Gauge Theory and Topology Seminar: Calabi-Yau monopoles, special Lagrangians, and Fueter sections
SEMINARS, GAUGE-TOPOLOGY-SYMPLECTIC
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March 8, 2024 3:30 pm - 4:30 pm
Science Center 507
Address:
1 Oxford Street, Cambridge, MA 02138 USA
Speaker:
Saman Habibi Esfahani - Duke University
This talk investigates two types of proposed invariants of Calabi-Yau 3-folds:
- from gauge theory: Calabi-Yau monopoles,
- from calibrated geometry: count of special Lagrangians weighted with their Fueter sections.
Here, we focus on three conjectures central to the definition of these invariants and their relations:
- The Donaldson-Segal conjecture on gauge theory/calibrated geometry duality: Calabi-Yau monopoles = weighted count of special Lagrangians,
- The Donaldson-Scaduto conjecture: the existence of the pair of pants special Lagrangians, related to the formation of special Lagrangian singularities,
- A hyperkähler variation of the Atiyah-Floer conjecture for Fueter sections: monopole Fueter Floer homology = Lagrangian Fueter Floer homology.
The discussion explores recent progress on these conjectures. This is joint work with Yang Li.