Speaker: Raphael Senghaas (University of Heidelberg)
Time: 2025 Jun 5th 16:00:00, Thursday
Location: Room 1610, SIMIS
Zoom Meeting ID: 830 8309 8578 (Passcode: 700291)
Abstract:
Exponential Networks have proven to be a powerful tool for studying BPS spectra of local Calabi-Yau manifolds, including ℂ³, local ℱ₀, and the resolved conifold. Aganagic and Vafa proposed a generalized SYZ conjecture suggesting that every knot in S³ gives rise to a mirror for the resolved conifold. The resulting mirror geometry takes the form of a conic bundle over the knot’s augmentation curve. Exponential Networks provide a framework to identify calibrated cycles on the mirror curve, and thereby determine the BPS states. By mirror symmetry, the closed BPS spectrum obtained in this way is expected to coincide with that of the resolved conifold. As a concrete example, we will examine the mirror associated with the Trefoil knot.
About speaker:
Raphael Senghaas is a PhD student in Mathematical Physics at the University of Heidelberg, specializing in String Geometry. His work explores geometric structures in string theory and supersymmetric field theories, primarily through Mirror Symmetry and Supersymmetry. His current research focuses on Exponential Networks arising from mirror curves of toric Calabi-Yau threefolds, aiming to relate these networks to mathematical invariants such as knot invariants.
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