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This lecture by Peter Kronheimer explores the relationship between SO(3) and SU(3) gauge theories in instanton homology for webs and foams. Discover how Kronheimer and Tom Mrowka's previous work constructing instanton homology using SO(3) gauge theory can be adapted by replacing the gauge group with SU(3), resulting in surprisingly minimal changes. Learn about the connections to foam evaluations in Khovanov-Robert's work, and understand why certain non-vanishing theorems from the SO(3) theory no longer apply in the SU(3) context, while other results transfer successfully and even simplify the overall structure.
