The role of flat SL(2,C) connections in counting special Lagrangians
Geometry and analysis of special structures on manifolds November 18, 2024 - November 22, 2024
Location: SLMath: Eisenbud Auditorium, Online/Virtual
The role of flat SL(2,C) connections in counting special Lagrangians
There are numerous speculative proposals for constructing enumerative invariants of Calabi-Yau 3-folds by counting special Lagrangian submanifolds. One of the many difficulties in defining such invariants is that special Lagrangians may collapse to multiple covers as parameters vary. For two-fold covers specifically, work of Siqi He shows that the local deformation theory is governed by the existence of Z_2-harmonic 1-forms. On the other hand, Taubes originally defined Z_2-harmonic 1-forms to describe limits of diverging sequences of flat SL(2,C) connections. In this talk I will discuss the connection between these two theories, and discuss progress toward and obstructions to gluing results providing the obverse of He's result in the realm of flat SL(2,C) connections.
The role of flat SL(2,C) connections in counting special Lagrangians
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