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Speaker: Zhi-Zhen Wang(Trinity College Dublin)Abstract:Eberhardt-Mizera (2023) evaluated the one-loop bosonic and Type I open string amplitude via Rademacher method. In this talk, we will introduce two other different strategies to treat the modular integrals appearing in one-loop bosonic and Type I amplitudes of both open and closed strings, and in particular their analytic continuation based on a string theoretic analog of the iε-prescription of quantum field theory. We will identify the two strategies and evaluate various zero- and two-point amplitudes. Beyond the perfect agreement to that obtained from the Rademacher method, our approach further provided an exact expression as a combination of three partition functions in terms of a temperature variable. While each individual term depends on this variable, the sum does not. In particular, the imaginary part of the one-loop amplitude, which accounts for the decay widths, has a compact analytical form. Its relation to the Regge limit will also be discussed. This talk is based on our recent work 2411.02517.

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Speaker: Jonte Gödicke (University of Hamburg) Abstract:TBA

Speaker: Wenyuan Li (University of Southern California) Abstract:Consider sheaves on manifolds with microsupport on a singular Legendrian subset inside the cosphere bundle, which are in particular (real) constructible sheaves. By microlocalization, one can define a sheaf of categories on the singular Legendrian in the cophere bundle, called microsheaves. We will show that the microlocalization functor from sheaves to microsheaves together with its left adjoint admits a strong smooth relative Calabi-Yau structure. This is a non-commutative analogue of the orientation class which induces the Poincare-Lefschetz duality on manifolds with boundary. Under some extra assumptions, we can show that the adjunction is a spherical adjunction. We will explain the connections to Fukaya categories and Legendrian contact homologies. This is joint work with Chris Kuo.

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