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Chin-Lung Wang (TIMS & National Taiwan University) 
2026-04-29  13:00 - 14:30
Room 202, Astronomy and Mathematics Building

Two projective manifolds $Y$ and $X$ are connected by an extremal transition if they are bridged by a crepant contraction $Y \to \bar{Y}$ followed by a smoothing to $X$. Because neither the quantum A-model (Gromov-Witten theory) nor the B-model (Variations of Hodge Structures) is invariant under such a geometric surgery, a central problem is to formulate a unifying framework that governs the transformation of quantum geometries.

The first lecture will focus on conifold transitions for Calabi-Yau threefolds. I will review the conceptual foundations established about a decade ago in collaboration with Y.-P. Lee and H.-W. Lin, introducing the notions of linked A and linked B models, and their asymptotic realization via the Basic Exact Sequence (BES).

In the second lecture, I will move from theory to effective computation. Through explicit examples, I will demonstrate how to extract quantum corrections across the transition based on linear system decomposition associated to the Weil divisor defining the small resolution. I will also extend the BES framework to govern other types of extremal transitions. Part of the content is based on recent and ongoing joint works with S.-Y. Lee, T.-J. Lee, and S.-S. Wang.