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This mathematical physics seminar presents Claudia Rella from IHES discussing the intersection of resurgence theory, number theory, and quantum mirror curves. Explore how resurgence techniques can uncover non-perturbative sectors hidden within divergent asymptotic series of quantum theories. Learn about the framework of modular resurgence, which formalizes the number-theoretic properties of non-perturbative data extracted through resurgent methods. The talk examines the TS/ST correspondence for toric Calabi-Yau threefolds, focusing on fermionic spectral traces of quantum mirror curves. Discover how the spectral theory of local P^2 demonstrates a complete realization of the modular resurgence paradigm, revealing an exact strong-weak symmetry that bridges non-perturbative physics and the arithmetic properties of geometry. The presentation covers research from multiple papers (arXiv:2212.10606, 2404.10695, 2404.11550) and ongoing work, extending these concepts to all local weighted projective spaces.
