding of the relationship between formality and holonomy. The presentation is designed to be accessible to those without prior knowledge of G_2 geometry or formality, making complex mathematical concepts approachable while exploring their implications for rational homotopy groups and cohomological properties.