Carlsbergfondet - Resurgence and Brane-quantization in Topological Quantum Field Theory

The overarching goal of this project in geometry and mathematical physics is to advance our understanding of topological quantum field theory (TQFT) [9] by developing a synthesis of the new theories of resurgence [2, 8] and bran e-quantization [6]. We propose the goals 2.1, 3.1 and 4.1 detailed below. Thecentral goal 4.1 is to define the Chern-Simons TQFT via brane-quantization and derive resurgence from this. In mathematics, attaining these goals will solve the long-standing Expansion Conjecture 1.1 as well as the new Resurgence Conjecture 1.2 and bridge the fields of quantum geometry, mirror symmetry and resurgence. In physics the attainment will advance techniques of potential foundational importance for quantum theory