A Categorification of Quinn's Finite Total Homotopy TQFT with Application to TQFTs and Once-Extended TQFTs Derived from Discrete Higher Gauge Theory

Explore a mathematical lecture on the categorification of Quinn's finite total homotopy topological quantum field theory (TQFT) and its applications to extended TQFTs derived from discrete higher gauge theory. Learn about Quinn's Finite Total Homotopy TQFT, a topological quantum field theory that works in any spatial dimension n and depends on choosing a homotopy finite space B, such as the classifying space of a finite group or finite 2-group. Discover recent collaborative research with Tim Porter on once-extended versions of Quinn's theory that take values in the symmetric monoidal bicategory of groupoids, linear profunctors, and natural transformations between linear profunctors. Understand how this construction operates across all dimensions, producing (0,1,2)-, (1,2,3)-, and (2,3,4)-extended TQFTs for any given homotopy finite space B. Examine computational methods for these once-extended TQFTs when B represents the classifying space of a homotopy 2-type through crossed modules of groups. Gain insights into advanced topics in algebraic topology, category theory, and mathematical physics through this specialized presentation delivered at Harvard's Center of Mathematical Sciences and Applications workshop on quantum field theory and topological phases.