The National Science Foundation (NSF) awarded a $141,963 Project Grant under the Integrative Activities (IA) program (CFDA 47.083) to Kansas State University (KSU) to develop a theory encompassing exponential integrals and their relationship to quantum physics and geometric structures. The 3-year project, starting on August 1, 2024, will study the de Rham and Betti cohomology theories associated with exponential integrals, including comparison isomorphisms, in the framework of complex manifolds. The research aims to establish a holomorphic Morse-Novikov theory and provide a conceptual explanation of resurgent properties of perturbative expansions of exponential integrals in finite and infinite dimensions. The project will also integrate educational efforts to develop new directions and projects for young researchers.
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